As with all known Haskell systems, GHC implements some extensions to the standard Haskell language. They can all be enabled or disabled by command line flags or language pragmas. By default GHC understands the most recent Haskell version it supports, plus a handful of extensions.
Some of the Glasgow extensions serve to give you access to the underlying facilities with which we implement Haskell. Thus, you can get at the Raw Iron, if you are willing to write some nonportable code at a more primitive level. You need not be “stuck” on performance because of the implementation costs of Haskell’s “highlevel” features—you can always code “under” them. In an extreme case, you can write all your timecritical code in C, and then just glue it together with Haskell!
Before you get too carried away working at the lowest level (e.g.,
sloshing MutableByteArray#
s around your program), you may wish to
check if there are libraries that provide a “Haskellised veneer” over
the features you want. The separate
libraries documentation describes all the
libraries that come with GHC.
9.1. Language options¶
The language option flags control what variation of the language are permitted.
Language options can be controlled in two ways:
 Every language option can switched on by a commandline flag
“
X...
” (e.g.XTemplateHaskell
), and switched off by the flag “XNo...
”; (e.g.XNoTemplateHaskell
).  Language options recognised by Cabal can also be enabled using the
LANGUAGE
pragma, thus{# LANGUAGE TemplateHaskell #}
(see LANGUAGE pragma).
The flag fglasgowexts
fglasgowexts
is equivalent to enabling
the following extensions:


Enabling these
options is the only effect of fglasgowexts
. We are trying to
move away from this portmanteau flag, and towards enabling features
individually.
9.2. Unboxed types and primitive operations¶
GHC is built on a raft of primitive data types and operations; “primitive” in the sense that they cannot be defined in Haskell itself. While you really can use this stuff to write fast code, we generally find it a lot less painful, and more satisfying in the long run, to use higherlevel language features and libraries. With any luck, the code you write will be optimised to the efficient unboxed version in any case. And if it isn’t, we’d like to know about it.
All these primitive data types and operations are exported by the
library GHC.Prim
, for which there is
detailed online documentation. (This
documentation is generated from the file compiler/prelude/primops.txt.pp
.)
If you want to mention any of the primitive data types or operations in
your program, you must first import GHC.Prim
to bring them into
scope. Many of them have names ending in #
, and to mention such names
you need the XMagicHash
extension (The magic hash).
The primops make extensive use of unboxed types and unboxed tuples, which we briefly summarise here.
9.2.1. Unboxed types¶
Unboxed types (Glasgow extension)
Most types in GHC are boxed, which means that values of that type are
represented by a pointer to a heap object. The representation of a
Haskell Int
, for example, is a twoword heap object. An unboxed
type, however, is represented by the value itself, no pointers or heap
allocation are involved.
Unboxed types correspond to the “raw machine” types you would use in C:
Int#
(long int), Double#
(double), Addr#
(void *), etc. The
primitive operations (PrimOps) on these types are what you might
expect; e.g., (+#)
is addition on Int#
s, and is the
machineaddition that we all know and love—usually one instruction.
Primitive (unboxed) types cannot be defined in Haskell, and are
therefore built into the language and compiler. Primitive types are
always unlifted; that is, a value of a primitive type cannot be bottom.
We use the convention (but it is only a convention) that primitive
types, values, and operations have a #
suffix (see
The magic hash). For some primitive types we have special syntax for
literals, also described in the same section.
Primitive values are often represented by a simple bitpattern, such as
Int#
, Float#
, Double#
. But this is not necessarily the case:
a primitive value might be represented by a pointer to a heapallocated
object. Examples include Array#
, the type of primitive arrays. A
primitive array is heapallocated because it is too big a value to fit
in a register, and would be too expensive to copy around; in a sense, it
is accidental that it is represented by a pointer. If a pointer
represents a primitive value, then it really does point to that value:
no unevaluated thunks, no indirections…nothing can be at the other end
of the pointer than the primitive value. A numericallyintensive program
using unboxed types can go a lot faster than its “standard”
counterpart—we saw a threefold speedup on one example.
There are some restrictions on the use of primitive types:
The main restriction is that you can’t pass a primitive value to a polymorphic function or store one in a polymorphic data type. This rules out things like
[Int#]
(i.e. lists of primitive integers). The reason for this restriction is that polymorphic arguments and constructor fields are assumed to be pointers: if an unboxed integer is stored in one of these, the garbage collector would attempt to follow it, leading to unpredictable space leaks. Or aseq
operation on the polymorphic component may attempt to dereference the pointer, with disastrous results. Even worse, the unboxed value might be larger than a pointer (Double#
for instance).You cannot define a newtype whose representation type (the argument type of the data constructor) is an unboxed type. Thus, this is illegal:
newtype A = MkA Int#
You cannot bind a variable with an unboxed type in a toplevel binding.
You cannot bind a variable with an unboxed type in a recursive binding.
You may bind unboxed variables in a (nonrecursive, nontoplevel) pattern binding, but you must make any such patternmatch strict. For example, rather than:
data Foo = Foo Int Int# f x = let (Foo a b, w) = ..rhs.. in ..body..
you must write:
data Foo = Foo Int Int# f x = let !(Foo a b, w) = ..rhs.. in ..body..
since
b
has typeInt#
.
9.2.2. Unboxed tuples¶
Unboxed tuples aren’t really exported by GHC.Exts
; they are a
syntactic extension enabled by the language flag XUnboxedTuples
. An
unboxed tuple looks like this:
(# e_1, ..., e_n #)
where e_1..e_n
are expressions of any type (primitive or
nonprimitive). The type of an unboxed tuple looks the same.
Note that when unboxed tuples are enabled, (#
is a single lexeme, so
for example when using operators like #
and #
you need to write
( # )
and ( # )
rather than (#)
and (#)
.
Unboxed tuples are used for functions that need to return multiple
values, but they avoid the heap allocation normally associated with
using fullyfledged tuples. When an unboxed tuple is returned, the
components are put directly into registers or on the stack; the unboxed
tuple itself does not have a composite representation. Many of the
primitive operations listed in primops.txt.pp
return unboxed tuples.
In particular, the IO
and ST
monads use unboxed tuples to avoid
unnecessary allocation during sequences of operations.
There are some restrictions on the use of unboxed tuples:
Values of unboxed tuple types are subject to the same restrictions as other unboxed types; i.e. they may not be stored in polymorphic data structures or passed to polymorphic functions.
The typical use of unboxed tuples is simply to return multiple values, binding those multiple results with a
case
expression, thus:f x y = (# x+1, y1 #) g x = case f x x of { (# a, b #) > a + b }
You can have an unboxed tuple in a pattern binding, thus
f x = let (# p,q #) = h x in ..body..
If the types of
p
andq
are not unboxed, the resulting binding is lazy like any other Haskell pattern binding. The above example desugars like this:f x = let t = case h x of { (# p,q #) > (p,q) } p = fst t q = snd t in ..body..
Indeed, the bindings can even be recursive.
9.3. Syntactic extensions¶
9.3.1. Unicode syntax¶
The language extension XUnicodeSyntax
XUnicodeSyntax
enables
Unicode characters to be used to stand for certain ASCII character
sequences. The following alternatives are provided:
ASCII  Unicode alternative  Code point  Name 

:: 
∷  0x2237  PROPORTION 
=> 
⇒  0x21D2  RIGHTWARDS DOUBLE ARROW 
> 
→  0x2192  RIGHTWARDS ARROW 
< 
←  0x2190  LEFTWARDS ARROW 
> 
⤚  0x291a  RIGHTWARDS ARROWTAIL 
< 
⤙  0x2919  LEFTWARDS ARROWTAIL 
>> 
⤜  0x291C  RIGHTWARDS DOUBLE ARROWTAIL 
<< 
⤛  0x291B  LEFTWARDS DOUBLE ARROWTAIL 
* 
★  0x2605  BLACK STAR 
forall 
∀  0x2200  FOR ALL 
9.3.2. The magic hash¶
The language extension XMagicHash
allows “#” as a postfix modifier
to identifiers. Thus, “x#” is a valid variable, and “T#” is a valid type
constructor or data constructor.
The hash sign does not change semantics at all. We tend to use variable
names ending in “#” for unboxed values or types (e.g. Int#
), but
there is no requirement to do so; they are just plain ordinary
variables. Nor does the XMagicHash
extension bring anything into
scope. For example, to bring Int#
into scope you must import
GHC.Prim
(see Unboxed types and primitive operations); the XMagicHash
extension then
allows you to refer to the Int#
that is now in scope. Note that
with this option, the meaning of x#y = 0
is changed: it defines a
function x#
taking a single argument y
; to define the operator
#
, put a space: x # y = 0
.
The XMagicHash
also enables some new forms of literals (see
Unboxed types):
'x'#
has typeChar#
"foo"#
has typeAddr#
3#
has typeInt#
. In general, any Haskell integer lexeme followed by a#
is anInt#
literal, e.g.0x3A#
as well as32#
.3##
has typeWord#
. In general, any nonnegative Haskell integer lexeme followed by##
is aWord#
.3.2#
has typeFloat#
.3.2##
has typeDouble#
9.3.3. Negative literals¶
The literal 123
is, according to Haskell98 and Haskell 2010,
desugared as negate (fromInteger 123)
. The language extension
XNegativeLiterals
means that it is instead desugared as
fromInteger (123)
.
This can make a difference when the positive and negative range of a
numeric data type don’t match up. For example, in 8bit arithmetic 128
is representable, but +128 is not. So negate (fromInteger 128)
will
elicit an unexpected integerliteraloverflow message.
9.3.4. Fractional looking integer literals¶
Haskell 2010 and Haskell 98 define floating literals with the syntax
1.2e6
. These literals have the type Fractional a => a
.
The language extension XNumDecimals
allows you to also use the
floating literal syntax for instances of Integral
, and have values
like (1.2e6 :: Num a => a)
9.3.5. Binary integer literals¶
Haskell 2010 and Haskell 98 allows for integer literals to be given in
decimal, octal (prefixed by 0o
or 0O
), or hexadecimal notation
(prefixed by 0x
or 0X
).
The language extension XBinaryLiterals
adds support for expressing
integer literals in binary notation with the prefix 0b
or 0B
.
For instance, the binary integer literal 0b11001001
will be
desugared into fromInteger 201
when XBinaryLiterals
is enabled.
9.3.6. Hierarchical Modules¶
GHC supports a small extension to the syntax of module names: a module
name is allowed to contain a dot ‘.’
. This is also known as the
“hierarchical module namespace” extension, because it extends the
normally flat Haskell module namespace into a more flexible hierarchy of
modules.
This extension has very little impact on the language itself; modules
names are always fully qualified, so you can just think of the fully
qualified module name as “the module name”. In particular, this means
that the full module name must be given after the module
keyword at
the beginning of the module; for example, the module A.B.C
must
begin
module A.B.C
It is a common strategy to use the as
keyword to save some typing
when using qualified names with hierarchical modules. For example:
import qualified Control.Monad.ST.Strict as ST
For details on how GHC searches for source and interface files in the presence of hierarchical modules, see The search path.
GHC comes with a large collection of libraries arranged hierarchically; see the accompanying library documentation. More libraries to install are available from HackageDB.
9.3.7. Pattern guards¶
Pattern guards (Glasgow extension) The discussion that follows is an abbreviated version of Simon Peyton Jones’s original proposal. (Note that the proposal was written before pattern guards were implemented, so refers to them as unimplemented.)
Suppose we have an abstract data type of finite maps, with a lookup operation:
lookup :: FiniteMap > Int > Maybe Int
The lookup returns Nothing
if the supplied key is not in the domain
of the mapping, and (Just v)
otherwise, where v
is the value
that the key maps to. Now consider the following definition:
clunky env var1 var2  ok1 && ok2 = val1 + val2
 otherwise = var1 + var2
where
m1 = lookup env var1
m2 = lookup env var2
ok1 = maybeToBool m1
ok2 = maybeToBool m2
val1 = expectJust m1
val2 = expectJust m2
The auxiliary functions are
maybeToBool :: Maybe a > Bool
maybeToBool (Just x) = True
maybeToBool Nothing = False
expectJust :: Maybe a > a
expectJust (Just x) = x
expectJust Nothing = error "Unexpected Nothing"
What is clunky
doing? The guard ok1 && ok2
checks that both
lookups succeed, using maybeToBool
to convert the Maybe
types to
booleans. The (lazily evaluated) expectJust
calls extract the values
from the results of the lookups, and binds the returned values to
val1
and val2
respectively. If either lookup fails, then clunky
takes the otherwise
case and returns the sum of its arguments.
This is certainly legal Haskell, but it is a tremendously verbose and unobvious way to achieve the desired effect. Arguably, a more direct way to write clunky would be to use case expressions:
clunky env var1 var2 = case lookup env var1 of
Nothing > fail
Just val1 > case lookup env var2 of
Nothing > fail
Just val2 > val1 + val2
where
fail = var1 + var2
This is a bit shorter, but hardly better. Of course, we can rewrite any
set of patternmatching, guarded equations as case expressions; that is
precisely what the compiler does when compiling equations! The reason
that Haskell provides guarded equations is because they allow us to
write down the cases we want to consider, one at a time, independently
of each other. This structure is hidden in the case version. Two of the
righthand sides are really the same (fail
), and the whole
expression tends to become more and more indented.
Here is how I would write clunky:
clunky env var1 var2
 Just val1 < lookup env var1
, Just val2 < lookup env var2
= val1 + val2
...other equations for clunky...
The semantics should be clear enough. The qualifiers are matched in
order. For a <
qualifier, which I call a pattern guard, the right
hand side is evaluated and matched against the pattern on the left. If
the match fails then the whole guard fails and the next equation is
tried. If it succeeds, then the appropriate binding takes place, and the
next qualifier is matched, in the augmented environment. Unlike list
comprehensions, however, the type of the expression to the right of the
<
is the same as the type of the pattern to its left. The bindings
introduced by pattern guards scope over all the remaining guard
qualifiers, and over the right hand side of the equation.
Just as with list comprehensions, boolean expressions can be freely mixed with among the pattern guards. For example:
f x  [y] < x
, y > 3
, Just z < h y
= ...
Haskell’s current guards therefore emerge as a special case, in which the qualifier list has just one element, a boolean expression.
9.3.8. View patterns¶
View patterns are enabled by the flag XViewPatterns
. More
information and examples of view patterns can be found on the
Wiki page.
View patterns are somewhat like pattern guards that can be nested inside of other patterns. They are a convenient way of patternmatching against values of abstract types. For example, in a programming language implementation, we might represent the syntax of the types of the language as follows:
type Typ
data TypView = Unit
 Arrow Typ Typ
view :: Typ > TypView
 additional operations for constructing Typ's ...
The representation of Typ is held abstract, permitting implementations to use a fancy representation (e.g., hashconsing to manage sharing). Without view patterns, using this signature a little inconvenient:
size :: Typ > Integer
size t = case view t of
Unit > 1
Arrow t1 t2 > size t1 + size t2
It is necessary to iterate the case, rather than using an equational
function definition. And the situation is even worse when the matching
against t
is buried deep inside another pattern.
View patterns permit calling the view function inside the pattern and matching against the result:
size (view > Unit) = 1
size (view > Arrow t1 t2) = size t1 + size t2
That is, we add a new form of pattern, written ⟨expression⟩ >
⟨pattern⟩ that means “apply the expression to whatever we’re trying to
match against, and then match the result of that application against the
pattern”. The expression can be any Haskell expression of function type,
and view patterns can be used wherever patterns are used.
The semantics of a pattern (
⟨exp⟩ >
⟨pat⟩ )
are as
follows:
Scoping: The variables bound by the view pattern are the variables bound by ⟨pat⟩.
Any variables in ⟨exp⟩ are bound occurrences, but variables bound “to the left” in a pattern are in scope. This feature permits, for example, one argument to a function to be used in the view of another argument. For example, the function
clunky
from Pattern guards can be written using view patterns as follows:clunky env (lookup env > Just val1) (lookup env > Just val2) = val1 + val2 ...other equations for clunky...
More precisely, the scoping rules are:
In a single pattern, variables bound by patterns to the left of a view pattern expression are in scope. For example:
example :: Maybe ((String > Integer,Integer), String) > Bool example Just ((f,_), f > 4) = True
Additionally, in function definitions, variables bound by matching earlier curried arguments may be used in view pattern expressions in later arguments:
example :: (String > Integer) > String > Bool example f (f > 4) = True
That is, the scoping is the same as it would be if the curried arguments were collected into a tuple.
In mutually recursive bindings, such as
let
,where
, or the top level, view patterns in one declaration may not mention variables bound by other declarations. That is, each declaration must be selfcontained. For example, the following program is not allowed:let {(x > y) = e1 ; (y > x) = e2 } in x
(For some amplification on this design choice see Trac #4061.
Typing: If ⟨exp⟩ has type ⟨T1⟩
>
⟨T2⟩ and ⟨pat⟩ matches a ⟨T2⟩, then the whole view pattern matches a ⟨T1⟩.Matching: To the equations in Section 3.17.3 of the Haskell 98 Report, add the following:
case v of { (e > p) > e1 ; _ > e2 } = case (e v) of { p > e1 ; _ > e2 }
That is, to match a variable ⟨v⟩ against a pattern
(
⟨exp⟩>
⟨pat⟩)
, evaluate(
⟨exp⟩ ⟨v⟩)
and match the result against ⟨pat⟩.Efficiency: When the same view function is applied in multiple branches of a function definition or a case expression (e.g., in
size
above), GHC makes an attempt to collect these applications into a single nested case expression, so that the view function is only applied once. Pattern compilation in GHC follows the matrix algorithm described in Chapter 4 of The Implementation of Functional Programming Languages. When the top rows of the first column of a matrix are all view patterns with the “same” expression, these patterns are transformed into a single nested case. This includes, for example, adjacent view patterns that line up in a tuple, as inf ((view > A, p1), p2) = e1 f ((view > B, p3), p4) = e2
The current notion of when two view pattern expressions are “the same” is very restricted: it is not even full syntactic equality. However, it does include variables, literals, applications, and tuples; e.g., two instances of
view ("hi", "there")
will be collected. However, the current implementation does not compare up to alphaequivalence, so two instances of(x, view x > y)
will not be coalesced.
9.3.9. Pattern synonyms¶
Pattern synonyms are enabled by the flag XPatternSynonyms
, which is
required for defining them, but not for using them. More information
and examples of view patterns can be found on the
Wiki page <PatternSynonyms>.
Pattern synonyms enable giving names to parametrized pattern schemes. They can also be thought of as abstract constructors that don’t have a bearing on data representation. For example, in a programming language implementation, we might represent types of the language as follows:
data Type = App String [Type]
Here are some examples of using said representation. Consider a few
types of the Type
universe encoded like this:
App ">" [t1, t2]  t1 > t2
App "Int" []  Int
App "Maybe" [App "Int" []]  Maybe Int
This representation is very generic in that no types are given special
treatment. However, some functions might need to handle some known types
specially, for example the following two functions collect all argument
types of (nested) arrow types, and recognize the Int
type,
respectively:
collectArgs :: Type > [Type]
collectArgs (App ">" [t1, t2]) = t1 : collectArgs t2
collectArgs _ = []
isInt :: Type > Bool
isInt (App "Int" []) = True
isInt _ = False
Matching on App
directly is both hard to read and error prone to
write. And the situation is even worse when the matching is nested:
isIntEndo :: Type > Bool
isIntEndo (App ">" [App "Int" [], App "Int" []]) = True
isIntEndo _ = False
Pattern synonyms permit abstracting from the representation to expose
matchers that behave in a constructorlike manner with respect to
pattern matching. We can create pattern synonyms for the known types we
care about, without committing the representation to them (note that
these don’t have to be defined in the same module as the Type
type):
pattern Arrow t1 t2 = App ">" [t1, t2]
pattern Int = App "Int" []
pattern Maybe t = App "Maybe" [t]
Which enables us to rewrite our functions in a much cleaner style:
collectArgs :: Type > [Type]
collectArgs (Arrow t1 t2) = t1 : collectArgs t2
collectArgs _ = []
isInt :: Type > Bool
isInt Int = True
isInt _ = False
isIntEndo :: Type > Bool
isIntEndo (Arrow Int Int) = True
isIntEndo _ = False
In general there are three kinds of pattern synonyms. Unidirectional, bidirectional and explicitly bidirectional. The examples given so far are examples of bidirectional pattern synonyms. A bidirectional synonym behaves the same as an ordinary data constructor. We can use it in a pattern context to deconstruct values and in an expression context to construct values. For example, we can construct the value intEndo using the pattern synonyms Arrow and Int as defined previously.
intEndo :: Type
intEndo = Arrow Int Int
This example is equivalent to the much more complicated construction if we had directly used the Type constructors.
intEndo :: Type
intEndo = App ">" [App "Int" [], App "Int" []]
Unidirectional synonyms can only be used in a pattern context and are defined as follows:
pattern Head x < x:xs
In this case, Head
⟨x⟩ cannot be used in expressions, only patterns,
since it wouldn’t specify a value for the ⟨xs⟩ on the righthand side. However,
we can define an explicitly bidirectional pattern synonym by separately
specifying how to construct and deconstruct a type. The syntax for
doing this is as follows:
pattern HeadC x < x:xs where
HeadC x = [x]
We can then use HeadC
in both expression and pattern contexts. In a pattern
context it will match the head of any list with length at least one. In an
expression context it will construct a singleton list.
The table below summarises where each kind of pattern synonym can be used.
Context  Unidirectional  Bidirectional  Explicitly Bidirectional 

Pattern  Yes  Yes  Yes 
Expression  No  Yes (Inferred)  Yes (Explicit) 
9.3.9.1. Record Pattern Synonyms¶
It is also possible to define pattern synonyms which behave just like record constructors. The syntax for doing this is as follows:
pattern Point :: (Int, Int)
pattern Point{x, y} = (x, y)
The idea is that we can then use Point
just as if we had defined a new
datatype MyPoint
with two fields x
and y
.
data MyPoint = Point { x :: Int, y :: Int }
Whilst a normal pattern synonym can be used in two ways, there are then seven
ways in which to use Point
. Precisely the ways in which a normal record
constructor can be used.
Usage  Example 

As a constructor  zero = Point 0 0 
As a constructor with record syntax  zero = Point { x = 0, y = 0} 
In a pattern context  isZero (Point 0 0) = True 
In a pattern context with record syntax  isZero (Point { x = 0, y = 0 } 
In a pattern context with field puns  getX (Point {x}) = x 
In a record update  (0, 0) { x = 1 } == (1,0) 
Using record selectors  x (0,0) == 0 
For a unidirectional record pattern synonym we define record selectors but do not allow record updates or construction.
The syntax and semantics of pattern synonyms are elaborated in the following subsections. See the Wiki page for more details.
9.3.9.2. Syntax and scoping of pattern synonyms¶
A pattern synonym declaration can be either unidirectional, bidirectional or explicitly bidirectional. The syntax for unidirectional pattern synonyms is:
pattern pat_lhs < pat
the syntax for bidirectional pattern synonyms is:
pattern pat_lhs = pat
and the syntax for explicitly bidirectional pattern synonyms is:
pattern pat_lhs < pat where
pat_lhs = expr
We can define either prefix, infix or record pattern synonyms by modifying the form of pat_lhs. The syntax for these is as follows:
Prefix  Name args 
Infix  arg1 `Name` arg2
or arg1 op arg2 
Record  Name{arg1,arg2,...,argn} 
Pattern synonym declarations can only occur in the top level of a module. In particular, they are not allowed as local definitions.
The variables in the lefthand side of the definition are bound by the pattern on the righthand side. For bidirectional pattern synonyms, all the variables of the righthand side must also occur on the lefthand side; also, wildcard patterns and view patterns are not allowed. For unidirectional and explicitly bidirectional pattern synonyms, there is no restriction on the righthand side pattern.
Pattern synonyms cannot be defined recursively.
9.3.9.3. Import and export of pattern synonyms¶
The name of the pattern synonym is in the same namespace as proper data constructors. Like normal data constructors, pattern synonyms can be imported and exported through association with a type constructor or independently.
To export them on their own, in an export or import specification, you must
prefix pattern names with the pattern
keyword, e.g.:
module Example (pattern Zero) where
data MyNum = MkNum Int
pattern Zero :: MyNum
pattern Zero = MkNum 0
Without the pattern
prefix, Zero
would be interpreted as a
type constructor in the export list.
You may also use the pattern
keyword in an import/export
specification to import or export an ordinary data constructor. For
example:
import Data.Maybe( pattern Just )
would bring into scope the data constructor Just
from the Maybe
type, without also bringing the type constructor Maybe
into scope.
To bundle a pattern synonym with a type constructor, we list the pattern
synonym in the export list of a module which exports the type constructor.
For example, to bundle Zero
with MyNum
we could write the following:
module Example ( MyNum(Zero) ) where
If a module was then to import MyNum
from Example
, it would also import
the pattern synonym Zero
.
It is also possible to use the special token ..
in an export list to mean
all currently bundled constructors. For example, we could write:
module Example ( MyNum(.., Zero) ) where
in which case, Example
would export the type constructor MyNum
with
the data constructor MkNum
and also the pattern synonym Zero
.
Bundled patterns synoyms are type checked to ensure that they are of the same type as the type constructor which they are bundled with. A pattern synonym P can not be bundled with a type constructor T if P‘s type is visibly incompatible with T.
A module which imports MyNum(..)
from Example
and then reexports
MyNum(..)
will also export any pattern synonyms bundled with MyNum
in
Example
. A more complete specification can be found on the
wiki.
9.3.9.4. Typing of pattern synonyms¶
Given a pattern synonym definition of the form
pattern P var1 var2 ... varN < pat
it is assigned a pattern type of the form
pattern P :: CReq => CProf => t1 > t2 > ... > tN > t
where ⟨CProv⟩ and ⟨CReq⟩ are type contexts, and ⟨t1⟩, ⟨t2⟩, ..., ⟨tN⟩ and ⟨t⟩ are types. Notice the unusual form of the type, with two contexts ⟨CProv⟩ and ⟨CReq⟩:
 ⟨CProv⟩ are the constraints made available (provided) by a successful pattern match.
 ⟨CReq⟩ are the constraints required to match the pattern.
For example, consider
data T a where
MkT :: (Show b) => a > b > T a
f1 :: (Eq a, Num a) => T a > String
f1 (MkT 42 x) = show x
pattern ExNumPat :: (Num a, Eq a) => (Show b) => b > T a
pattern ExNumPat x = MkT 42 x
f2 :: (Eq a, Num a) => T a > String
f2 (ExNumPat x) = show x
Here f1
does not use pattern synonyms. To match against the numeric
pattern 42
requires the caller to satisfy the constraints
(Num a, Eq a)
, so they appear in f1
‘s type. The call to show
generates a (Show b)
constraint, where b
is an existentially
type variable bound by the pattern match on MkT
. But the same
pattern match also provides the constraint (Show b)
(see MkT
‘s
type), and so all is well.
Exactly the same reasoning applies to ExNumPat
: matching against
ExNumPat
requires the constraints (Num a, Eq a)
, and
provides the constraint (Show b)
.
Note also the following points
In the common case where
Prov
is empty,()
, it can be omitted altogether.You may specify an explicit pattern signature, as we did for
ExNumPat
above, to specify the type of a pattern, just as you can for a function. As usual, the type signature can be less polymorphic than the inferred type. For example Inferred type would be 'a > [a]' pattern SinglePair :: (a, a) > [(a, a)] pattern SinglePair x = [x]
The GHCi
:info
command shows pattern types in this format.For a bidirectional pattern synonym, a use of the pattern synonym as an expression has the type
(CReq, CProv) => t1 > t2 > ... > tN > t
So in the previous example, when used in an expression,
ExNumPat
has typeExNumPat :: (Num a, Eq a, Show b) => b > T t
Notice that this is a tiny bit more restrictive than the expression
MkT 42 x
which would not require(Eq a)
.Consider these two pattern synonyms:
data S a where S1 :: Bool > S Bool pattern P1 :: Bool > Maybe Bool pattern P1 b = Just b pattern P2 :: () => (b ~ Bool) => Bool > S b pattern P2 b = S1 b f :: Maybe a > String f (P1 x) = "no no no"  Typeincorrect g :: S a > String g (P2 b) = "yes yes yes"  Fine
Pattern
P1
can only match against a value of typeMaybe Bool
, so functionf
is rejected because the type signature isMaybe a
. (To see this, imagine expanding the pattern synonym.)On the other hand, function
g
works fine, because matching againstP2
(which wraps the GADTS
) provides the local equality(a~Bool)
. If you were to give an explicit pattern signatureP2 :: Bool > S Bool
, thenP2
would become less polymorphic, and would behave exactly likeP1
so thatg
would then be rejected.In short, if you want GADTlike behaviour for pattern synonyms, then (unlike unlike concrete data constructors like
S1
) you must write its type with explicit provided equalities. For a concrete data constructor likeS1
you can write its type signature as eitherS1 :: Bool > S Bool
orS1 :: (b~Bool) => Bool > S b
; the two are equivalent. Not so for pattern synonyms: the two forms are different, in order to distinguish the two cases above. (See Trac #9953 for discussion of this choice.)
9.3.9.5. Matching of pattern synonyms¶
A pattern synonym occurrence in a pattern is evaluated by first matching
against the pattern synonym itself, and then on the argument patterns.
For example, in the following program, f
and f'
are equivalent:
pattern Pair x y < [x, y]
f (Pair True True) = True
f _ = False
f' [x, y]  True < x, True < y = True
f' _ = False
Note that the strictness of f
differs from that of g
defined
below:
g [True, True] = True
g _ = False
*Main> f (False:undefined)
*** Exception: Prelude.undefined
*Main> g (False:undefined)
False
9.3.10. n+k patterns¶
n+k
pattern support is disabled by default. To enable it, you can
use the XNPlusKPatterns
flag.
9.3.11. The recursive donotation¶
The donotation of Haskell 98 does not allow recursive bindings, that is, the variables bound in a doexpression are visible only in the textually following code block. Compare this to a letexpression, where bound variables are visible in the entire binding group.
It turns out that such recursive bindings do indeed make sense for a
variety of monads, but not all. In particular, recursion in this sense
requires a fixedpoint operator for the underlying monad, captured by
the mfix
method of the MonadFix
class, defined in
Control.Monad.Fix
as follows:
class Monad m => MonadFix m where
mfix :: (a > m a) > m a
Haskell’s Maybe
, []
(list), ST
(both strict and lazy
versions), IO
, and many other monads have MonadFix
instances. On
the negative side, the continuation monad, with the signature
(a > r) > r
, does not.
For monads that do belong to the MonadFix
class, GHC provides an
extended version of the donotation that allows recursive bindings. The
XRecursiveDo
(language pragma: RecursiveDo
) provides the
necessary syntactic support, introducing the keywords mdo
and
rec
for higher and lower levels of the notation respectively. Unlike
bindings in a do
expression, those introduced by mdo
and rec
are recursively defined, much like in an ordinary letexpression. Due to
the new keyword mdo
, we also call this notation the mdonotation.
Here is a simple (albeit contrived) example:
{# LANGUAGE RecursiveDo #}
justOnes = mdo { xs < Just (1:xs)
; return (map negate xs) }
or equivalently
{# LANGUAGE RecursiveDo #}
justOnes = do { rec { xs < Just (1:xs) }
; return (map negate xs) }
As you can guess justOnes
will evaluate to Just [1,1,1,...
.
GHC’s implementation the mdonotation closely follows the original
translation as described in the paper A recursive do for
Haskell, which
in turn is based on the work Value Recursion in Monadic
Computations.
Furthermore, GHC extends the syntax described in the former paper with a
lower level syntax flagged by the rec
keyword, as we describe next.
9.3.11.1. Recursive binding groups¶
The flag XRecursiveDo
also introduces a new keyword rec
, which
wraps a mutuallyrecursive group of monadic statements inside a do
expression, producing a single statement. Similar to a let
statement
inside a do
, variables bound in the rec
are visible throughout
the rec
group, and below it. For example, compare
do { a < getChar do { a < getChar
; let { r1 = f a r2 ; rec { r1 < f a r2
; ; r2 = g r1 } ; ; r2 < g r1 }
; return (r1 ++ r2) } ; return (r1 ++ r2) }
In both cases, r1
and r2
are available both throughout the
let
or rec
block, and in the statements that follow it. The
difference is that let
is nonmonadic, while rec
is monadic. (In
Haskell let
is really letrec
, of course.)
The semantics of rec
is fairly straightforward. Whenever GHC finds a
rec
group, it will compute its set of bound variables, and will
introduce an appropriate call to the underlying monadic valuerecursion
operator mfix
, belonging to the MonadFix
class. Here is an
example:
rec { b < f a c ===> (b,c) < mfix (\ ~(b,c) > do { b < f a c
; c < f b a } ; c < f b a
; return (b,c) })
As usual, the metavariables b
, c
etc., can be arbitrary
patterns. In general, the statement rec ss
is desugared to the
statement
vs < mfix (\ ~vs > do { ss; return vs })
where vs
is a tuple of the variables bound by ss
.
Note in particular that the translation for a rec
block only
involves wrapping a call to mfix
: it performs no other analysis on
the bindings. The latter is the task for the mdo
notation, which is
described next.
9.3.11.2. The mdo
notation¶
A rec
block tells the compiler where precisely the recursive knot
should be tied. It turns out that the placement of the recursive knots
can be rather delicate: in particular, we would like the knots to be
wrapped around as minimal groups as possible. This process is known as
segmentation, and is described in detail in Section 3.2 of A
recursive do for
Haskell.
Segmentation improves polymorphism and reduces the size of the recursive
knot. Most importantly, it avoids unnecessary interference caused by a
fundamental issue with the socalled rightshrinking axiom for monadic
recursion. In brief, most monads of interest (IO, strict state, etc.) do
not have recursion operators that satisfy this axiom, and thus not
performing segmentation can cause unnecessary interference, changing the
termination behavior of the resulting translation. (Details can be found
in Sections 3.1 and 7.2.2 of Value Recursion in Monadic
Computations.)
The mdo
notation removes the burden of placing explicit rec
blocks in the code. Unlike an ordinary do
expression, in which
variables bound by statements are only in scope for later statements,
variables bound in an mdo
expression are in scope for all statements
of the expression. The compiler then automatically identifies minimal
mutually recursively dependent segments of statements, treating them as
if the user had wrapped a rec
qualifier around them.
The definition is syntactic:
 A generator ⟨g⟩ depends on a textually following generator ⟨g’⟩, if
 ⟨g’⟩ defines a variable that is used by ⟨g⟩, or
 ⟨g’⟩ textually appears between ⟨g⟩ and ⟨g’‘⟩, where ⟨g⟩ depends on ⟨g’‘⟩.
 A segment of a given
mdo
expression is a minimal sequence of generators such that no generator of the sequence depends on an outside generator. As a special case, although it is not a generator, the final expression in anmdo
expression is considered to form a segment by itself.
Segments in this sense are related to stronglyconnected components analysis, with the exception that bindings in a segment cannot be reordered and must be contiguous.
Here is an example mdo
expression, and its translation to rec
blocks:
mdo { a < getChar ===> do { a < getChar
; b < f a c ; rec { b < f a c
; c < f b a ; ; c < f b a }
; z < h a b ; z < h a b
; d < g d e ; rec { d < g d e
; e < g a z ; ; e < g a z }
; putChar c } ; putChar c }
Note that a given mdo
expression can cause the creation of multiple
rec
blocks. If there are no recursive dependencies, mdo
will
introduce no rec
blocks. In this latter case an mdo
expression
is precisely the same as a do
expression, as one would expect.
In summary, given an mdo
expression, GHC first performs
segmentation, introducing rec
blocks to wrap over minimal recursive
groups. Then, each resulting rec
is desugared, using a call to
Control.Monad.Fix.mfix
as described in the previous section. The
original mdo
expression typechecks exactly when the desugared
version would do so.
Here are some other important points in using the recursivedo notation:
 It is enabled with the flag
XRecursiveDo
, or theLANGUAGE RecursiveDo
pragma. (The same flag enables bothmdo
notation, and the use ofrec
blocks insidedo
expressions.) rec
blocks can also be used insidemdo
expressions, which will be treated as a single statement. However, it is good style to either usemdo
orrec
blocks in a single expression. If recursive bindings are required for a monad, then that monad must
be declared an instance of the
MonadFix
class.  The following instances of
MonadFix
are automatically provided: List, Maybe, IO. Furthermore, theControl.Monad.ST
andControl.Monad.ST.Lazy
modules provide the instances of theMonadFix
class for Haskell’s internal state monad (strict and lazy, respectively).  Like
let
andwhere
bindings, name shadowing is not allowed within anmdo
expression or arec
block; that is, all the names bound in a singlerec
must be distinct. (GHC will complain if this is not the case.)
9.3.12. Applicative donotation¶
The language option XApplicativeDo
enables an alternative translation for
the donotation, which uses the operators <$>
, <*>
, along with join
as far as possible. There are two main reasons for wanting to do this:
 We can use donotation with types that are an instance of
Applicative
andFunctor
, but notMonad
 In some monads, using the applicative operators is more efficient than monadic bind. For example, it may enable more parallelism.
Applicative donotation desugaring preserves the original semantics, provided
that the Applicative
instance satisfies <*> = ap
and pure = return
(these are true of all the common monadic types). Thus, you can normally turn on
XApplicativeDo
without fear of breaking your program. There is one pitfall
to watch out for; see Things to watch out for.
There are no syntactic changes with XApplicativeDo
. The only way it shows
up at the source level is that you can have a do
expression that doesn’t
require a Monad
constraint. For example, in GHCi:
Prelude> :set XApplicativeDo
Prelude> :t \m > do { x < m; return (not x) }
\m > do { x < m; return (not x) }
:: Functor f => f Bool > f Bool
This example only requires Functor
, because it is translated into (\x >
not x) <$> m
. A more complex example requires Applicative
,
Prelude> :t \m > do { x < m 'a'; y < m 'b'; return (x  y) }
\m > do { x < m 'a'; y < m 'b'; return (x  y) }
:: Applicative f => (Char > f Bool) > f Bool
Here GHC has translated the expression into
(\x y > x  y) <$> m 'a' <*> m 'b'
It is possible to see the actual translation by using ddumpds
, but be
warned, the output is quite verbose.
Note that if the expression can’t be translated into uses of <$>
, <*>
only, then it will incur a Monad
constraint as usual. This happens when
there is a dependency on a value produced by an earlier statement in the
do
block:
Prelude> :t \m > do { x < m True; y < m x; return (x  y) }
\m > do { x < m True; y < m x; return (x  y) }
:: Monad m => (Bool > m Bool) > m Bool
Here, m x
depends on the value of x
produced by the first statement, so
the expression cannot be translated using <*>
.
In general, the rule for when a do
statement incurs a Monad
constraint
is as follows. If the doexpression has the following form:
do p1 < E1; ...; pn < En; return E
where none of the variables defined by p1...pn
are mentioned in E1...En
,
then the expression will only require Applicative
. Otherwise, the expression
will require Monad
.
9.3.12.1. Things to watch out for¶
Your code should just work as before when XApplicativeDo
is enabled,
provided you use conventional Applicative
instances. However, if you define
a Functor
or Applicative
instance using donotation, then it will likely
get turned into an infinite loop by GHC. For example, if you do this:
instance Functor MyType where
fmap f m = do x < m; return (f x)
Then applicative desugaring will turn it into
instance Functor MyType where
fmap f m = fmap (\x > f x) m
And the program will loop at runtime. Similarly, an Applicative
instance
like this
instance Applicative MyType where
pure = return
x <*> y = do f < x; a < y; return (f a)
will result in an infinte loop when <*>
is called.
Just as you wouldn’t define a Monad
instance using the donotation, you
shouldn’t define Functor
or Applicative
instance using donotation (when
using ApplicativeDo
) either. The correct way to define these instances in
terms of Monad
is to use the Monad
operations directly, e.g.
instance Functor MyType where
fmap f m = m >>= return . f
instance Applicative MyType where
pure = return
(<*>) = ap
9.3.13. Parallel List Comprehensions¶
Parallel list comprehensions are a natural extension to list
comprehensions. List comprehensions can be thought of as a nice syntax
for writing maps and filters. Parallel comprehensions extend this to
include the zipWith
family.
A parallel list comprehension has multiple independent branches of
qualifier lists, each separated by a 
symbol. For example, the
following zips together two lists:
[ (x, y)  x < xs  y < ys ]
The behaviour of parallel list comprehensions follows that of zip, in that the resulting list will have the same length as the shortest branch.
We can define parallel list comprehensions by translation to regular comprehensions. Here’s the basic idea:
Given a parallel comprehension of the form:
[ e  p1 < e11, p2 < e12, ...
 q1 < e21, q2 < e22, ...
...
]
This will be translated to:
[ e  ((p1,p2), (q1,q2), ...) < zipN [(p1,p2)  p1 < e11, p2 < e12, ...]
[(q1,q2)  q1 < e21, q2 < e22, ...]
...
]
where zipN
is the appropriate zip for the given number of branches.
9.3.14. Generalised (SQLLike) List Comprehensions¶
Generalised list comprehensions are a further enhancement to the list comprehension syntactic sugar to allow operations such as sorting and grouping which are familiar from SQL. They are fully described in the paper Comprehensive comprehensions: comprehensions with “order by” and “group by”, except that the syntax we use differs slightly from the paper.
The extension is enabled with the flag XTransformListComp
.
Here is an example:
employees = [ ("Simon", "MS", 80)
, ("Erik", "MS", 100)
, ("Phil", "Ed", 40)
, ("Gordon", "Ed", 45)
, ("Paul", "Yale", 60)]
output = [ (the dept, sum salary)
 (name, dept, salary) < employees
, then group by dept using groupWith
, then sortWith by (sum salary)
, then take 5 ]
In this example, the list output
would take on the value:
[("Yale", 60), ("Ed", 85), ("MS", 180)]
There are three new keywords: group
, by
, and using
. (The
functions sortWith
and groupWith
are not keywords; they are
ordinary functions that are exported by GHC.Exts
.)
There are five new forms of comprehension qualifier, all introduced by
the (existing) keyword then
:
then f
This statement requires that f have the type forall a. [a] > [a] . You can see an example of its use in the motivating example, as this form is used to apply take 5 .
then f by e
This form is similar to the previous one, but allows you to create a function which will be passed as the first argument to f. As a consequence f must have the type
forall a. (a > t) > [a] > [a]
. As you can see from the type, this function lets f “project out” some information from the elements of the list it is transforming.An example is shown in the opening example, where
sortWith
is supplied with a function that lets it find out thesum salary
for any item in the list comprehension it transforms.then group by e using f
This is the most general of the groupingtype statements. In this form, f is required to have type
forall a. (a > t) > [a] > [[a]]
. As with thethen f by e
case above, the first argument is a function supplied to f by the compiler which lets it compute e on every element of the list being transformed. However, unlike the nongrouping case, f additionally partitions the list into a number of sublists: this means that at every point after this statement, binders occurring before it in the comprehension refer to lists of possible values, not single values. To help understand this, let’s look at an example: This works similarly to groupWith in GHC.Exts, but doesn't sort its input first groupRuns :: Eq b => (a > b) > [a] > [[a]] groupRuns f = groupBy (\x y > f x == f y) output = [ (the x, y)  x < ([1..3] ++ [1..2]) , y < [4..6] , then group by x using groupRuns ]
This results in the variable
output
taking on the value below:[(1, [4, 5, 6]), (2, [4, 5, 6]), (3, [4, 5, 6]), (1, [4, 5, 6]), (2, [4, 5, 6])]
Note that we have used the
the
function to change the type of x from a list to its original numeric type. The variable y, in contrast, is left unchanged from the list form introduced by the grouping.then group using f
With this form of the group statement, f is required to simply have the type
forall a. [a] > [[a]]
, which will be used to group up the comprehension so far directly. An example of this form is as follows:output = [ x  y < [1..5] , x < "hello" , then group using inits]
This will yield a list containing every prefix of the word “hello” written out 5 times:
["","h","he","hel","hell","hello","helloh","hellohe","hellohel","hellohell","hellohello","hellohelloh",...]
9.3.15. Monad comprehensions¶
Monad comprehensions generalise the list comprehension notation, including parallel comprehensions (Parallel List Comprehensions) and transform comprehensions (Generalised (SQLLike) List Comprehensions) to work for any monad.
Monad comprehensions support:
Bindings:
[ x + y  x < Just 1, y < Just 2 ]
Bindings are translated with the
(>>=)
andreturn
functions to the usual donotation:do x < Just 1 y < Just 2 return (x+y)
Guards:
[ x  x < [1..10], x <= 5 ]
Guards are translated with the
guard
function, which requires aMonadPlus
instance:do x < [1..10] guard (x <= 5) return x
Transform statements (as with
XTransformListComp
):[ x+y  x < [1..10], y < [1..x], then take 2 ]
This translates to:
do (x,y) < take 2 (do x < [1..10] y < [1..x] return (x,y)) return (x+y)
Group statements (as with
XTransformListComp
):[ x  x < [1,1,2,2,3], then group by x using GHC.Exts.groupWith ] [ x  x < [1,1,2,2,3], then group using myGroup ]
Parallel statements (as with
XParallelListComp
):[ (x+y)  x < [1..10]  y < [11..20] ]
Parallel statements are translated using the
mzip
function, which requires aMonadZip
instance defined in Control.Monad.Zip:do (x,y) < mzip (do x < [1..10] return x) (do y < [11..20] return y) return (x+y)
All these features are enabled by default if the MonadComprehensions
extension is enabled. The types and more detailed examples on how to use
comprehensions are explained in the previous chapters
Generalised (SQLLike) List Comprehensions and
Parallel List Comprehensions. In general you just have to replace
the type [a]
with the type Monad m => m a
for monad
comprehensions.
Note
Even though most of these examples are using the list monad, monad
comprehensions work for any monad. The base
package offers all
necessary instances for lists, which make MonadComprehensions
backward compatible to builtin, transform and parallel list
comprehensions.
More formally, the desugaring is as follows. We write D[ e  Q]
to
mean the desugaring of the monad comprehension [ e  Q]
:
Expressions: e
Declarations: d
Lists of qualifiers: Q,R,S
 Basic forms
D[ e  ] = return e
D[ e  p < e, Q ] = e >>= \p > D[ e  Q ]
D[ e  e, Q ] = guard e >> \p > D[ e  Q ]
D[ e  let d, Q ] = let d in D[ e  Q ]
 Parallel comprehensions (iterate for multiple parallel branches)
D[ e  (Q  R), S ] = mzip D[ Qv  Q ] D[ Rv  R ] >>= \(Qv,Rv) > D[ e  S ]
 Transform comprehensions
D[ e  Q then f, R ] = f D[ Qv  Q ] >>= \Qv > D[ e  R ]
D[ e  Q then f by b, R ] = f (\Qv > b) D[ Qv  Q ] >>= \Qv > D[ e  R ]
D[ e  Q then group using f, R ] = f D[ Qv  Q ] >>= \ys >
case (fmap selQv1 ys, ..., fmap selQvn ys) of
Qv > D[ e  R ]
D[ e  Q then group by b using f, R ] = f (\Qv > b) D[ Qv  Q ] >>= \ys >
case (fmap selQv1 ys, ..., fmap selQvn ys) of
Qv > D[ e  R ]
where Qv is the tuple of variables bound by Q (and used subsequently)
selQvi is a selector mapping Qv to the ith component of Qv
Operator Standard binding Expected type

return GHC.Base t1 > m t2
(>>=) GHC.Base m1 t1 > (t2 > m2 t3) > m3 t3
(>>) GHC.Base m1 t1 > m2 t2 > m3 t3
guard Control.Monad t1 > m t2
fmap GHC.Base forall a b. (a>b) > n a > n b
mzip Control.Monad.Zip forall a b. m a > m b > m (a,b)
The comprehension should typecheck when its desugaring would typecheck,
except that (as discussed in Generalised (SQLLike) List Comprehensions) in the
“then f
” and “then group using f
” clauses, when the “by b
” qualifier
is omitted, argument f
should have a polymorphic type. In particular, “then
Data.List.sort
” and “then group using Data.List.group
” are
insufficiently polymorphic.
Monad comprehensions support rebindable syntax
(Rebindable syntax and the implicit Prelude import). Without rebindable syntax, the operators
from the “standard binding” module are used; with rebindable syntax, the
operators are looked up in the current lexical scope. For example,
parallel comprehensions will be typechecked and desugared using whatever
“mzip
” is in scope.
The rebindable operators must have the “Expected type” given in the table above. These types are surprisingly general. For example, you can use a bind operator with the type
(>>=) :: T x y a > (a > T y z b) > T x z b
In the case of transform comprehensions, notice that the groups are
parameterised over some arbitrary type n
(provided it has an
fmap
, as well as the comprehension being over an arbitrary monad.
9.3.16. New monadic failure desugaring mechanism¶
The XMonadFailDesugaring
extension switches the desugaring of
do
blocks to use MonadFail.fail
instead of Monad.fail
. This will
eventually be the default behaviour in a future GHC release, under the
MonadFail Proposal (MFP).
This extension is temporary, and will be deprecated in a future release. It is included so that library authors have a hard check for whether their code will work with future GHC versions.
9.3.17. Rebindable syntax and the implicit Prelude import¶
GHC normally imports Prelude.hi
files for
you. If you’d rather it didn’t, then give it a XNoImplicitPrelude
option. The idea is that you can then import a Prelude of your own. (But
don’t call it Prelude
; the Haskell module namespace is flat, and you
must not conflict with any Prelude module.)
Suppose you are importing a Prelude of your own in order to define your
own numeric class hierarchy. It completely defeats that purpose if the
literal “1” means “Prelude.fromInteger 1
”, which is what the Haskell
Report specifies. So the XRebindableSyntax
flag causes the
following pieces of builtin syntax to refer to whatever is in scope,
not the Prelude versions:
 An integer literal
368
means “fromInteger (368::Integer)
”, rather than “Prelude.fromInteger (368::Integer)
”.  Fractional literals are handed in just the same way, except that the
translation is
fromRational (3.68::Rational)
.  The equality test in an overloaded numeric pattern uses whatever
(==)
is in scope.  The subtraction operation, and the greaterthanorequal test, in
n+k
patterns use whatever()
and(>=)
are in scope.  Negation (e.g. “
 (f x)
”) means “negate (f x)
”, both in numeric patterns, and expressions.  Conditionals (e.g. “
if
e1then
e2else
e3”) means “ifThenElse
e1 e2 e3”. Howevercase
expressions are unaffected.  “Do” notation is translated using whatever functions
(>>=)
,(>>)
, andfail
, are in scope (not the Prelude versions). List comprehensions,mdo
(The recursive donotation), and parallel array comprehensions, are unaffected.  Arrow notation (see Arrow notation) uses whatever
arr
,(>>>)
,first
,app
,()
andloop
functions are in scope. But unlike the other constructs, the types of these functions must match the Prelude types very closely. Details are in flux; if you want to use this, ask!
XRebindableSyntax
implies XNoImplicitPrelude
.
In all cases (apart from arrow notation), the static semantics should be
that of the desugared form, even if that is a little unexpected. For
example, the static semantics of the literal 368
is exactly that of
fromInteger (368::Integer)
; it’s fine for fromInteger
to have
any of the types:
fromInteger :: Integer > Integer
fromInteger :: forall a. Foo a => Integer > a
fromInteger :: Num a => a > Integer
fromInteger :: Integer > Bool > Bool
Be warned: this is an experimental facility, with fewer checks than
usual. Use dcorelint
to typecheck the desugared program. If Core
Lint is happy you should be all right.
9.3.18. Postfix operators¶
The XPostfixOperators
flag enables a small extension to the syntax
of left operator sections, which allows you to define postfix operators.
The extension is this: the left section
(e !)
is equivalent (from the point of view of both type checking and execution) to the expression
((!) e)
(for any expression e
and operator (!)
. The strict Haskell 98
interpretation is that the section is equivalent to
(\y > (!) e y)
That is, the operator must be a function of two arguments. GHC allows it to take only one argument, and that in turn allows you to write the function postfix.
The extension does not extend to the lefthand side of function definitions; you must define such a function in prefix form.
9.3.19. Tuple sections¶
The XTupleSections
flag enables Pythonstyle partially applied
tuple constructors. For example, the following program
(, True)
is considered to be an alternative notation for the more unwieldy alternative
\x > (x, True)
You can omit any combination of arguments to the tuple, as in the following
(, "I", , , "Love", , 1337)
which translates to
\a b c d > (a, "I", b, c, "Love", d, 1337)
If you have unboxed tuples enabled, tuple sections will also be available for them, like so
(# , True #)
Because there is no unboxed unit tuple, the following expression
(# #)
continues to stand for the unboxed singleton tuple data constructor.
9.3.20. Lambdacase¶
The XLambdaCase
flag enables expressions of the form
\case { p1 > e1; ...; pN > eN }
which is equivalent to
\freshName > case freshName of { p1 > e1; ...; pN > eN }
Note that \case
starts a layout, so you can write
\case
p1 > e1
...
pN > eN
9.3.21. Empty case alternatives¶
The XEmptyCase
flag enables case expressions, or lambdacase
expressions, that have no alternatives, thus:
case e of { }  No alternatives
or
\case { }  XLambdaCase is also required
This can be useful when you know that the expression being scrutinised has no nonbottom values. For example:
data Void
f :: Void > Int
f x = case x of { }
With dependentlytyped features it is more useful (see Trac #2431`). For
example, consider these two candidate definitions of absurd
:
data a :==: b where
Refl :: a :==: a
absurd :: True :~: False > a
absurd x = error "absurd"  (A)
absurd x = case x of {}  (B)
We much prefer (B). Why? Because GHC can figure out that
(True :~: False)
is an empty type. So (B) has no partiality and GHC
should be able to compile with fwarnincompletepatterns
. (Though
the pattern match checking is not yet clever enough to do that.) On the
other hand (A) looks dangerous, and GHC doesn’t check to make sure that,
in fact, the function can never get called.
9.3.22. Multiway ifexpressions¶
With XMultiWayIf
flag GHC accepts conditional expressions with
multiple branches:
if  guard1 > expr1
 ...
 guardN > exprN
which is roughly equivalent to
case () of
_  guard1 > expr1
...
_  guardN > exprN
Multiway if expressions introduce a new layout context. So the example above is equivalent to:
if {  guard1 > expr1
;  ...
;  guardN > exprN
}
The following behaves as expected:
if  guard1 > if  guard2 > expr2
 guard3 > expr3
 guard4 > expr4
because layout translates it as
if {  guard1 > if {  guard2 > expr2
;  guard3 > expr3
}
;  guard4 > expr4
}
Layout with multiway if works in the same way as other layout contexts, except that the semicolons between guards in a multiway if are optional. So it is not necessary to line up all the guards at the same column; this is consistent with the way guards work in function definitions and case expressions.
9.3.23. Local Fixity Declarations¶
A careful reading of the Haskell 98 Report reveals that fixity
declarations (infix
, infixl
, and infixr
) are permitted to
appear inside local bindings such those introduced by let
and
where
. However, the Haskell Report does not specify the semantics of
such bindings very precisely.
In GHC, a fixity declaration may accompany a local binding:
let f = ...
infixr 3 `f`
in
...
and the fixity declaration applies wherever the binding is in scope. For
example, in a let
, it applies in the righthand sides of other
let
bindings and the body of the let
C. Or, in recursive do
expressions (The recursive donotation), the local fixity
declarations of a let
statement scope over other statements in the
group, just as the bound name does.
Moreover, a local fixity declaration must accompany a local binding of that name: it is not possible to revise the fixity of name bound elsewhere, as in
let infixr 9 $ in ...
Because local fixity declarations are technically Haskell 98, no flag is necessary to enable them.
9.3.24. Import and export extensions¶
9.3.24.1. Hiding things the imported module doesn’t export¶
Technically in Haskell 2010 this is illegal:
module A( f ) where
f = True
module B where
import A hiding( g )  A does not export g
g = f
The import A hiding( g )
in module B
is technically an error
(Haskell Report,
5.3.1)
because A
does not export g
. However GHC allows it, in the
interests of supporting backward compatibility; for example, a newer
version of A
might export g
, and you want B
to work in
either case.
The warning fwarndodgyimports
, which is off by default but
included with W
, warns if you hide something that the imported
module does not export.
9.3.24.2. Packagequalified imports¶
With the XPackageImports
flag, GHC allows import declarations to be
qualified by the package name that the module is intended to be imported
from. For example:
import "network" Network.Socket
would import the module Network.Socket
from the package network
(any version). This may be used to disambiguate an import when the same
module is available from multiple packages, or is present in both the
current package being built and an external package.
The special package name this
can be used to refer to the current
package being built.
Note
You probably don’t need to use this feature, it was added mainly so that we can build backwardscompatible versions of packages when APIs change. It can lead to fragile dependencies in the common case: modules occasionally move from one package to another, rendering any packagequalified imports broken. See also Thinning and renaming modules for an alternative way of disambiguating between module names.
9.3.24.3. Safe imports¶
With the XSafe
, XTrustworthy
and XUnsafe
language flags,
GHC extends the import declaration syntax to take an optional safe
keyword after the import
keyword. This feature is part of the Safe
Haskell GHC extension. For example:
import safe qualified Network.Socket as NS
would import the module Network.Socket
with compilation only
succeeding if Network.Socket
can be safely imported. For a description of
when a import is considered safe see Safe Haskell.
9.3.24.4. Explicit namespaces in import/export¶
In an import or export list, such as
module M( f, (++) ) where ...
import N( f, (++) )
...
the entities f
and (++)
are values. However, with type
operators (Type operators) it becomes possible to declare
(++)
as a type constructor. In that case, how would you export or
import it?
The XExplicitNamespaces
extension allows you to prefix the name of
a type constructor in an import or export list with “type
” to
disambiguate this case, thus:
module M( f, type (++) ) where ...
import N( f, type (++) )
...
module N( f, type (++) ) where
data family a ++ b = L a  R b
The extension XExplicitNamespaces
is implied by XTypeOperators
and (for some reason) by XTypeFamilies
.
In addition, with XPatternSynonyms
you can prefix the name of a
data constructor in an import or export list with the keyword
pattern
, to allow the import or export of a data constructor without
its parent type constructor (see Import and export of pattern synonyms).
9.3.25. Summary of stolen syntax¶
Turning on an option that enables special syntax might cause working Haskell 98 code to fail to compile, perhaps because it uses a variable name which has become a reserved word. This section lists the syntax that is “stolen” by language extensions. We use notation and nonterminal names from the Haskell 98 lexical syntax (see the Haskell 98 Report). We only list syntax changes here that might affect existing working programs (i.e. “stolen” syntax). Many of these extensions will also enable new contextfree syntax, but in all cases programs written to use the new syntax would not be compilable without the option enabled.
There are two classes of special syntax:
 New reserved words and symbols: character sequences which are no longer available for use as identifiers in the program.
 Other special syntax: sequences of characters that have a different meaning when this particular option is turned on.
The following syntax is stolen:
forall
Stolen (in types) by:
XExplicitForAll
, and hence byXScopedTypeVariables
,XLiberalTypeSynonyms
,XRankNTypes
,XExistentialQuantification
mdo
Stolen by:
XRecursiveDo
foreign
Stolen by:
XForeignFunctionInterface
rec
,proc
,<
,>
,<<
,>>
,(
,)
Stolen by:
XArrows
?varid
Stolen by:
XImplicitParams
[
,[e
,[p
,[d
,[t
,$(
,$$(
,[
,[e
,$varid
,$$varid
Stolen by:
XTemplateHaskell
[varid
Stolen by:
XQuasiQuotes
 ⟨varid⟩,
#
⟨char⟩,#
, ⟨string⟩,#
, ⟨integer⟩,#
, ⟨float⟩,#
, ⟨float⟩,##
 Stolen by:
XMagicHash
(#
,#)
 Stolen by:
XUnboxedTuples
 ⟨varid⟩,
!
, ⟨varid⟩  Stolen by:
XBangPatterns
pattern
 Stolen by:
XPatternSynonyms
9.4. Extensions to data types and type synonyms¶
9.4.1. Data types with no constructors¶
With the XEmptyDataDecls
flag (or equivalent LANGUAGE
pragma), GHC
lets you declare a data type with no constructors. For example:
data S  S :: *
data T a  T :: * > *
Syntactically, the declaration lacks the “= constrs” part. The type can
be parameterised over types of any kind, but if the kind is not *
then an explicit kind annotation must be used (see Explicitlykinded quantification).
Such data types have only one value, namely bottom. Nevertheless, they can be useful when defining “phantom types”.
9.4.2. Data type contexts¶
Haskell allows datatypes to be given contexts, e.g.
data Eq a => Set a = NilSet  ConsSet a (Set a)
give constructors with types:
NilSet :: Set a
ConsSet :: Eq a => a > Set a > Set a
This is widely considered a misfeature, and is going to be removed from
the language. In GHC, it is controlled by the deprecated extension
DatatypeContexts
.
9.4.3. Infix type constructors, classes, and type variables¶
GHC allows type constructors, classes, and type variables to be operators, and to be written infix, very much like expressions. More specifically:
A type constructor or class can be any nonreserved operator. Symbols used in types are always like capitalized identifiers; they are never variables. Note that this is different from the lexical syntax of data constructors, which are required to begin with a
:
.Data type and typesynonym declarations can be written infix, parenthesised if you want further arguments. E.g.
data a :*: b = Foo a b type a :+: b = Either a b class a :=: b where ... data (a :**: b) x = Baz a b x type (a :++: b) y = Either (a,b) y
Types, and class constraints, can be written infix. For example
x :: Int :*: Bool f :: (a :=: b) => a > b
Backquotes work as for expressions, both for type constructors and type variables; e.g.
Int `Either` Bool
, orInt `a` Bool
. Similarly, parentheses work the same; e.g.(:*:) Int Bool
.Fixities may be declared for type constructors, or classes, just as for data constructors. However, one cannot distinguish between the two in a fixity declaration; a fixity declaration sets the fixity for a data constructor and the corresponding type constructor. For example:
infixl 7 T, :*:
sets the fixity for both type constructor
T
and data constructorT
, and similarly for:*:
.Int `a` Bool
.Function arrow is
infixr
with fixity 0 (this might change; it’s not clear what it should be).
9.4.4. Type operators¶
In types, an operator symbol like (+)
is normally treated as a type
variable, just like a
. Thus in Haskell 98 you can say
type T (+) = ((+), (+))
 Just like: type T a = (a,a)
f :: T Int > Int
f (x,y)= x
As you can see, using operators in this way is not very useful, and Haskell 98 does not even allow you to write them infix.
The language XTypeOperators
changes this behaviour:
Operator symbols become type constructors rather than type variables.
Operator symbols in types can be written infix, both in definitions and uses. For example:
data a + b = Plus a b type Foo = Int + Bool
There is now some potential ambiguity in import and export lists; for example if you write
import M( (+) )
do you mean the function(+)
or the type constructor(+)
? The default is the former, but withXExplicitNamespaces
(which is implied byXTypeOperators
) GHC allows you to specify the latter by preceding it with the keywordtype
, thus:import M( type (+) )
The fixity of a type operator may be set using the usual fixity declarations but, as in Infix type constructors, classes, and type variables, the function and type constructor share a single fixity.
9.4.5. Liberalised type synonyms¶
Type synonyms are like macros at the type level, but Haskell 98 imposes
many rules on individual synonym declarations. With the
XLiberalTypeSynonyms
extension, GHC does validity checking on types
only after expanding type synonyms. That means that GHC can be very
much more liberal about type synonyms than Haskell 98.
You can write a
forall
(including overloading) in a type synonym, thus:type Discard a = forall b. Show b => a > b > (a, String) f :: Discard a f x y = (x, show y) g :: Discard Int > (Int,String)  A rank2 type g f = f 3 True
If you also use
XUnboxedTuples
, you can write an unboxed tuple in a type synonym:type Pr = (# Int, Int #) h :: Int > Pr h x = (# x, x #)
You can apply a type synonym to a forall type:
type Foo a = a > a > Bool f :: Foo (forall b. b>b)
After expanding the synonym,
f
has the legal (in GHC) type:f :: (forall b. b>b) > (forall b. b>b) > Bool
You can apply a type synonym to a partially applied type synonym:
type Generic i o = forall x. i x > o x type Id x = x foo :: Generic Id []
After expanding the synonym,
foo
has the legal (in GHC) type:foo :: forall x. x > [x]
GHC currently does kind checking before expanding synonyms (though even that could be changed)..
After expanding type synonyms, GHC does validity checking on types, looking for the following malformedness which isn’t detected simply by kind checking:
 Type constructor applied to a type involving foralls (if
XImpredicativeTypes
is off)  Partiallyapplied type synonym.
So, for example, this will be rejected:
type Pr = forall a. a
h :: [Pr]
h = ...
because GHC does not allow type constructors applied to forall types.
9.4.6. Existentially quantified data constructors¶
The idea of using existential quantification in data type declarations
was suggested by Perry, and implemented in Hope+ (Nigel Perry, The
Implementation of Practical Functional Programming Languages, PhD
Thesis, University of London, 1991). It was later formalised by Laufer
and Odersky (Polymorphic type inference and abstract data types,
TOPLAS, 16(5), pp. 14111430, 1994). It’s been in Lennart Augustsson’s
hbc
Haskell compiler for several years, and proved very useful.
Here’s the idea. Consider the declaration:
data Foo = forall a. MkFoo a (a > Bool)
 Nil
The data type Foo
has two constructors with types:
MkFoo :: forall a. a > (a > Bool) > Foo
Nil :: Foo
Notice that the type variable a
in the type of MkFoo
does not
appear in the data type itself, which is plain Foo
. For example, the
following expression is fine:
[MkFoo 3 even, MkFoo 'c' isUpper] :: [Foo]
Here, (MkFoo 3 even)
packages an integer with a function even
that maps an integer to Bool
; and MkFoo 'c'
isUpper
packages a character with a compatible function. These two
things are each of type Foo
and can be put in a list.
What can we do with a value of type Foo
? In particular, what
happens when we patternmatch on MkFoo
?
f (MkFoo val fn) = ???
Since all we know about val
and fn
is that they are compatible,
the only (useful) thing we can do with them is to apply fn
to
val
to get a boolean. For example:
f :: Foo > Bool
f (MkFoo val fn) = fn val
What this allows us to do is to package heterogeneous values together with a bunch of functions that manipulate them, and then treat that collection of packages in a uniform manner. You can express quite a bit of objectorientedlike programming this way.
9.4.6.1. Why existential?¶
What has this to do with existential quantification? Simply that
MkFoo
has the (nearly) isomorphic type
MkFoo :: (exists a . (a, a > Bool)) > Foo
But Haskell programmers can safely think of the ordinary universally quantified type given above, thereby avoiding adding a new existential quantification construct.
9.4.6.2. Existentials and type classes¶
An easy extension is to allow arbitrary contexts before the constructor. For example:
data Baz = forall a. Eq a => Baz1 a a
 forall b. Show b => Baz2 b (b > b)
The two constructors have the types you’d expect:
Baz1 :: forall a. Eq a => a > a > Baz
Baz2 :: forall b. Show b => b > (b > b) > Baz
But when pattern matching on Baz1
the matched values can be compared
for equality, and when pattern matching on Baz2
the first matched
value can be converted to a string (as well as applying the function to
it). So this program is legal:
f :: Baz > String
f (Baz1 p q)  p == q = "Yes"
 otherwise = "No"
f (Baz2 v fn) = show (fn v)
Operationally, in a dictionarypassing implementation, the constructors
Baz1
and Baz2
must store the dictionaries for Eq
and
Show
respectively, and extract it on pattern matching.
9.4.6.3. Record Constructors¶
GHC allows existentials to be used with records syntax as well. For example:
data Counter a = forall self. NewCounter
{ _this :: self
, _inc :: self > self
, _display :: self > IO ()
, tag :: a
}
Here tag
is a public field, with a welltyped selector function
tag :: Counter a > a
. The self
type is hidden from the outside;
any attempt to apply _this
, _inc
or _display
as functions
will raise a compiletime error. In other words, GHC defines a record
selector function only for fields whose type does not mention the
existentiallyquantified variables. (This example used an underscore in
the fields for which record selectors will not be defined, but that is
only programming style; GHC ignores them.)
To make use of these hidden fields, we need to create some helper functions:
inc :: Counter a > Counter a
inc (NewCounter x i d t) = NewCounter
{ _this = i x, _inc = i, _display = d, tag = t }
display :: Counter a > IO ()
display NewCounter{ _this = x, _display = d } = d x
Now we can define counters with different underlying implementations:
counterA :: Counter String
counterA = NewCounter
{ _this = 0, _inc = (1+), _display = print, tag = "A" }
counterB :: Counter String
counterB = NewCounter
{ _this = "", _inc = ('#':), _display = putStrLn, tag = "B" }
main = do
display (inc counterA)  prints "1"
display (inc (inc counterB))  prints "##"
Record update syntax is supported for existentials (and GADTs):
setTag :: Counter a > a > Counter a
setTag obj t = obj{ tag = t }
The rule for record update is this:
the types of the updated fields may mention only the universallyquantified type variables of the data constructor. For GADTs, the field may mention only types that appear as a simple typevariable argument in the constructor’s result type.
For example:
data T a b where { T1 { f1::a, f2::b, f3::(b,c) } :: T a b }  c is existential
upd1 t x = t { f1=x }  OK: upd1 :: T a b > a' > T a' b
upd2 t x = t { f3=x }  BAD (f3's type mentions c, which is
 existentially quantified)
data G a b where { G1 { g1::a, g2::c } :: G a [c] }
upd3 g x = g { g1=x }  OK: upd3 :: G a b > c > G c b
upd4 g x = g { g2=x }  BAD (f2's type mentions c, which is not a simple
 typevariable argument in G1's result type)
9.4.6.4. Restrictions¶
There are several restrictions on the ways in which existentiallyquantified constructors can be used.
When pattern matching, each pattern match introduces a new, distinct, type for each existential type variable. These types cannot be unified with any other type, nor can they escape from the scope of the pattern match. For example, these fragments are incorrect:
f1 (MkFoo a f) = a
Here, the type bound by
MkFoo
“escapes”, becausea
is the result off1
. One way to see why this is wrong is to ask what typef1
has:f1 :: Foo > a  Weird!
What is this “
a
” in the result type? Clearly we don’t mean this:f1 :: forall a. Foo > a  Wrong!
The original program is just plain wrong. Here’s another sort of error
f2 (Baz1 a b) (Baz1 p q) = a==q
It’s ok to say
a==b
orp==q
, buta==q
is wrong because it equates the two distinct types arising from the twoBaz1
constructors.You can’t patternmatch on an existentially quantified constructor in a
let
orwhere
group of bindings. So this is illegal:f3 x = a==b where { Baz1 a b = x }
Instead, use a
case
expression:f3 x = case x of Baz1 a b > a==b
In general, you can only patternmatch on an existentiallyquantified constructor in a
case
expression or in the patterns of a function definition. The reason for this restriction is really an implementation one. Typechecking binding groups is already a nightmare without existentials complicating the picture. Also an existential pattern binding at the top level of a module doesn’t make sense, because it’s not clear how to prevent the existentiallyquantified type “escaping”. So for now, there’s a simpletostate restriction. We’ll see how annoying it is.You can’t use existential quantification for
newtype
declarations. So this is illegal:newtype T = forall a. Ord a => MkT a
Reason: a value of type
T
must be represented as a pair of a dictionary forOrd t
and a value of typet
. That contradicts the idea thatnewtype
should have no concrete representation. You can get just the same efficiency and effect by usingdata
instead ofnewtype
. If there is no overloading involved, then there is more of a case for allowing an existentiallyquantifiednewtype
, because thedata
version does carry an implementation cost, but singlefield existentially quantified constructors aren’t much use. So the simple restriction (no existential stuff onnewtype
) stands, unless there are convincing reasons to change it.You can’t use
deriving
to define instances of a data type with existentially quantified data constructors. Reason: in most cases it would not make sense. For example:;data T = forall a. MkT [a] deriving( Eq )
To derive
Eq
in the standard way we would need to have equality between the single component of twoMkT
constructors:instance Eq T where (MkT a) == (MkT b) = ???
But
a
andb
have distinct types, and so can’t be compared. It’s just about possible to imagine examples in which the derived instance would make sense, but it seems altogether simpler simply to prohibit such declarations. Define your own instances!
9.4.7. Declaring data types with explicit constructor signatures¶
When the GADTSyntax
extension is enabled, GHC allows you to declare
an algebraic data type by giving the type signatures of constructors
explicitly. For example:
data Maybe a where
Nothing :: Maybe a
Just :: a > Maybe a
The form is called a “GADTstyle declaration” because Generalised Algebraic Data Types, described in Generalised Algebraic Data Types (GADTs), can only be declared using this form.
Notice that GADTstyle syntax generalises existential types (Existentially quantified data constructors). For example, these two declarations are equivalent:
data Foo = forall a. MkFoo a (a > Bool)
data Foo' where { MKFoo :: a > (a>Bool) > Foo' }
Any data type that can be declared in standard Haskell 98 syntax can also be declared using GADTstyle syntax. The choice is largely stylistic, but GADTstyle declarations differ in one important respect: they treat class constraints on the data constructors differently. Specifically, if the constructor is given a typeclass context, that context is made available by pattern matching. For example:
data Set a where
MkSet :: Eq a => [a] > Set a
makeSet :: Eq a => [a] > Set a
makeSet xs = MkSet (nub xs)
insert :: a > Set a > Set a
insert a (MkSet as)  a `elem` as = MkSet as
 otherwise = MkSet (a:as)
A use of MkSet
as a constructor (e.g. in the definition of
makeSet
) gives rise to a (Eq a)
constraint, as you would expect.
The new feature is that patternmatching on MkSet
(as in the
definition of insert
) makes available an (Eq a)
context. In
implementation terms, the MkSet
constructor has a hidden field that
stores the (Eq a)
dictionary that is passed to MkSet
; so when
patternmatching that dictionary becomes available for the righthand
side of the match. In the example, the equality dictionary is used to
satisfy the equality constraint generated by the call to elem
, so
that the type of insert
itself has no Eq
constraint.
For example, one possible application is to reify dictionaries:
data NumInst a where
MkNumInst :: Num a => NumInst a
intInst :: NumInst Int
intInst = MkNumInst
plus :: NumInst a > a > a > a
plus MkNumInst p q = p + q
Here, a value of type NumInst a
is equivalent to an explicit
(Num a)
dictionary.
All this applies to constructors declared using the syntax of
Existentials and type classes. For example, the NumInst
data type
above could equivalently be declared like this:
data NumInst a
= Num a => MkNumInst (NumInst a)
Notice that, unlike the situation when declaring an existential, there
is no forall
, because the Num
constrains the data type’s
universally quantified type variable a
. A constructor may have both
universal and existential type variables: for example, the following two
declarations are equivalent:
data T1 a
= forall b. (Num a, Eq b) => MkT1 a b
data T2 a where
MkT2 :: (Num a, Eq b) => a > b > T2 a
All this behaviour contrasts with Haskell 98’s peculiar treatment of contexts on a data type declaration (Section 4.2.1 of the Haskell 98 Report). In Haskell 98 the definition
data Eq a => Set' a = MkSet' [a]
gives MkSet'
the same type as MkSet
above. But instead of
making available an (Eq a)
constraint, patternmatching on
MkSet'
requires an (Eq a)
constraint! GHC faithfully
implements this behaviour, odd though it is. But for GADTstyle
declarations, GHC’s behaviour is much more useful, as well as much more
intuitive.
The rest of this section gives further details about GADTstyle data type declarations.
The result type of each data constructor must begin with the type constructor being defined. If the result type of all constructors has the form
T a1 ... an
, wherea1 ... an
are distinct type variables, then the data type is ordinary; otherwise is a generalised data type (Generalised Algebraic Data Types (GADTs)).As with other type signatures, you can give a single signature for several data constructors. In this example we give a single signature for
T1
andT2
:data T a where T1,T2 :: a > T a T3 :: T a
The type signature of each constructor is independent, and is implicitly universally quantified as usual. In particular, the type variable(s) in the “
data T a where
” header have no scope, and different constructors may have different universallyquantified type variables:data T a where  The 'a' has no scope T1,T2 :: b > T b  Means forall b. b > T b T3 :: T a  Means forall a. T a
A constructor signature may mention type class constraints, which can differ for different constructors. For example, this is fine:
data T a where T1 :: Eq b => b > b > T b T2 :: (Show c, Ix c) => c > [c] > T c
When pattern matching, these constraints are made available to discharge constraints in the body of the match. For example:
f :: T a > String f (T1 x y)  x==y = "yes"  otherwise = "no" f (T2 a b) = show a
Note that
f
is not overloaded; theEq
constraint arising from the use of==
is discharged by the pattern match onT1
and similarly theShow
constraint arising from the use ofshow
.Unlike a Haskell98style data type declaration, the type variable(s) in the “
data Set a where
” header have no scope. Indeed, one can write a kind signature instead:data Set :: * > * where ...
or even a mixture of the two:
data Bar a :: (* > *) > * where ...
The type variables (if given) may be explicitly kinded, so we could also write the header for
Foo
like this:data Bar a (b :: * > *) where ...
You can use strictness annotations, in the obvious places in the constructor type:
data Term a where Lit :: !Int > Term Int If :: Term Bool > !(Term a) > !(Term a) > Term a Pair :: Term a > Term b > Term (a,b)
You can use a
deriving
clause on a GADTstyle data type declaration. For example, these two declarations are equivalentdata Maybe1 a where { Nothing1 :: Maybe1 a ; Just1 :: a > Maybe1 a } deriving( Eq, Ord ) data Maybe2 a = Nothing2  Just2 a deriving( Eq, Ord )
The type signature may have quantified type variables that do not appear in the result type:
data Foo where MkFoo :: a > (a>Bool) > Foo Nil :: Foo
Here the type variable
a
does not appear in the result type of either constructor. Although it is universally quantified in the type of the constructor, such a type variable is often called “existential”. Indeed, the above declaration declares precisely the same type as thedata Foo
in Existentially quantified data constructors.The type may contain a class context too, of course:
data Showable where MkShowable :: Show a => a > Showable
You can use record syntax on a GADTstyle data type declaration:
data Person where Adult :: { name :: String, children :: [Person] } > Person Child :: Show a => { name :: !String, funny :: a } > Person
As usual, for every constructor that has a field
f
, the type of fieldf
must be the same (modulo alpha conversion). TheChild
constructor above shows that the signature may have a context, existentiallyquantified variables, and strictness annotations, just as in the nonrecord case. (NB: the “type” that follows the doublecolon is not really a type, because of the record syntax and strictness annotations. A “type” of this form can appear only in a constructor signature.)Record updates are allowed with GADTstyle declarations, only fields that have the following property: the type of the field mentions no existential type variables.
As in the case of existentials declared using the Haskell98like record syntax (Record Constructors), recordselector functions are generated only for those fields that have welltyped selectors. Here is the example of that section, in GADTstyle syntax:
data Counter a where NewCounter :: { _this :: self , _inc :: self > self , _display :: self > IO () , tag :: a } > Counter a
As before, only one selector function is generated here, that for
tag
. Nevertheless, you can still use all the field names in pattern matching and record construction.In a GADTstyle data type declaration there is no obvious way to specify that a data constructor should be infix, which makes a difference if you derive
Show
for the type. (Data constructors declared infix are displayed infix by the derivedshow
.) So GHC implements the following design: a data constructor declared in a GADTstyle data type declaration is displayed infix byShow
iff (a) it is an operator symbol, (b) it has two arguments, (c) it has a programmersupplied fixity declaration. For exampleinfix 6 (::) data T a where (::) :: Int > Bool > T Int
9.4.8. Generalised Algebraic Data Types (GADTs)¶
Generalised Algebraic Data Types generalise ordinary algebraic data types by allowing constructors to have richer return types. Here is an example:
data Term a where
Lit :: Int > Term Int
Succ :: Term Int > Term Int
IsZero :: Term Int > Term Bool
If :: Term Bool > Term a > Term a > Term a
Pair :: Term a > Term b > Term (a,b)
Notice that the return type of the constructors is not always
Term a
, as is the case with ordinary data types. This generality
allows us to write a welltyped eval
function for these Terms
:
eval :: Term a > a
eval (Lit i) = i
eval (Succ t) = 1 + eval t
eval (IsZero t) = eval t == 0
eval (If b e1 e2) = if eval b then eval e1 else eval e2
eval (Pair e1 e2) = (eval e1, eval e2)
The key point about GADTs is that pattern matching causes type refinement. For example, in the right hand side of the equation
eval :: Term a > a
eval (Lit i) = ...
the type a
is refined to Int
. That’s the whole point! A precise
specification of the type rules is beyond what this user manual aspires
to, but the design closely follows that described in the paper Simple
unificationbased type inference for
GADTs, (ICFP
2006). The general principle is this: type refinement is only carried
out based on usersupplied type annotations. So if no type signature is
supplied for eval
, no type refinement happens, and lots of obscure
error messages will occur. However, the refinement is quite general. For
example, if we had:
eval :: Term a > a > a
eval (Lit i) j = i+j
the pattern match causes the type a
to be refined to Int
(because of the type of the constructor Lit
), and that refinement
also applies to the type of j
, and the result type of the case
expression. Hence the addition i+j
is legal.
These and many other examples are given in papers by Hongwei Xi, and Tim Sheard. There is a longer introduction on the wiki, and Ralf Hinze’s Fun with phantom types also has a number of examples. Note that papers may use different notation to that implemented in GHC.
The rest of this section outlines the extensions to GHC that support
GADTs. The extension is enabled with XGADTs
. The XGADTs
flag
also sets XGADTSyntax
and XMonoLocalBinds
.
A GADT can only be declared using GADTstyle syntax (Declaring data types with explicit constructor signatures); the old Haskell 98 syntax for data declarations always declares an ordinary data type. The result type of each constructor must begin with the type constructor being defined, but for a GADT the arguments to the type constructor can be arbitrary monotypes. For example, in the
Term
data type above, the type of each constructor must end withTerm ty
, but thety
need not be a type variable (e.g. theLit
constructor).It is permitted to declare an ordinary algebraic data type using GADTstyle syntax. What makes a GADT into a GADT is not the syntax, but rather the presence of data constructors whose result type is not just
T a b
.You cannot use a
deriving
clause for a GADT; only for an ordinary data type.As mentioned in Declaring data types with explicit constructor signatures, record syntax is supported. For example:
data Term a where Lit :: { val :: Int } > Term Int Succ :: { num :: Term Int } > Term Int Pred :: { num :: Term Int } > Term Int IsZero :: { arg :: Term Int } > Term Bool Pair :: { arg1 :: Term a , arg2 :: Term b } > Term (a,b) If :: { cnd :: Term Bool , tru :: Term a , fls :: Term a } > Term a
However, for GADTs there is the following additional constraint: every constructor that has a field
f
must have the same result type (modulo alpha conversion) Hence, in the above example, we cannot merge thenum
andarg
fields above into a single name. Although their field types are bothTerm Int
, their selector functions actually have different types:num :: Term Int > Term Int arg :: Term Bool > Term Int
When patternmatching against data constructors drawn from a GADT, for example in a
case
expression, the following rules apply: The type of the scrutinee must be rigid.
 The type of the entire
case
expression must be rigid.  The type of any free variable mentioned in any of the
case
alternatives must be rigid.
A type is “rigid” if it is completely known to the compiler at its binding site. The easiest way to ensure that a variable a rigid type is to give it a type signature. For more precise details see Simple unificationbased type inference for GADTs. The criteria implemented by GHC are given in the Appendix.
9.5. Extensions to the record system¶
9.5.1. Traditional record syntax¶
Traditional record syntax, such as C {f = x}
, is enabled by default.
To disable it, you can use the XNoTraditionalRecordSyntax
flag.
9.5.2. Record field disambiguation¶
In record construction and record pattern matching it is entirely unambiguous which field is referred to, even if there are two different data types in scope with a common field name. For example:
module M where
data S = MkS { x :: Int, y :: Bool }
module Foo where
import M
data T = MkT { x :: Int }
ok1 (MkS { x = n }) = n+1  Unambiguous
ok2 n = MkT { x = n+1 }  Unambiguous
bad1 k = k { x = 3 }  Ambiguous
bad2 k = x k  Ambiguous
Even though there are two x
‘s in scope, it is clear that the x
in the pattern in the definition of ok1
can only mean the field
x
from type S
. Similarly for the function ok2
. However, in
the record update in bad1
and the record selection in bad2
it is
not clear which of the two types is intended.
Haskell 98 regards all four as ambiguous, but with the
XDisambiguateRecordFields
flag, GHC will accept the former two. The
rules are precisely the same as those for instance declarations in
Haskell 98, where the method names on the lefthand side of the method
bindings in an instance declaration refer unambiguously to the method of
that class (provided they are in scope at all), even if there are other
variables in scope with the same name. This reduces the clutter of
qualified names when you import two records from different modules that
use the same field name.
Some details:
Field disambiguation can be combined with punning (see Record puns). For example:
module Foo where import M x=True ok3 (MkS { x }) = x+1  Uses both disambiguation and punning
With
XDisambiguateRecordFields
you can use unqualified field names even if the corresponding selector is only in scope qualified For example, assuming the same moduleM
as in our earlier example, this is legal:module Foo where import qualified M  Note qualified ok4 (M.MkS { x = n }) = n+1  Unambiguous
Since the constructor
MkS
is only in scope qualified, you must name itM.MkS
, but the fieldx
does not need to be qualified even thoughM.x
is in scope butx
is not (In effect, it is qualified by the constructor).
9.5.3. Duplicate record fields¶
Going beyond XDisambiguateRecordFields
(see Record field disambiguation),
the XDuplicateRecordFields
extension allows multiple datatypes to be
declared using the same field names in a single module. For example, it allows
this:
module M where
data S = MkS { x :: Int }
data T = MkT { x :: Bool }
Uses of fields that are always unambiguous because they mention the constructor,
including construction and patternmatching, may freely use duplicated field
names. For example, the following are permitted (just as with
XDisambiguateRecordFields
):
s = MkS { x = 3 }
f (MkT { x = b }) = b
Field names used as selector functions or in record updates must be unambiguous, either because there is only one such field in scope, or because a type signature is supplied, as described in the following sections.
9.5.3.1. Selector functions¶
Fields may be used as selector functions only if they are unambiguous, so this
is still not allowed if both S(x)
and T(x)
are in scope:
bad r = x r
An ambiguous selector may be disambiguated by the type being “pushed down” to the occurrence of the selector (see Type inference for more details on what “pushed down” means). For example, the following are permitted:
ok1 = x :: S > Int
ok2 :: S > Int
ok2 = x
ok3 = k x  assuming we already have k :: (S > Int) > _
In addition, the datatype that is meant may be given as a type signature on the argument to the selector:
ok4 s = x (s :: S)
However, we do not infer the type of the argument to determine the datatype, or have any way of deferring the choice to the constraint solver. Thus the following is ambiguous:
bad :: S > Int
bad s = x s
Even though a field label is duplicated in its defining module, it may be
possible to use the selector unambiguously elsewhere. For example, another
module could import S(x)
but not T(x)
, and then use x
unambiguously.
9.5.3.2. Record updates¶
In a record update such as e { x = 1 }
, if there are multiple x
fields
in scope, then the type of the context must fix which record datatype is
intended, or a type annotation must be supplied. Consider the following
definitions:
data S = MkS { foo :: Int }
data T = MkT { foo :: Int, bar :: Int }
data U = MkU { bar :: Int, baz :: Int }
Without XDuplicateRecordFields
, an update mentioning foo
will always be
ambiguous if all these definitions were in scope. When the extension is enabled,
there are several options for disambiguating updates:
Check for types that have all the fields being updated. For example:
f x = x { foo = 3, bar = 2 }
Here
f
must be updatingT
because neitherS
norU
have both fields.Use the type being pushed in to the record update, as in the following:
g1 :: T > T g1 x = x { foo = 3 } g2 x = x { foo = 3 } :: T g3 = k (x { foo = 3 })  assuming we already have k :: T > _
Use an explicit type signature on the record expression, as in:
h x = (x :: T) { foo = 3 }
The type of the expression being updated will not be inferred, and no constraintsolving will be performed, so the following will be rejected as ambiguous:
let x :: T
x = blah
in x { foo = 3 }
\x > [x { foo = 3 }, blah :: T ]
\ (x :: T) > x { foo = 3 }
9.5.3.3. Import and export of record fields¶
When XDuplicateRecordFields
is enabled, an ambiguous field must be exported
as part of its datatype, rather than at the top level. For example, the
following is legal:
module M (S(x), T(..)) where
data S = MkS { x :: Int }
data T = MkT { x :: Bool }
However, this would not be permitted, because x
is ambiguous:
module M (x) where ...
Similar restrictions apply on import.
9.5.4. Record puns¶
Record puns are enabled by the flag XNamedFieldPuns
.
When using records, it is common to write a pattern that binds a variable with the same name as a record field, such as:
data C = C {a :: Int}
f (C {a = a}) = a
Record punning permits the variable name to be elided, so one can simply write
f (C {a}) = a
to mean the same pattern as above. That is, in a record pattern, the
pattern a
expands into the pattern a = a
for the same name
a
.
Note that:
Record punning can also be used in an expression, writing, for example,
let a = 1 in C {a}
instead of
let a = 1 in C {a = a}
The expansion is purely syntactic, so the expanded righthand side expression refers to the nearest enclosing variable that is spelled the same as the field name.
Puns and other patterns can be mixed in the same record:
data C = C {a :: Int, b :: Int} f (C {a, b = 4}) = a
Puns can be used wherever record patterns occur (e.g. in
let
bindings or at the toplevel).A pun on a qualified field name is expanded by stripping off the module qualifier. For example:
f (C {M.a}) = a
means
f (M.C {M.a = a}) = a
(This is useful if the field selector
a
for constructorM.C
is only in scope in qualified form.)
9.5.5. Record wildcards¶
Record wildcards are enabled by the flag XRecordWildCards
. This
flag implies XDisambiguateRecordFields
.
For records with many fields, it can be tiresome to write out each field individually in a record pattern, as in
data C = C {a :: Int, b :: Int, c :: Int, d :: Int}
f (C {a = 1, b = b, c = c, d = d}) = b + c + d
Record wildcard syntax permits a “..
” in a record pattern, where
each elided field f
is replaced by the pattern f = f
. For
example, the above pattern can be written as
f (C {a = 1, ..}) = b + c + d
More details:
Record wildcards in patterns can be mixed with other patterns, including puns (Record puns); for example, in a pattern
(C {a = 1, b, ..})
. Additionally, record wildcards can be used wherever record patterns occur, including inlet
bindings and at the toplevel. For example, the toplevel bindingC {a = 1, ..} = e
defines
b
,c
, andd
.Record wildcards can also be used in an expression, when constructing a record. For example,
let {a = 1; b = 2; c = 3; d = 4} in C {..}
in place of
let {a = 1; b = 2; c = 3; d = 4} in C {a=a, b=b, c=c, d=d}
The expansion is purely syntactic, so the record wildcard expression refers to the nearest enclosing variables that are spelled the same as the omitted field names.
Record wildcards may not be used in record updates. For example this is illegal:
f r = r { x = 3, .. }
For both pattern and expression wildcards, the “
..
” expands to the missing inscope record fields. Specifically the expansion of “C {..}
” includesf
if and only if:f
is a record field of constructorC
. The record field
f
is in scope somehow (either qualified or unqualified).  In the case of expressions (but not patterns), the variable
f
is in scope unqualified, apart from the binding of the record selector itself.
These rules restrict record wildcards to the situations in which the user could have written the expanded version. For example
module M where data R = R { a,b,c :: Int } module X where import M( R(a,c) ) f b = R { .. }
The
R{..}
expands toR{M.a=a}
, omittingb
since the record field is not in scope, and omittingc
since the variablec
is not in scope (apart from the binding of the record selectorc
, of course).Record wildcards cannot be used (a) in a record update construct, and (b) for data constructors that are not declared with record fields. For example:
f x = x { v=True, .. }  Illegal (a) data T = MkT Int Bool g = MkT { .. }  Illegal (b) h (MkT { .. }) = True  Illegal (b)
9.6. Extensions to the “deriving” mechanism¶
9.6.1. Inferred context for deriving clauses¶
The Haskell Report is vague about exactly when a deriving
clause is
legal. For example:
data T0 f a = MkT0 a deriving( Eq )
data T1 f a = MkT1 (f a) deriving( Eq )
data T2 f a = MkT2 (f (f a)) deriving( Eq )
The natural generated Eq
code would result in these instance
declarations:
instance Eq a => Eq (T0 f a) where ...
instance Eq (f a) => Eq (T1 f a) where ...
instance Eq (f (f a)) => Eq (T2 f a) where ...
The first of these is obviously fine. The second is still fine, although less obviously. The third is not Haskell 98, and risks losing termination of instances.
GHC takes a conservative position: it accepts the first two, but not the third. The rule is this: each constraint in the inferred instance context must consist only of type variables, with no repetitions.
This rule is applied regardless of flags. If you want a more exotic context, you can write it yourself, using the standalone deriving mechanism.
9.6.2. Standalone deriving declarations¶
GHC allows standalone deriving
declarations, enabled by
XStandaloneDeriving
:
data Foo a = Bar a  Baz String
deriving instance Eq a => Eq (Foo a)
The syntax is identical to that of an ordinary instance declaration
apart from (a) the keyword deriving
, and (b) the absence of the
where
part.
However, standalone deriving differs from a deriving
clause in a
number of important ways:
The standalone deriving declaration does not need to be in the same module as the data type declaration. (But be aware of the dangers of orphan instances (Orphan modules and instance declarations).
You must supply an explicit context (in the example the context is
(Eq a)
), exactly as you would in an ordinary instance declaration. (In contrast, in aderiving
clause attached to a data type declaration, the context is inferred.)Unlike a
deriving
declaration attached to adata
declaration, the instance can be more specific than the data type (assuming you also useXFlexibleInstances
, Relaxed rules for instance contexts). Consider for exampledata Foo a = Bar a  Baz String deriving instance Eq a => Eq (Foo [a]) deriving instance Eq a => Eq (Foo (Maybe a))
This will generate a derived instance for
(Foo [a])
and(Foo (Maybe a))
, but other types such as(Foo (Int,Bool))
will not be an instance ofEq
.Unlike a
deriving
declaration attached to adata
declaration, GHC does not restrict the form of the data type. Instead, GHC simply generates the appropriate boilerplate code for the specified class, and typechecks it. If there is a type error, it is your problem. (GHC will show you the offending code if it has a type error.)The merit of this is that you can derive instances for GADTs and other exotic data types, providing only that the boilerplate code does indeed typecheck. For example:
data T a where T1 :: T Int T2 :: T Bool deriving instance Show (T a)
In this example, you cannot say
... deriving( Show )
on the data type declaration forT
, becauseT
is a GADT, but you can generate the instance declaration using standalone deriving.The downside is that, if the boilerplate code fails to typecheck, you will get an error message about that code, which you did not write. Whereas, with a
deriving
clause the sideconditions are necessarily more conservative, but any error message may be more comprehensible.
In other ways, however, a standalone deriving obeys the same rules as ordinary deriving:
A
deriving instance
declaration must obey the same rules concerning form and termination as ordinary instance declarations, controlled by the same flags; see Instance declarations.The standalone syntax is generalised for newtypes in exactly the same way that ordinary
deriving
clauses are generalised (Generalised derived instances for newtypes). For example:newtype Foo a = MkFoo (State Int a) deriving instance MonadState Int Foo
GHC always treats the last parameter of the instance (
Foo
in this example) as the type whose instance is being derived.
9.6.3. Deriving instances of extra classes (Data
, etc.)¶
Haskell 98 allows the programmer to add “deriving( Eq, Ord )
” to a
data type declaration, to generate a standard instance declaration for
classes specified in the deriving
clause. In Haskell 98, the only
classes that may appear in the deriving
clause are the standard
classes Eq
, Ord
, Enum
, Ix
, Bounded
, Read
, and
Show
.
GHC extends this list with several more classes that may be automatically derived:
 With
XDeriveGeneric
, you can derive instances of the classesGeneric
andGeneric1
, defined inGHC.Generics
. You can use these to define generic functions, as described in Generic programming.  With
XDeriveFunctor
, you can derive instances of the classFunctor
, defined inGHC.Base
. See Deriving Functor instances.  With
XDeriveDataTypeable
, you can derive instances of the classData
, defined inData.Data
. See Deriving Typeable instances for derivingTypeable
.  With
XDeriveFoldable
, you can derive instances of the classFoldable
, defined inData.Foldable
. See Deriving Foldable instances.  With
XDeriveTraversable
, you can derive instances of the classTraversable
, defined inData.Traversable
. Since theTraversable
instance dictates the instances ofFunctor
andFoldable
, you’ll probably want to derive them too, soXDeriveTraversable
impliesXDeriveFunctor
andXDeriveFoldable
. See Deriving Traversable instances.  With
XDeriveLift
, you can derive instances of the classLift
, defined in theLanguage.Haskell.TH.Syntax
module of thetemplatehaskell
package. See Deriving Lift instances.
You can also use a standalone deriving declaration instead (see Standalone deriving declarations).
In each case the appropriate class must be in scope before it can be
mentioned in the deriving
clause.
9.6.4. Deriving Functor
instances¶
With XDeriveFunctor
, one can derive Functor
instances for data types
of kind * > *
. For example, this declaration:
data Example a = Ex a Char (Example a) (Example Char)
deriving Functor
would generate the following instance:
instance Functor Example where
fmap f (Ex a1 a2 a3 a4) = Ex (f a1) a2 (fmap f a3) a4
The basic algorithm for XDeriveFunctor
walks the arguments of each
constructor of a data type, applying a mapping function depending on the type
of each argument. If a plain type variable is found that is syntactically
equivalent to the last type parameter of the data type (a
in the above
example), then we apply the function f
directly to it. If a type is
encountered that is not syntactically equivalent to the last type parameter
but does mention the last type parameter somewhere in it, then a recursive
call to fmap
is made. If a type is found which doesn’t mention the last
type paramter at all, then it is left alone.
The second of those cases, in which a type is unequal to the type parameter but does contain the type parameter, can be surprisingly tricky. For example, the following example compiles:
newtype Right a = Right (Either Int a) deriving Functor
Modifying the code slightly, however, produces code which will not compile:
newtype Wrong a = Wrong (Either a Int) deriving Functor
The difference involves the placement of the last type parameter, a
. In the
Right
case, a
occurs within the type Either Int a
, and moreover, it
appears as the last type argument of Either
. In the Wrong
case,
however, a
is not the last type argument to Either
; rather, Int
is.
This distinction is important because of the way XDeriveFunctor
works. The
derived Functor Right
instance would be:
instance Functor Right where
fmap f (Right a) = Right (fmap f a)
Given a value of type Right a
, GHC must produce a value of type
Right b
. Since the argument to the Right
constructor has type
Either Int a
, the code recursively calls fmap
on it to produce a value
of type Either Int b
, which is used in turn to construct a final value of
type Right b
.
The generated code for the Functor Wrong
instance would look exactly the
same, except with Wrong
replacing every occurrence of Right
. The
problem is now that fmap
is being applied recursively to a value of type
Either a Int
. This cannot possibly produce a value of type
Either b Int
, as fmap
can only change the last type parameter! This
causes the generated code to be illtyped.
As a general rule, if a data type has a derived Functor
instance and its
last type parameter occurs on the righthand side of the data declaration, then
either it must (1) occur bare (e.g., newtype Id a = a
), or (2) occur as the
last argument of a type constructor (as in Right
above).
There are two exceptions to this rule:
Tuple types. When a nonunit tuple is used on the righthand side of a data declaration,
XDeriveFunctor
treats it as a product of distinct types. In other words, the following code:newtype Triple a = Triple (a, Int, [a]) deriving Functor
Would result in a generated
Functor
instance like so:instance Functor Triple where fmap f (Triple a) = Triple (case a of (a1, a2, a3) > (f a1, a2, fmap f a3))
That is,
XDeriveFunctor
patternmatches its way into tuples and maps over each type that constitutes the tuple. The generated code is reminiscient of what would be generated fromdata Triple a = Triple a Int [a]
, except with extra machinery to handle the tuple.Function types. The last type parameter can appear anywhere in a function type as long as it occurs in a covariant position. To illustrate what this means, consider the following three examples:
newtype CovFun1 a = CovFun1 (Int > a) deriving Functor newtype CovFun2 a = CovFun2 ((a > Int) > a) deriving Functor newtype CovFun3 a = CovFun3 (((Int > a) > Int) > a) deriving Functor
All three of these examples would compile without issue. On the other hand:
newtype ContraFun1 a = ContraFun1 (a > Int) deriving Functor newtype ContraFun2 a = ContraFun2 ((Int > a) > Int) deriving Functor newtype ContraFun3 a = ContraFun3 (((a > Int) > a) > Int) deriving Functor
While these examples look similar, none of them would successfully compile. This is because all occurrences of the last type parameter
a
occur in contravariant positions, not covariant ones.Intuitively, a covariant type is produced, and a contravariant type is consumed. Most types in Haskell are covariant, but the function type is special in that the lefthand side of a function arrow reverses variance. If a function type
a > b
appears in a covariant position (e.g.,CovFun1
above), thena
is in a contravariant position andb
is in a covariant position. Similarly, ifa > b
appears in a contravariant position (e.g.,CovFun2
above), thena
is ina
covariant position andb
is in a contravariant position.To see why a data type with a contravariant occurrence of its last type parameter cannot have a derived
Functor
instance, let’s suppose that aFunctor ContraFun1
instance exists. The implementation would look something like this:instance Functor ContraFun1 where fmap f (ContraFun g) = ContraFun (\x > _)
We have
f :: a > b
,g :: a > Int
, andx :: b
. Using these, we must somehow fill in the hole (denoted with an underscore) with a value of typeInt
. What are our options?We could try applying
g
tox
. This won’t work though, asg
expects an argument of typea
, andx :: b
. Even worse, we can’t turnx
into something of typea
, sincef
also needs an argument of typea
! In short, there’s no good way to make this work.On the other hand, a derived
Functor
instances for theCovFun
s are within the realm of possibility:instance Functor CovFun1 where fmap f (CovFun1 g) = CovFun1 (\x > f (g x)) instance Functor CovFun2 where fmap f (CovFun2 g) = CovFun2 (\h > f (g (\x > h (f x)))) instance Functor CovFun3 where fmap f (CovFun3 g) = CovFun3 (\h > f (g (\k > h (\x > f (k x)))))
There are some other scenarios in which a derived Functor
instance will
fail to compile:
A data type has no type parameters (e.g.,
data Nothing = Nothing
).A data type’s last type variable is used in a
XDatatypeContexts
constraint (e.g.,data Ord a => O a = O a
).A data type’s last type variable is used in an
XExistentialQuantification
constraint, or is refined in a GADT. For example,data T a b where T4 :: Ord b => b > T a b T5 :: b > T b b T6 :: T a (b,b) deriving instance Functor (T a)
would not compile successfully due to the way in which
b
is constrained.
9.6.5. Deriving Foldable
instances¶
With XDeriveFoldable
, one can derive Foldable
instances for data types
of kind * > *
. For example, this declaration:
data Example a = Ex a Char (Example a) (Example Char)
deriving Foldable
would generate the following instance:
instance Foldable Example where
foldr f z (Ex a1 a2 a3 a4) = f a1 (foldr f z a3)
foldMap f (Ex a1 a2 a3 a4) = mappend (f a1) (foldMap f a3)
The algorithm for XDeriveFoldable
is adapted from the XDeriveFunctor
algorithm, but it generates definitions for foldMap
and foldr
instead
of fmap
. Here are the differences between the generated code in each
extension:
 When a bare type variable
a
is encountered,XDeriveFunctor
would generatef a
for anfmap
definition.XDeriveFoldable
would generatef a z
forfoldr
, andf a
forfoldMap
.  When a type that is not syntactically equivalent to
a
, but which does containa
, is encountered,XDeriveFunctor
recursively callsfmap
on it. Similarly,XDeriveFoldable
would recursively callfoldr
andfoldMap
.  When a type that does not mention
a
is encountered,XDeriveFunctor
leaves it alone. On the other hand,XDeriveFoldable
would generatez
(the state value) forfoldr
andmempty
forfoldMap
. XDeriveFunctor
puts everything back together again at the end by invoking the constructor.XDeriveFoldable
, however, builds up a value of some type. Forfoldr
, this is accomplished by chaining applications off
and recursivefoldr
calls on the state valuez
. ForfoldMap
, this happens by combining all values withmappend
.
There are some other differences regarding what data types can have derived
Foldable
instances:
Data types containing function types on the righthand side cannot have derived
Foldable
instances.Foldable
instances can be derived for data types in which the last type parameter is existentially constrained or refined in a GADT. For example, this data type:data E a where E1 :: (a ~ Int) => a > E a E2 :: Int > E Int E3 :: (a ~ Int) => a > E Int E4 :: (a ~ Int) => Int > E a deriving instance Foldable E
would have the following generated
Foldable
instance:instance Foldable E where foldr f z (E1 e) = f e z foldr f z (E2 e) = z foldr f z (E3 e) = z foldr f z (E4 e) = z foldMap f (E1 e) = f e foldMap f (E2 e) = mempty foldMap f (E3 e) = mempty foldMap f (E4 e) = mempty
Notice how every constructor of
E
utilizes some sort of existential quantification, but only the argument ofE1
is actually “folded over”. This is because we make a deliberate choice to only fold over universally polymorphic types that are syntactically equivalent to the last type parameter. In particular:
 We don’t fold over the arguments of
E1
orE4
beacause even though(a ~ Int)
,Int
is not syntactically equivalent toa
. We don’t fold over the argument of
E3
becausea
is not universally polymorphic. Thea
inE3
is (implicitly) existentially quantified, so it is not the same as the last type parameter ofE
.
9.6.6. Deriving Traversable
instances¶
With XDeriveTraversable
, one can derive Traversable
instances for data
types of kind * > *
. For example, this declaration:
data Example a = Ex a Char (Example a) (Example Char)
deriving (Functor, Foldable, Traversable)
would generate the following Traversable
instance:
instance Traversable Example where
traverse f (Ex a1 a2 a3 a4)
= fmap Ex (f a1) <*> traverse f a3
The algorithm for XDeriveTraversable
is adapted from the
XDeriveFunctor
algorithm, but it generates a definition for traverse
instead of fmap
. Here are the differences between the generated code in
each extension:
 When a bare type variable
a
is encountered, bothXDeriveFunctor
andXDeriveTraversable
would generatef a
for anfmap
andtraverse
definition, respectively.  When a type that is not syntactically equivalent to
a
, but which does containa
, is encountered,XDeriveFunctor
recursively callsfmap
on it. Similarly,XDeriveTraversable
would recursively calltraverse
.  When a type that does not mention
a
is encountered,XDeriveFunctor
leaves it alone. On the other hand,XDeriveTravserable
would callpure
on the value of that type. XDeriveFunctor
puts everything back together again at the end by invoking the constructor.XDeriveTraversable
does something similar, but it works in anApplicative
context by chaining everything together with(<*>)
.
Unlike XDeriveFunctor
, XDeriveTraversable
cannot be used on data
types containing a function type on the righthand side.
For a full specification of the algorithms used in XDeriveFunctor
,
XDeriveFoldable
, and XDeriveTraversable
, see
this wiki page.
9.6.7. Deriving Typeable
instances¶
The class Typeable
is very special:
Typeable
is kindpolymorphic (see Kind polymorphism).GHC has a custom solver for discharging constraints that involve class
Typeable
, and handwritten instances are forbidden. This ensures that the programmer cannot subvert the type system by writing bogus instances.Derived instances of
Typeable
are ignored, and may be reported as an error in a later version of the compiler.The rules for solving `Typeable` constraints are as follows:
A concrete type constructor applied to some types.
instance (Typeable t1, .., Typeable t_n) => Typeable (T t1 .. t_n)
This rule works for any concrete type constructor, including type constructors with polymorphic kinds. The only restriction is that if the type constructor has a polymorphic kind, then it has to be applied to all of its kinds parameters, and these kinds need to be concrete (i.e., they cannot mention kind variables).
A type variable applied to some types. instance (Typeable f, Typeable t1, .., Typeable t_n) => Typeable (f t1 .. t_n)
A concrete type literal. instance Typeable 0  Type natural literals instance Typeable "Hello"  Typelevel symbols
9.6.8. Deriving Lift
instances¶
The class Lift
, unlike other derivable classes, lives in
templatehaskell
instead of base
. Having a data type be an instance of
Lift
permits its values to be promoted to Template Haskell expressions (of
type ExpQ
), which can then be spliced into Haskell source code.
Here is an example of how one can derive Lift
:
{# LANGUAGE DeriveLift #}
module Bar where
import Language.Haskell.TH.Syntax
data Foo a = Foo a  a :^: a deriving Lift
{
instance (Lift a) => Lift (Foo a) where
lift (Foo a)
= appE
(conE
(mkNameG_d "packagename" "Bar" "Foo"))
(lift a)
lift (u :^: v)
= infixApp
(lift u)
(conE
(mkNameG_d "packagename" "Bar" ":^:"))
(lift v)
}

{# LANGUAGE TemplateHaskell #}
module Baz where
import Bar
import Language.Haskell.TH.Lift
foo :: Foo String
foo = $(lift $ Foo "foo")
fooExp :: Lift a => Foo a > Q Exp
fooExp f = [ f ]
XDeriveLift
also works for certain unboxed types (Addr#
, Char#
,
Double#
, Float#
, Int#
, and Word#
):
{# LANGUAGE DeriveLift, MagicHash #}
module Unboxed where
import GHC.Exts
import Language.Haskell.TH.Syntax
data IntHash = IntHash Int# deriving Lift
{
instance Lift IntHash where
lift (IntHash i)
= appE
(conE
(mkNameG_d "packagename" "Unboxed" "IntHash"))
(litE
(intPrimL (toInteger (I# i))))
}
9.6.9. Generalised derived instances for newtypes¶
When you define an abstract type using newtype
, you may want the new
type to inherit some instances from its representation. In Haskell 98,
you can inherit instances of Eq
, Ord
, Enum
and Bounded
by deriving them, but for any other classes you have to write an
explicit instance declaration. For example, if you define
newtype Dollars = Dollars Int
and you want to use arithmetic on Dollars
, you have to explicitly
define an instance of Num
:
instance Num Dollars where
Dollars a + Dollars b = Dollars (a+b)
...
All the instance does is apply and remove the newtype
constructor.
It is particularly galling that, since the constructor doesn’t appear at
runtime, this instance declaration defines a dictionary which is
wholly equivalent to the Int
dictionary, only slower!
9.6.9.1. Generalising the deriving clause¶
GHC now permits such instances to be derived instead, using the flag
XGeneralizedNewtypeDeriving
, so one can write
newtype Dollars = Dollars Int deriving (Eq,Show,Num)
and the implementation uses the same Num
dictionary for
Dollars
as for Int
. Notionally, the compiler derives an instance
declaration of the form
instance Num Int => Num Dollars
which just adds or removes the newtype
constructor according to the
type.
We can also derive instances of constructor classes in a similar way. For example, suppose we have implemented state and failure monad transformers, such that
instance Monad m => Monad (State s m)
instance Monad m => Monad (Failure m)
In Haskell 98, we can define a parsing monad by
type Parser tok m a = State [tok] (Failure m) a
which is automatically a monad thanks to the instance declarations
above. With the extension, we can make the parser type abstract, without
needing to write an instance of class Monad
, via
newtype Parser tok m a = Parser (State [tok] (Failure m) a)
deriving Monad
In this case the derived instance declaration is of the form
instance Monad (State [tok] (Failure m)) => Monad (Parser tok m)
Notice that, since Monad
is a constructor class, the instance is a
partial application of the new type, not the entire left hand side. We
can imagine that the type declaration is “etaconverted” to generate the
context of the instance declaration.
We can even derive instances of multiparameter classes, provided the
newtype is the last class parameter. In this case, a “partial
application” of the class appears in the deriving
clause. For
example, given the class
class StateMonad s m  m > s where ...
instance Monad m => StateMonad s (State s m) where ...
then we can derive an instance of StateMonad
for Parser
by
newtype Parser tok m a = Parser (State [tok] (Failure m) a)
deriving (Monad, StateMonad [tok])
The derived instance is obtained by completing the application of the class to the new type:
instance StateMonad [tok] (State [tok] (Failure m)) =>
StateMonad [tok] (Parser tok m)
As a result of this extension, all derived instances in newtype
declarations are treated uniformly (and implemented just by reusing the
dictionary for the representation type), except Show
and Read
,
which really behave differently for the newtype and its representation.
9.6.9.2. A more precise specification¶
A derived instance is derived only for declarations of these forms (after expansion of any type synonyms)
newtype T v1..vn = MkT (t vk+1..vn) deriving (C t1..tj)
newtype instance T s1..sk vk+1..vn = MkT (t vk+1..vn) deriving (C t1..tj)
where
v1..vn
are type variables, andt
,s1..sk
,t1..tj
are types. The
(C t1..tj)
is a partial applications of the classC
, where the arity ofC
is exactlyj+1
. That is,C
lacks exactly one type argument. k
is chosen so thatC t1..tj (T v1...vk)
is wellkinded. (Or, in the case of adata instance
, so thatC t1..tj (T s1..sk)
is well kinded.) The type
t
is an arbitrary type.  The type variables
vk+1...vn
do not occur in the typest
,s1..sk
, ort1..tj
. C
is notRead
,Show
,Typeable
, orData
. These classes should not “look through” the type or its constructor. You can still derive these classes for a newtype, but it happens in the usual way, not via this new mechanism. It is safe to coerce each of the methods of
C
. That is, the missing last argument toC
is not used at a nominal role in any of theC
‘s methods. (See Roles.)
Then the derived instance declaration is of the form
instance C t1..tj t => C t1..tj (T v1...vk)
As an example which does not work, consider
newtype NonMonad m s = NonMonad (State s m s) deriving Monad
Here we cannot derive the instance
instance Monad (State s m) => Monad (NonMonad m)
because the type variable s
occurs in State s m
, and so cannot
be “etaconverted” away. It is a good thing that this deriving
clause is rejected, because NonMonad m
is not, in fact, a monad —
for the same reason. Try defining >>=
with the correct type: you
won’t be able to.
Notice also that the order of class parameters becomes important,
since we can only derive instances for the last one. If the
StateMonad
class above were instead defined as
class StateMonad m s  m > s where ...
then we would not have been able to derive an instance for the
Parser
type above. We hypothesise that multiparameter classes
usually have one “main” parameter for which deriving new instances is
most interesting.
Lastly, all of this applies only for classes other than Read
,
Show
, Typeable
, and Data
, for which the builtin derivation
applies (section 4.3.3. of the Haskell Report). (For the standard
classes Eq
, Ord
, Ix
, and Bounded
it is immaterial
whether the standard method is used or the one described here.)
9.6.10. Deriving any other class¶
With XDeriveAnyClass
you can derive any other class. The compiler
will simply generate an instance declaration with no explicitlydefined
methods.
This is
mostly useful in classes whose minimal set is
empty, and especially when writing
generic functions.
As an example, consider a simple prettyprinter class SPretty
, which outputs
pretty strings:
{# LANGUAGE DefaultSignatures, DeriveAnyClass #}
class SPretty a where
sPpr :: a > String
default sPpr :: Show a => a > String
sPpr = show
If a user does not provide a manual implementation for sPpr
, then it will
default to show
. Now we can leverage the XDeriveAnyClass
extension to
easily implement a SPretty
instance for a new data type:
data Foo = Foo deriving (Show, SPretty)
The above code is equivalent to:
data Foo = Foo deriving Show
instance SPretty Foo
That is, an SPretty Foo
instance will be created with empty implementations
for all methods. Since we are using XDefaultSignatures
in this example, a
default implementation of sPpr
is filled in automatically.
Note the following details
In case you try to derive some class on a newtype, and
XGeneralizedNewtypeDeriving
is also on,XDeriveAnyClass
takes precedence.XDeriveAnyClass
is allowed only when the last argument of the class has kind*
or(* > *)
. So this is not allowed:data T a b = MkT a b deriving( Bifunctor )
because the last argument of
Bifunctor :: (* > * > *) > Constraint
has the wrong kind.The instance context will be generated according to the same rules used when deriving
Eq
(if the kind of the type is*
), or the rules forFunctor
(if the kind of the type is(* > *)
). For exampleinstance C a => C (a,b) where ... data T a b = MkT a (a,b) deriving( C )
The
deriving
clause will generateinstance C a => C (T a b) where {}
The constraints C a and C (a,b) are generated from the data constructor arguments, but the latter simplifies to C a.
XDeriveAnyClass
can be used with partially applied classes, such asdata T a = MKT a deriving( D Int )
which generates
instance D Int a => D Int (T a) where {}
XDeriveAnyClass
can be used to fill in default instances for associated type families:{# LANGUAGE DeriveAnyClass, TypeFamilies #} class Sizable a where type Size a type Size a = Int data Bar = Bar deriving Sizable doubleBarSize :: Size Bar > Size Bar doubleBarSize s = 2*s
The
deriving( Sizable )
is equivalent to sayinginstance Sizeable Bar where {}
and then the normal rules for filling in associated types from the default will apply, making
Size Bar
equal toInt
.
9.7. Class and instances declarations¶
9.7.1. Class declarations¶
This section, and the next one, documents GHC’s typeclass extensions. There’s lots of background in the paper Type classes: exploring the design space (Simon Peyton Jones, Mark Jones, Erik Meijer).
9.7.1.1. Multiparameter type classes¶
Multiparameter type classes are permitted, with flag
XMultiParamTypeClasses
. For example:
class Collection c a where
union :: c a > c a > c a
...etc.
9.7.1.2. The superclasses of a class declaration¶
In Haskell 98 the context of a class declaration (which introduces
superclasses) must be simple; that is, each predicate must consist of a
class applied to type variables. The flag XFlexibleContexts
(The context of a type signature) lifts this restriction, so that the only
restriction on the context in a class declaration is that the class
hierarchy must be acyclic. So these class declarations are OK:
class Functor (m k) => FiniteMap m k where
...
class (Monad m, Monad (t m)) => Transform t m where
lift :: m a > (t m) a
As in Haskell 98, The class hierarchy must be acyclic. However, the definition of “acyclic” involves only the superclass relationships. For example, this is OK:
class C a where {
op :: D b => a > b > b
}
class C a => D a where { ... }
Here, C
is a superclass of D
, but it’s OK for a class operation
op
of C
to mention D
. (It would not be OK for D
to be a
superclass of C
.)
With the extension that adds a kind of constraints, you can write more exotic superclass definitions. The superclass cycle check is even more liberal in these case. For example, this is OK:
class A cls c where
meth :: cls c => c > c
class A B c => B c where
A superclass context for a class C
is allowed if, after expanding
type synonyms to their righthandsides, and uses of classes (other than
C
) to their superclasses, C
does not occur syntactically in the
context.
9.7.1.3. Class method types¶
Haskell 98 prohibits class method types to mention constraints on the class type variable, thus:
class Seq s a where
fromList :: [a] > s a
elem :: Eq a => a > s a > Bool
The type of elem
is illegal in Haskell 98, because it contains the
constraint Eq a
, which constrains only the class type variable (in
this case a
).
GHC lifts this restriction with language extension
XConstrainedClassMethods
. The restriction is a pretty stupid one in
the first place, so XConstrainedClassMethods
is implied by
XMultiParamTypeClasses
.
9.7.1.4. Default method signatures¶
Haskell 98 allows you to define a default implementation when declaring a class:
class Enum a where
enum :: [a]
enum = []
The type of the enum
method is [a]
, and this is also the type of
the default method. You can lift this restriction and give another type
to the default method using the flag XDefaultSignatures
. For
instance, if you have written a generic implementation of enumeration in
a class GEnum
with method genum
in terms of GHC.Generics
,
you can specify a default method that uses that generic implementation:
class Enum a where
enum :: [a]
default enum :: (Generic a, GEnum (Rep a)) => [a]
enum = map to genum
We reuse the keyword default
to signal that a signature applies to
the default method only; when defining instances of the Enum
class,
the original type [a]
of enum
still applies. When giving an
empty instance, however, the default implementation map to genum
is
filledin, and typechecked with the type
(Generic a, GEnum (Rep a)) => [a]
.
We use default signatures to simplify generic programming in GHC (Generic programming).
9.7.1.5. Nullary type classes¶
Nullary (no parameter) type classes are enabled with XMultiTypeClasses
;
historically, they were enabled with the (now deprecated)
XNullaryTypeClasses
. Since there are no available parameters, there can be
at most one instance of a nullary class. A nullary type class might be used to
document some assumption in a type signature (such as reliance on the Riemann
hypothesis) or add some globally configurable settings in a program. For
example,
class RiemannHypothesis where
assumeRH :: a > a
 Deterministic version of the Miller test
 correctness depends on the generalised Riemann hypothesis
isPrime :: RiemannHypothesis => Integer > Bool
isPrime n = assumeRH (...)
The type signature of isPrime
informs users that its correctness depends on
an unproven conjecture. If the function is used, the user has to acknowledge the
dependence with:
instance RiemannHypothesis where
assumeRH = id
9.7.2. Functional dependencies¶
Functional dependencies are implemented as described by Mark Jones in “Type Classes with Functional Dependencies”, Mark P. Jones, In Proceedings of the 9th European Symposium on Programming, ESOP 2000, Berlin, Germany, March 2000, SpringerVerlag LNCS 1782, .
Functional dependencies are introduced by a vertical bar in the syntax of a class declaration; e.g.
class (Monad m) => MonadState s m  m > s where ...
class Foo a b c  a b > c where ...
There should be more documentation, but there isn’t (yet). Yell if you need it.
9.7.2.1. Rules for functional dependencies¶
In a class declaration, all of the class type variables must be reachable (in the sense mentioned in The context of a type signature) from the free variables of each method type. For example:
class Coll s a where
empty :: s
insert :: s > a > s
is not OK, because the type of empty
doesn’t mention a
.
Functional dependencies can make the type variable reachable:
class Coll s a  s > a where
empty :: s
insert :: s > a > s
Alternatively Coll
might be rewritten
class Coll s a where
empty :: s a
insert :: s a > a > s a
which makes the connection between the type of a collection of a
‘s
(namely (s a)
) and the element type a
. Occasionally this really
doesn’t work, in which case you can split the class like this:
class CollE s where
empty :: s
class CollE s => Coll s a where
insert :: s > a > s
9.7.2.2. Background on functional dependencies¶
The following description of the motivation and use of functional dependencies is taken from the Hugs user manual, reproduced here (with minor changes) by kind permission of Mark Jones.
Consider the following class, intended as part of a library for collection types:
class Collects e ce where
empty :: ce
insert :: e > ce > ce
member :: e > ce > Bool
The type variable e
used here represents the element type, while ce
is
the type of the container itself. Within this framework, we might want to define
instances of this class for lists or characteristic functions (both of which can
be used to represent collections of any equality type), bit sets (which can be
used to represent collections of characters), or hash tables (which can be used
to represent any collection whose elements have a hash function). Omitting
standard implementation details, this would lead to the following declarations:
instance Eq e => Collects e [e] where ...
instance Eq e => Collects e (e > Bool) where ...
instance Collects Char BitSet where ...
instance (Hashable e, Collects a ce)
=> Collects e (Array Int ce) where ...
All this looks quite promising; we have a class and a range of interesting implementations. Unfortunately, there are some serious problems with the class declaration. First, the empty function has an ambiguous type:
empty :: Collects e ce => ce
By “ambiguous” we mean that there is a type variable e
that appears on
the left of the =>
symbol, but not on the right. The problem with
this is that, according to the theoretical foundations of Haskell
overloading, we cannot guarantee a welldefined semantics for any term
with an ambiguous type.
We can sidestep this specific problem by removing the empty member from the class declaration. However, although the remaining members, insert and member, do not have ambiguous types, we still run into problems when we try to use them. For example, consider the following two functions:
f x y = insert x . insert y
g = f True 'a'
for which GHC infers the following types:
f :: (Collects a c, Collects b c) => a > b > c > c
g :: (Collects Bool c, Collects Char c) => c > c
Notice that the type for f
allows the two parameters x
and y
to be
assigned different types, even though it attempts to insert each of the
two values, one after the other, into the same collection. If we’re
trying to model collections that contain only one type of value, then
this is clearly an inaccurate type. Worse still, the definition for g is
accepted, without causing a type error. As a result, the error in this
code will not be flagged at the point where it appears. Instead, it will
show up only when we try to use g
, which might even be in a different
module.
9.7.2.2.1. An attempt to use constructor classes¶
Faced with the problems described above, some Haskell programmers might be tempted to use something like the following version of the class declaration:
class Collects e c where
empty :: c e
insert :: e > c e > c e
member :: e > c e > Bool
The key difference here is that we abstract over the type constructor c
that is used to form the collection type c e
, and not over that
collection type itself, represented by ce
in the original class
declaration. This avoids the immediate problems that we mentioned above:
empty has type Collects e c => c e
, which is not ambiguous.
The function f
from the previous section has a more accurate type:
f :: (Collects e c) => e > e > c e > c e
The function g
from the previous section is now rejected with a type
error as we would hope because the type of f
does not allow the two
arguments to have different types. This, then, is an example of a
multiple parameter class that does actually work quite well in practice,
without ambiguity problems. There is, however, a catch. This version of
the Collects
class is nowhere near as general as the original class
seemed to be: only one of the four instances for Collects
given
above can be used with this version of Collects because only one of them—the
instance for lists—has a collection type that can be written in the form c
e
, for some type constructor c
, and element type e
.
9.7.2.2.2. Adding functional dependencies¶
To get a more useful version of the Collects
class, GHC provides a
mechanism that allows programmers to specify dependencies between the
parameters of a multiple parameter class (For readers with an interest
in theoretical foundations and previous work: The use of dependency
information can be seen both as a generalisation of the proposal for
“parametric type classes” that was put forward by Chen, Hudak, and
Odersky, or as a special case of Mark Jones’s later framework for
“improvement” of qualified types. The underlying ideas are also
discussed in a more theoretical and abstract setting in a manuscript
[implparam], where they are identified as one point in a general design
space for systems of implicit parameterisation). To start with an
abstract example, consider a declaration such as:
class C a b where ...
which tells us simply that C
can be thought of as a binary relation on
types (or type constructors, depending on the kinds of a
and b
). Extra
clauses can be included in the definition of classes to add information
about dependencies between parameters, as in the following examples:
class D a b  a > b where ...
class E a b  a > b, b > a where ...
The notation a > b
used here between the 
and where
symbols —
not to be confused with a function type — indicates that the a
parameter uniquely determines the b
parameter, and might be read as “a
determines b
.” Thus D
is not just a relation, but actually a (partial)
function. Similarly, from the two dependencies that are included in the
definition of E
, we can see that E
represents a (partial) onetoone
mapping between types.
More generally, dependencies take the form x1 ... xn > y1 ... ym
,
where x1
, ..., xn
, and y1
, ..., yn
are type variables with n>0 and m>=0,
meaning that the y
parameters are uniquely determined by the x
parameters. Spaces can be used as separators if more than one variable
appears on any single side of a dependency, as in t > a b
. Note
that a class may be annotated with multiple dependencies using commas as
separators, as in the definition of E
above. Some dependencies that we
can write in this notation are redundant, and will be rejected because
they don’t serve any useful purpose, and may instead indicate an error
in the program. Examples of dependencies like this include a > a
,
a > a a
, a >
, etc. There can also be some redundancy if
multiple dependencies are given, as in a>b
, b>c
, a>c
, and
in which some subset implies the remaining dependencies. Examples like
this are not treated as errors. Note that dependencies appear only in
class declarations, and not in any other part of the language. In
particular, the syntax for instance declarations, class constraints, and
types is completely unchanged.
By including dependencies in a class declaration, we provide a mechanism
for the programmer to specify each multiple parameter class more
precisely. The compiler, on the other hand, is responsible for ensuring
that the set of instances that are in scope at any given point in the
program is consistent with any declared dependencies. For example, the
following pair of instance declarations cannot appear together in the
same scope because they violate the dependency for D
, even though either
one on its own would be acceptable:
instance D Bool Int where ...
instance D Bool Char where ...
Note also that the following declaration is not allowed, even by itself:
instance D [a] b where ...
The problem here is that this instance would allow one particular choice
of [a]
to be associated with more than one choice for b
, which
contradicts the dependency specified in the definition of D
. More
generally, this means that, in any instance of the form:
instance D t s where ...
for some particular types t
and s
, the only variables that can appear in
s
are the ones that appear in t
, and hence, if the type t
is known,
then s
will be uniquely determined.
The benefit of including dependency information is that it allows us to
define more general multiple parameter classes, without ambiguity
problems, and with the benefit of more accurate types. To illustrate
this, we return to the collection class example, and annotate the
original definition of Collects
with a simple dependency:
class Collects e ce  ce > e where
empty :: ce
insert :: e > ce > ce
member :: e > ce > Bool
The dependency ce > e
here specifies that the type e
of elements is
uniquely determined by the type of the collection ce
. Note that both
parameters of Collects are of kind *
; there are no constructor classes
here. Note too that all of the instances of Collects
that we gave
earlier can be used together with this new definition.
What about the ambiguity problems that we encountered with the original
definition? The empty function still has type Collects e ce => ce
, but
it is no longer necessary to regard that as an ambiguous type: Although
the variable e
does not appear on the right of the =>
symbol, the
dependency for class Collects
tells us that it is uniquely determined by
ce
, which does appear on the right of the =>
symbol. Hence the context
in which empty is used can still give enough information to determine
types for both ce
and e
, without ambiguity. More generally, we need only
regard a type as ambiguous if it contains a variable on the left of the
=>
that is not uniquely determined (either directly or indirectly) by
the variables on the right.
Dependencies also help to produce more accurate types for user defined
functions, and hence to provide earlier detection of errors, and less
cluttered types for programmers to work with. Recall the previous
definition for a function f
:
f x y = insert x y = insert x . insert y
for which we originally obtained a type:
f :: (Collects a c, Collects b c) => a > b > c > c
Given the dependency information that we have for Collects
, however, we
can deduce that a
and b
must be equal because they both appear as the
second parameter in a Collects
constraint with the same first parameter
c
. Hence we can infer a shorter and more accurate type for f
:
f :: (Collects a c) => a > a > c > c
In a similar way, the earlier definition of g
will now be flagged as a
type error.
Although we have given only a few examples here, it should be clear that the addition of dependency information can help to make multiple parameter classes more useful in practice, avoiding ambiguity problems, and allowing more general sets of instance declarations.
9.7.3. Instance declarations¶
An instance declaration has the form
instance ( assertion1, ..., assertionn) => class type1 ... typem where ...
The part before the “=>
” is the context, while the part after the
“=>
” is the head of the instance declaration.
9.7.3.1. Instance resolution¶
When GHC tries to resolve, say, the constraint C Int Bool
, it tries
to match every instance declaration against the constraint, by
instantiating the head of the instance declaration. Consider these
declarations:
instance context1 => C Int a where ...  (A)
instance context2 => C a Bool where ...  (B)
GHC’s default behaviour is that exactly one instance must match the
constraint it is trying to resolve. For example, the constraint
C Int Bool
matches instances (A) and (B), and hence would be
rejected; while C Int Char
matches only (A) and hence (A) is chosen.
Notice that
 When matching, GHC takes no account of the context of the instance
declaration (
context1
etc).  It is fine for there to be a potential of overlap (by including both declarations (A) and (B), say); an error is only reported if a particular constraint matches more than one.
See also Overlapping instances for flags that loosen the instance resolution rules.
9.7.3.2. Relaxed rules for the instance head¶
In Haskell 98 the head of an instance declaration must be of the form
C (T a1 ... an)
, where C
is the class, T
is a data type
constructor, and the a1 ... an
are distinct type variables. In the
case of multiparameter type classes, this rule applies to each
parameter of the instance head (Arguably it should be okay if just one
has this form and the others are type variables, but that’s the rules at
the moment).
GHC relaxes this rule in two ways:
With the
XTypeSynonymInstances
flag, instance heads may use type synonyms. As always, using a type synonym is just shorthand for writing the RHS of the type synonym definition. For example:type Point a = (a,a) instance C (Point a) where ...
is legal. The instance declaration is equivalent to
instance C (a,a) where ...
As always, type synonyms must be fully applied. You cannot, for example, write:
instance Monad Point where ...
The
XFlexibleInstances
flag allows the head of the instance declaration to mention arbitrary nested types. For example, this becomes a legal instance declarationinstance C (Maybe Int) where ...
See also the rules on overlap.
The
XFlexibleInstances
flag impliesXTypeSynonymInstances
.
However, the instance declaration must still conform to the rules for instance termination: see Instance termination rules.
9.7.3.3. Relaxed rules for instance contexts¶
In Haskell 98, the class constraints in the context of the instance
declaration must be of the form C a
where a
is a type variable
that occurs in the head.
The XFlexibleContexts
flag relaxes this rule, as well as relaxing
the corresponding rule for type signatures (see
The context of a type signature). Specifically, XFlexibleContexts
, allows
(wellkinded) class constraints of form (C t1 ... tn)
in the context
of an instance declaration.
Notice that the flag does not affect equality constraints in an instance
context; they are permitted by XTypeFamilies
or XGADTs
.
However, the instance declaration must still conform to the rules for instance termination: see Instance termination rules.
9.7.3.4. Instance termination rules¶
Regardless of XFlexibleInstances
and XFlexibleContexts
,
instance declarations must conform to some rules that ensure that
instance resolution will terminate. The restrictions can be lifted with
XUndecidableInstances
(see Undecidable instances).
The rules are these:
 The Paterson Conditions: for each class constraint
(C t1 ... tn)
in the context No type variable has more occurrences in the constraint than in the head
 The constraint has fewer constructors and variables (taken together and counting repetitions) than the head
 The constraint mentions no type functions. A type function application can in principle expand to a type of arbitrary size, and so are rejected out of hand
 The Coverage Condition. For each functional dependency,
⟨tvs⟩_{left}
>
⟨tvs⟩_{right}, of the class, every type variable in S(⟨tvs⟩_{right}) must appear in S(⟨tvs⟩_{left}), where S is the substitution mapping each type variable in the class declaration to the corresponding type in the instance head.
These restrictions ensure that instance resolution terminates: each reduction step makes the problem smaller by at least one constructor. You can find lots of background material about the reason for these restrictions in the paper Understanding functional dependencies via Constraint Handling Rules.
For example, these are okay:
instance C Int [a]  Multiple parameters
instance Eq (S [a])  Structured type in head
 Repeated type variable in head
instance C4 a a => C4 [a] [a]
instance Stateful (ST s) (MutVar s)
 Head can consist of type variables only
instance C a
instance (Eq a, Show b) => C2 a b
 Nontype variables in context
instance Show (s a) => Show (Sized s a)
instance C2 Int a => C3 Bool [a]
instance C2 Int a => C3 [a] b
But these are not:
 Context assertion no smaller than head
instance C a => C a where ...
 (C b b) has more occurrences of b than the head
instance C b b => Foo [b] where ...
The same restrictions apply to instances generated by deriving
clauses. Thus the following is accepted:
data MinHeap h a = H a (h a)
deriving (Show)
because the derived instance
instance (Show a, Show (h a)) => Show (MinHeap h a)
conforms to the above rules.
A useful idiom permitted by the above rules is as follows. If one allows overlapping instance declarations then it’s quite convenient to have a “default instance” declaration that applies if something more specific does not:
instance C a where
op = ...  Default
9.7.3.5. Undecidable instances¶
Sometimes even the termination rules of Instance termination rules are
too onerous. So GHC allows you to experiment with more liberal rules: if
you use the experimental flag XUndecidableInstances
, both the Paterson
Conditions and the Coverage
Condition (described in Instance termination rules) are lifted.
Termination is still ensured by having a fixeddepth recursion stack. If
you exceed the stack depth you get a sort of backtrace, and the
opportunity to increase the stack depth with
freductiondepth=
N. However, if you should exceed the default
reduction depth limit, it is probably best just to disable depth
checking, with freductiondepth=0
. The exact depth your program
requires depends on minutiae of your code, and it may change between
minor GHC releases. The safest bet for released code – if you’re sure
that it should compile in finite time – is just to disable the check.
For example, sometimes you might want to use the following to get the effect of a “class synonym”:
class (C1 a, C2 a, C3 a) => C a where { }
instance (C1 a, C2 a, C3 a) => C a where { }
This allows you to write shorter signatures:
f :: C a => ...
instead of
f :: (C1 a, C2 a, C3 a) => ...
The restrictions on functional dependencies (Functional dependencies) are particularly troublesome. It is tempting to introduce type variables in the context that do not appear in the head, something that is excluded by the normal rules. For example:
class HasConverter a b  a > b where
convert :: a > b
data Foo a = MkFoo a
instance (HasConverter a b,Show b) => Show (Foo a) where
show (MkFoo value) = show (convert value)
This is dangerous territory, however. Here, for example, is a program that would make the typechecker loop:
class D a
class F a b  a>b
instance F [a] [[a]]
instance (D c, F a c) => D [a]  'c' is not mentioned in the head
Similarly, it can be tempting to lift the coverage condition:
class Mul a b c  a b > c where
(.*.) :: a > b > c
instance Mul Int Int Int where (.*.) = (*)
instance Mul Int Float Float where x .*. y = fromIntegral x * y
instance Mul a b c => Mul a [b] [c] where x .*. v = map (x.*.) v
The third instance declaration does not obey the coverage condition; and indeed the (somewhat strange) definition:
f = \ b x y > if b then x .*. [y] else y
makes instance inference go into a loop, because it requires the
constraint (Mul a [b] b)
.
The XUndecidableInstances
flag is also used to lift some of the
restrictions imposed on type family instances. See
Decidability of type synonym instances.
9.7.3.6. Overlapping instances¶
In general, as discussed in Instance resolution, GHC requires that it be unambiguous which instance declaration should be used to resolve a typeclass constraint. GHC also provides a way to to loosen the instance resolution, by allowing more than one instance to match, provided there is a most specific one. Moreover, it can be loosened further, by allowing more than one instance to match irrespective of whether there is a most specific one. This section gives the details.
To control the choice of instance, it is possible to specify the overlap
behavior for individual instances with a pragma, written immediately
after the instance
keyword. The pragma may be one of:
{# OVERLAPPING #}
, {# OVERLAPPABLE #}
, {# OVERLAPS #}
,
or {# INCOHERENT #}
.
The matching behaviour is also influenced by two modulelevel language
extension flags: XOverlappingInstances
XOverlappingInstances and
XIncoherentInstances
XIncoherentInstances. These flags are now
deprecated (since GHC 7.10) in favour of the finegrained perinstance
pragmas.
A more precise specification is as follows. The willingness to be overlapped or incoherent is a property of the instance declaration itself, controlled as follows:
 An instance is incoherent if: it has an
INCOHERENT
pragma; or if the instance has no pragma and it appears in a module compiled withXIncoherentInstances
.  An instance is overlappable if: it has an
OVERLAPPABLE
orOVERLAPS
pragma; or if the instance has no pragma and it appears in a module compiled withXOverlappingInstances
; or if the instance is incoherent.  An instance is overlapping if: it has an
OVERLAPPING
orOVERLAPS
pragma; or if the instance has no pragma and it appears in a module compiled withXOverlappingInstances
; or if the instance is incoherent.
Now suppose that, in some client module, we are searching for an
instance of the target constraint (C ty1 .. tyn)
. The search works
like this:
 Find all instances I that match the target constraint; that is, the target constraint is a substitution instance of I. These instance declarations are the candidates.
 Eliminate any candidate IX for which both of the following hold:
 There is another candidate IY that is strictly more specific; that is, IY is a substitution instance of IX but not vice versa.
 Either IX is overlappable, or IY is overlapping. (This “either/or” design, rather than a “both/and” design, allow a client to deliberately override an instance from a library, without requiring a change to the library.)
 If exactly one nonincoherent candidate remains, select it. If all remaining candidates are incoherent, select an arbitrary one. Otherwise the search fails (i.e. when more than one surviving candidate is not incoherent).
 If the selected candidate (from the previous step) is incoherent, the search succeeds, returning that candidate.
 If not, find all instances that unify with the target constraint, but do not match it. Such noncandidate instances might match when the target constraint is further instantiated. If all of them are incoherent, the search succeeds, returning the selected candidate; if not, the search fails.
Notice that these rules are not influenced by flag settings in the client module, where the instances are used. These rules make it possible for a library author to design a library that relies on overlapping instances without the client having to know.
Errors are reported lazily (when attempting to solve a constraint), rather than eagerly (when the instances themselves are defined). Consider, for example
instance C Int b where ..
instance C a Bool where ..
These potentially overlap, but GHC will not complain about the instance
declarations themselves, regardless of flag settings. If we later try to
solve the constraint (C Int Char)
then only the first instance
matches, and all is well. Similarly with (C Bool Bool)
. But if we
try to solve (C Int Bool)
, both instances match and an error is
reported.
As a more substantial example of the rules in action, consider
instance {# OVERLAPPABLE #} context1 => C Int b where ...  (A)
instance {# OVERLAPPABLE #} context2 => C a Bool where ...  (B)
instance {# OVERLAPPABLE #} context3 => C a [b] where ...  (C)
instance {# OVERLAPPING #} context4 => C Int [Int] where ...  (D)
Now suppose that the type inference engine needs to solve the constraint
C Int [Int]
. This constraint matches instances (A), (C) and (D), but
the last is more specific, and hence is chosen.
If (D) did not exist then (A) and (C) would still be matched, but
neither is most specific. In that case, the program would be rejected,
unless XIncoherentInstances
is enabled, in which case it would be
accepted and (A) or (C) would be chosen arbitrarily.
An instance declaration is more specific than another iff the head of
former is a substitution instance of the latter. For example (D) is
“more specific” than (C) because you can get from (C) to (D) by
substituting a := Int
.
GHC is conservative about committing to an overlapping instance. For example:
f :: [b] > [b]
f x = ...
Suppose that from the RHS of f
we get the constraint C b [b]
.
But GHC does not commit to instance (C), because in a particular call of
f
, b
might be instantiate to Int
, in which case instance (D)
would be more specific still. So GHC rejects the program.
If, however, you add the flag XIncoherentInstances
when compiling
the module that contains (D), GHC will instead pick (C), without
complaining about the problem of subsequent instantiations.
Notice that we gave a type signature to f
, so GHC had to check
that f
has the specified type. Suppose instead we do not give a type
signature, asking GHC to infer it instead. In this case, GHC will
refrain from simplifying the constraint C Int [b]
(for the same
reason as before) but, rather than rejecting the program, it will infer
the type
f :: C b [b] => [b] > [b]
That postpones the question of which instance to pick to the call site
for f
by which time more is known about the type b
. You can
write this type signature yourself if you use the
XFlexibleContexts flag.
Exactly the same situation can arise in instance declarations themselves. Suppose we have
class Foo a where
f :: a > a
instance Foo [b] where
f x = ...
and, as before, the constraint C Int [b]
arises from f
‘s right
hand side. GHC will reject the instance, complaining as before that it
does not know how to resolve the constraint C Int [b]
, because it
matches more than one instance declaration. The solution is to postpone
the choice by adding the constraint to the context of the instance
declaration, thus:
instance C Int [b] => Foo [b] where
f x = ...
(You need XFlexibleInstances to do this.)
Warning
Overlapping instances must be used with care. They can give
rise to incoherence (i.e. different instance choices are made in
different parts of the program) even without XIncoherentInstances
.
Consider:
{# LANGUAGE OverlappingInstances #}
module Help where
class MyShow a where
myshow :: a > String
instance MyShow a => MyShow [a] where
myshow xs = concatMap myshow xs
showHelp :: MyShow a => [a] > String
showHelp xs = myshow xs
{# LANGUAGE FlexibleInstances, OverlappingInstances #}
module Main where
import Help
data T = MkT
instance MyShow T where
myshow x = "Used generic instance"
instance MyShow [T] where
myshow xs = "Used more specific instance"
main = do { print (myshow [MkT]); print (showHelp [MkT]) }
In function showHelp
GHC sees no overlapping instances, and so uses
the MyShow [a]
instance without complaint. In the call to myshow
in main
, GHC resolves the MyShow [T]
constraint using the
overlapping instance declaration in module Main
. As a result, the
program prints
"Used more specific instance"
"Used generic instance"
(An alternative possible behaviour, not currently implemented, would be
to reject module Help
on the grounds that a later instance
declaration might overlap the local one.)
9.7.3.7. Instance signatures: type signatures in instance declarations¶
In Haskell, you can’t write a type signature in an instance declaration,
but it is sometimes convenient to do so, and the language extension
XInstanceSigs
allows you to do so. For example:
data T a = MkT a a
instance Eq a => Eq (T a) where
(==) :: T a > T a > Bool  The signature
(==) (MkT x1 x2) (MkTy y1 y2) = x1==y1 && x2==y2
Some details
The type signature in the instance declaration must be more polymorphic than (or the same as) the one in the class declaration, instantiated with the instance type. For example, this is fine:
instance Eq a => Eq (T a) where (==) :: forall b. b > b > Bool (==) x y = True
Here the signature in the instance declaration is more polymorphic than that required by the instantiated class method.
The code for the method in the instance declaration is typechecked against the type signature supplied in the instance declaration, as you would expect. So if the instance signature is more polymorphic than required, the code must be too.
One stylistic reason for wanting to write a type signature is simple documentation. Another is that you may want to bring scoped type variables into scope. For example:
class C a where foo :: b > a > (a, [b]) instance C a => C (T a) where foo :: forall b. b > T a > (T a, [b]) foo x (T y) = (T y, xs) where xs :: [b] xs = [x,x,x]
Provided that you also specify
XScopedTypeVariables
(Lexically scoped type variables), theforall b
scopes over the definition offoo
, and in particular over the type signature forxs
.
9.7.4. Overloaded string literals¶
GHC supports overloaded string literals. Normally a string literal has
type String
, but with overloaded string literals enabled (with
XOverloadedStrings
) a string literal has type
(IsString a) => a
.
This means that the usual string syntax can be used, e.g., for
ByteString
, Text
, and other variations of string like types.
String literals behave very much like integer literals, i.e., they can
be used in both expressions and patterns. If used in a pattern the
literal with be replaced by an equality test, in the same way as an
integer literal is.
The class IsString
is defined as:
class IsString a where
fromString :: String > a
The only predefined instance is the obvious one to make strings work as usual:
instance IsString [Char] where
fromString cs = cs
The class IsString
is not in scope by default. If you want to
mention it explicitly (for example, to give an instance declaration for
it), you can import it from module GHC.Exts
.
Haskell’s defaulting mechanism (Haskell Report, Section
4.3.4) is
extended to cover string literals, when XOverloadedStrings
is
specified. Specifically:
 Each type in a
default
declaration must be an instance ofNum
or ofIsString
.  If no
default
declaration is given, then it is just as if the module contained the declarationdefault( Integer, Double, String)
.  The standard defaulting rule is extended thus: defaulting applies
when all the unresolved constraints involve standard classes or
IsString
; and at least one is a numeric class orIsString
.
So, for example, the expression length "foo"
will give rise to an
ambiguous use of IsString a0
which, because of the above rules, will
default to String
.
A small example:
module Main where
import GHC.Exts( IsString(..) )
newtype MyString = MyString String deriving (Eq, Show)
instance IsString MyString where
fromString = MyString
greet :: MyString > MyString
greet "hello" = "world"
greet other = other
main = do
print $ greet "hello"
print $ greet "fool"
Note that deriving Eq
is necessary for the pattern matching to work
since it gets translated into an equality comparison.
9.7.5. Overloaded lists¶
GHC supports overloading of the list notation. Let us recap the notation for constructing lists. In Haskell, the list notation can be be used in the following seven ways:
[]  Empty list
[x]  x : []
[x,y,z]  x : y : z : []
[x .. ]  enumFrom x
[x,y ..]  enumFromThen x y
[x .. y]  enumFromTo x y
[x,y .. z]  enumFromThenTo x y z
When the OverloadedLists
extension is turned on, the aforementioned
seven notations are desugared as follows:
[]  fromListN 0 []
[x]  fromListN 1 (x : [])
[x,y,z]  fromListN 3 (x : y : z : [])
[x .. ]  fromList (enumFrom x)
[x,y ..]  fromList (enumFromThen x y)
[x .. y]  fromList (enumFromTo x y)
[x,y .. z]  fromList (enumFromThenTo x y z)
This extension allows programmers to use the list notation for
construction of structures like: Set
, Map
, IntMap
,
Vector
, Text
and Array
. The following code listing gives a
few examples:
['0' .. '9'] :: Set Char
[1 .. 10] :: Vector Int
[("default",0), (k1,v1)] :: Map String Int
['a' .. 'z'] :: Text
List patterns are also overloaded. When the OverloadedLists
extension is turned on, these definitions are desugared as follows
f [] = ...  f (toList > []) = ...
g [x,y,z] = ...  g (toList > [x,y,z]) = ...
(Here we are using viewpattern syntax for the translation, see View patterns.)
9.7.5.1. The IsList
class¶
In the above desugarings, the functions toList
, fromList
and
fromListN
are all methods of the IsList
class, which is itself
exported from the GHC.Exts
module. The type class is defined as
follows:
class IsList l where
type Item l
fromList :: [Item l] > l
toList :: l > [Item l]
fromListN :: Int > [Item l] > l
fromListN _ = fromList
The IsList
class and its methods are intended to be used in
conjunction with the OverloadedLists
extension.
 The type function
Item
returns the type of items of the structurel
.  The function
fromList
constructs the structurel
from the given list ofItem l
.  The function
fromListN
takes the input list’s length as a hint. Its behaviour should be equivalent tofromList
. The hint can be used for more efficient construction of the structurel
compared tofromList
. If the given hint is not equal to the input list’s length the behaviour offromListN
is not specified.  The function
toList
should be the inverse offromList
.
It is perfectly fine to declare new instances of IsList
, so that
list notation becomes useful for completely new data types. Here are
several example instances:
instance IsList [a] where
type Item [a] = a
fromList = id
toList = id
instance (Ord a) => IsList (Set a) where
type Item (Set a) = a
fromList = Set.fromList
toList = Set.toList
instance (Ord k) => IsList (Map k v) where
type Item (Map k v) = (k,v)
fromList = Map.fromList
toList = Map.toList
instance IsList (IntMap v) where
type Item (IntMap v) = (Int,v)
fromList = IntMap.fromList
toList = IntMap.toList
instance IsList Text where
type Item Text = Char
fromList = Text.pack
toList = Text.unpack
instance IsList (Vector a) where
type Item (Vector a) = a
fromList = Vector.fromList
fromListN = Vector.fromListN
toList = Vector.toList
9.7.5.2. Rebindable syntax¶
When desugaring list notation with XOverloadedLists
GHC uses the
fromList
(etc) methods from module GHC.Exts
. You do not need to
import GHC.Exts
for this to happen.
However if you use XRebindableSyntax
, then GHC instead uses
whatever is in scope with the names of toList
, fromList
and
fromListN
. That is, these functions are rebindable; c.f.
Rebindable syntax and the implicit Prelude import.
9.7.5.3. Defaulting¶
Currently, the IsList
class is not accompanied with defaulting
rules. Although feasible, not much thought has gone into how to specify
the meaning of the default declarations like:
default ([a])
9.7.5.4. Speculation about the future¶
The current implementation of the OverloadedLists
extension can be
improved by handling the lists that are only populated with literals in
a special way. More specifically, the compiler could allocate such lists
statically using a compact representation and allow IsList
instances
to take advantage of the compact representation. Equipped with this
capability the OverloadedLists
extension will be in a good position
to subsume the OverloadedStrings
extension (currently, as a special
case, string literals benefit from statically allocated compact
representation).
9.8. Type families¶
Indexed type families form an extension to facilitate typelevel programming. Type families are a generalisation of associated data types [AssocDataTypes2005] and associated type synonyms [AssocTypeSyn2005] Type families themselves are described in Schrijvers 2008 [TypeFamilies2008]. Type families essentially provide typeindexed data types and named functions on types, which are useful for generic programming and highly parameterised library interfaces as well as interfaces with enhanced static information, much like dependent types. They might also be regarded as an alternative to functional dependencies, but provide a more functional style of typelevel programming than the relational style of functional dependencies.
Indexed type families, or type families for short, are type constructors that represent sets of types. Set members are denoted by supplying the type family constructor with type parameters, which are called type indices. The difference between vanilla parametrised type constructors and family constructors is much like between parametrically polymorphic functions and (adhoc polymorphic) methods of type classes. Parametric polymorphic functions behave the same at all type instances, whereas class methods can change their behaviour in dependence on the class type parameters. Similarly, vanilla type constructors imply the same data representation for all type instances, but family constructors can have varying representation types for varying type indices.
Indexed type families come in three flavours: data families, open type synonym families, and closed type synonym families. They are the indexed family variants of algebraic data types and type synonyms, respectively. The instances of data families can be data types and newtypes.
Type families are enabled by the flag XTypeFamilies
. Additional
information on the use of type families in GHC is available on the
Haskell wiki page on type
families.
[AssocDataTypes2005]  “Associated Types with Class”, M. Chakravarty, G. Keller, S. Peyton Jones, and S. Marlow. In Proceedings of “The 32nd Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages (POPL‘05)”, pages 113, ACM Press, 2005) 
[AssocTypeSyn2005]  “Type Associated Type Synonyms”. M. Chakravarty, G. Keller, and S. Peyton Jones. In Proceedings of “The Tenth ACM SIGPLAN International Conference on Functional Programming”, ACM Press, pages 241253, 2005). 
[TypeFamilies2008]  “Type Checking with Open Type Functions”, T. Schrijvers, S. PeytonJones, M. Chakravarty, and M. Sulzmann, in Proceedings of “ICFP 2008: The 13th ACM SIGPLAN International Conference on Functional Programming”, ACM Press, pages 5162, 2008. 
9.8.1. Data families¶
Data families appear in two flavours: (1) they can be defined on the toplevel or (2) they can appear inside type classes (in which case they are known as associated types). The former is the more general variant, as it lacks the requirement for the typeindexes to coincide with the class parameters. However, the latter can lead to more clearly structured code and compiler warnings if some type instances were  possibly accidentally  omitted. In the following, we always discuss the general toplevel form first and then cover the additional constraints placed on associated types.
9.8.1.1. Data family declarations¶
Indexed data families are introduced by a signature, such as
data family GMap k :: * > *
The special family
distinguishes family from standard data
declarations. The result kind annotation is optional and, as usual,
defaults to *
if omitted. An example is
data family Array e
Named arguments can also be given explicit kind signatures if needed.
Just as with GADT declarations named arguments are
entirely optional, so that we can declare Array
alternatively with
data family Array :: * > *
9.8.1.2. Data instance declarations¶
Instance declarations of data and newtype families are very similar to
standard data and newtype declarations. The only two differences are
that the keyword data
or newtype
is followed by instance
and
that some or all of the type arguments can be nonvariable types, but
may not contain forall types or type synonym families. However, data
families are generally allowed in type parameters, and type synonyms are
allowed as long as they are fully applied and expand to a type that is
itself admissible  exactly as this is required for occurrences of type
synonyms in class instance parameters. For example, the Either
instance for GMap
is
data instance GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
In this example, the declaration has only one variant. In general, it can be any number.
When the name of a type argument of a data or newtype instance
declaration doesn’t matter, it can be replaced with an underscore
(_
). This is the same as writing a type variable with a unique name.
data family F a b :: *
data instance F Int _ = Int
 Equivalent to
data instance F Int b = Int
This resembles the wildcards that can be used in
Partial Type Signatures. However, there are some differences.
Only anonymous wildcards are allowed in these instance declarations,
named and extraconstraints wildcards are not. No error messages
reporting the inferred types are generated, nor does the flag
XPartialTypeSignatures
have any effect.
Data and newtype instance declarations are only permitted when an appropriate family declaration is in scope  just as a class instance declaration requires the class declaration to be visible. Moreover, each instance declaration has to conform to the kind determined by its family declaration. This implies that the number of parameters of an instance declaration matches the arity determined by the kind of the family.
A data family instance declaration can use the full expressiveness of
ordinary data
or newtype
declarations:
Although, a data family is introduced with the keyword “
data
”, a data family instance can use eitherdata
ornewtype
. For example:data family T a data instance T Int = T1 Int  T2 Bool newtype instance T Char = TC Bool
A
data instance
can use GADT syntax for the data constructors, and indeed can define a GADT. For example:data family G a b data instance G [a] b where G1 :: c > G [Int] b G2 :: G [a] Bool
You can use a
deriving
clause on adata instance
ornewtype instance
declaration.
Even if data families are defined as toplevel declarations, functions that perform different computations for different family instances may still need to be defined as methods of type classes. In particular, the following is not possible:
data family T a
data instance T Int = A
data instance T Char = B
foo :: T a > Int
foo A = 1  WRONG: These two equations together...
foo B = 2  ...will produce a type error.
Instead, you would have to write foo
as a class operation, thus:
class Foo a where
foo :: T a > Int
instance Foo Int where
foo A = 1
instance Foo Char where
foo B = 2
Given the functionality provided by GADTs (Generalised Algebraic Data Types), it might seem as if a definition, such as the above, should be feasible. However, type families are  in contrast to GADTs  are open; i.e., new instances can always be added, possibly in other modules. Supporting pattern matching across different data instances would require a form of extensible case construct.
9.8.1.3. Overlap of data instances¶
The instance declarations of a data family used in a single program may not overlap at all, independent of whether they are associated or not. In contrast to type class instances, this is not only a matter of consistency, but one of type safety.
9.8.2. Synonym families¶
Type families appear in three flavours: (1) they can be defined as open families on the toplevel, (2) they can be defined as closed families on the toplevel, or (3) they can appear inside type classes (in which case they are known as associated type synonyms). Toplevel families are more general, as they lack the requirement for the typeindexes to coincide with the class parameters. However, associated type synonyms can lead to more clearly structured code and compiler warnings if some type instances were  possibly accidentally  omitted. In the following, we always discuss the general toplevel forms first and then cover the additional constraints placed on associated types. Note that closed associated type synonyms do not exist.
9.8.2.1. Type family declarations¶
Open indexed type families are introduced by a signature, such as
type family Elem c :: *
The special family
distinguishes family from standard type
declarations. The result kind annotation is optional and, as usual,
defaults to *
if omitted. An example is
type family Elem c
Parameters can also be given explicit kind signatures if needed. We call the number of parameters in a type family declaration, the family’s arity, and all applications of a type family must be fully saturated with respect to to that arity. This requirement is unlike ordinary type synonyms and it implies that the kind of a type family is not sufficient to determine a family’s arity, and hence in general, also insufficient to determine whether a type family application is well formed. As an example, consider the following declaration:
type family F a b :: * > *  F's arity is 2,
 although its overall kind is * > * > * > *
Given this declaration the following are examples of wellformed and malformed types:
F Char [Int]  OK! Kind: * > *
F Char [Int] Bool  OK! Kind: *
F IO Bool  WRONG: kind mismatch in the first argument
F Bool  WRONG: unsaturated application
The result kind annotation is optional and defaults to *
(like
argument kinds) if omitted. Polykinded type families can be declared
using a parameter in the kind annotation:
type family F a :: k
In this case the kind parameter k
is actually an implicit parameter
of the type family.
9.8.2.2. Type instance declarations¶
Instance declarations of type families are very similar to standard type
synonym declarations. The only two differences are that the keyword
type
is followed by instance
and that some or all of the type
arguments can be nonvariable types, but may not contain forall types or
type synonym families. However, data families are generally allowed, and
type synonyms are allowed as long as they are fully applied and expand
to a type that is admissible  these are the exact same requirements as
for data instances. For example, the [e]
instance for Elem
is
type instance Elem [e] = e
Type arguments can be replaced with underscores (_
) if the names of
the arguments don’t matter. This is the same as writing type variables
with unique names. The same rules apply as for
Data instance declarations.
Type family instance declarations are only legitimate when an appropriate family declaration is in scope  just like class instances require the class declaration to be visible. Moreover, each instance declaration has to conform to the kind determined by its family declaration, and the number of type parameters in an instance declaration must match the number of type parameters in the family declaration. Finally, the righthand side of a type instance must be a monotype (i.e., it may not include foralls) and after the expansion of all saturated vanilla type synonyms, no synonyms, except family synonyms may remain.
9.8.2.3. Closed type families¶
A type family can also be declared with a where
clause, defining the
full set of equations for that family. For example:
type family F a where
F Int = Double
F Bool = Char
F a = String
A closed type family’s equations are tried in order, from top to bottom,
when simplifying a type family application. In this example, we declare
an instance for F
such that F Int
simplifies to Double
,
F Bool
simplifies to Char
, and for any other type a
that is
known not to be Int
or Bool
, F a
simplifies to String
.
Note that GHC must be sure that a
cannot unify with Int
or
Bool
in that last case; if a programmer specifies just F a
in
their code, GHC will not be able to simplify the type. After all, a
might later be instantiated with Int
.
A closed type family’s equations have the same restrictions as the equations for open type family instances.
A closed type family may be declared with no equations. Such closed type
families are opaque typelevel definitions that will never reduce, are
not necessarily injective (unlike empty data types), and cannot be given
any instances. This is different from omitting the equations of a closed
type family in a hsboot
file, which uses the syntax where ..
,
as in that case there may or may not be equations given in the hs
file.
9.8.2.4. Type family examples¶
Here are some examples of admissible and illegal type instances:
type family F a :: *
type instance F [Int] = Int  OK!
type instance F String = Char  OK!
type instance F (F a) = a  WRONG: type parameter mentions a type family
type instance
F (forall a. (a, b)) = b  WRONG: a forall type appears in a type parameter
type instance
F Float = forall a.a  WRONG: righthand side may not be a forall type
type family H a where  OK!
H Int = Int
H Bool = Bool
H a = String
type instance H Char = Char  WRONG: cannot have instances of closed family
type family K a where  OK!
type family G a b :: * > *
type instance G Int = (,)  WRONG: must be two type parameters
type instance G Int Char Float = Double  WRONG: must be two type parameters
9.8.2.5. Compatibility and apartness of type family equations¶
There must be some restrictions on the equations of type families, lest we define an ambiguous rewrite system. So, equations of open type families are restricted to be compatible. Two type patterns are compatible if
 all corresponding types and implicit kinds in the patterns are apart, or
 the two patterns unify producing a substitution, and the righthand sides are equal under that substitution.
Two types are considered apart if, for all possible substitutions, the types cannot reduce to a common reduct.
The first clause of “compatible” is the more straightforward one. It says that the patterns of two distinct type family instances cannot overlap. For example, the following is disallowed:
type instance F Int = Bool
type instance F Int = Char
The second clause is a little more interesting. It says that two overlapping type family instances are allowed if the righthand sides coincide in the region of overlap. Some examples help here:
type instance F (a, Int) = [a]
type instance F (Int, b) = [b]  overlap permitted
type instance G (a, Int) = [a]
type instance G (Char, a) = [a]  ILLEGAL overlap, as [Char] /= [Int]
Note that this compatibility condition is independent of whether the type family is associated or not, and it is not only a matter of consistency, but one of type safety.
For a polykinded type family, the kinds are checked for apartness just like types. For example, the following is accepted:
type family J a :: k
type instance J Int = Bool
type instance J Int = Maybe
These instances are compatible because they differ in their implicit
kind parameter; the first uses *
while the second uses * > *
.
The definition for “compatible” uses a notion of “apart”, whose definition in turn relies on type family reduction. This condition of “apartness”, as stated, is impossible to check, so we use this conservative approximation: two types are considered to be apart when the two types cannot be unified, even by a potentially infinite unifier. Allowing the unifier to be infinite disallows the following pair of instances:
type instance H x x = Int
type instance H [x] x = Bool
The type patterns in this pair equal if x
is replaced by an infinite
nesting of lists. Rejecting instances such as these is necessary for
type soundness.
Compatibility also affects closed type families. When simplifying an application of a closed type family, GHC will select an equation only when it is sure that no incompatible previous equation will ever apply. Here are some examples:
type family F a where
F Int = Bool
F a = Char
type family G a where
G Int = Int
G a = a
In the definition for F
, the two equations are incompatible – their
patterns are not apart, and yet their righthand sides do not coincide.
Thus, before GHC selects the second equation, it must be sure that the
first can never apply. So, the type F a
does not simplify; only a
type such as F Double
will simplify to Char
. In G
, on the
other hand, the two equations are compatible. Thus, GHC can ignore the
first equation when looking at the second. So, G a
will simplify to
a
.
However see Type, class and other declarations for the overlap rules in GHCi.
9.8.2.6. Decidability of type synonym instances¶
In order to guarantee that type inference in the presence of type families decidable, we need to place a number of additional restrictions on the formation of type instance declarations (c.f., Definition 5 (Relaxed Conditions) of “Type Checking with Open Type Functions”). Instance declarations have the general form
type instance F t1 .. tn = t
where we require that for every type family application (G s1 .. sm)
in t
,
s1 .. sm
do not contain any type family constructors, the total number of symbols (data type constructors and type
variables) in
s1 .. sm
is strictly smaller than int1 .. tn
, and  for every type variable
a
,a
occurs ins1 .. sm
at most as often as int1 .. tn
.
These restrictions are easily verified and ensure termination of type
inference. However, they are not sufficient to guarantee completeness of
type inference in the presence of, so called, ‘’loopy equalities’‘, such
as a ~ [F a]
, where a recursive occurrence of a type variable is
underneath a family application and data constructor application  see
the above mentioned paper for details.
If the option XUndecidableInstances
is passed to the compiler, the
above restrictions are not enforced and it is on the programmer to
ensure termination of the normalisation of type families during type
inference.
9.8.3. Associated data and type families¶
A data or type synonym family can be declared as part of a type class, thus:
class GMapKey k where
data GMap k :: * > *
...
class Collects ce where
type Elem ce :: *
...
When doing so, we (optionally) may drop the “family
” keyword.
The type parameters must all be type variables, of course, and some (but not necessarily all) of then can be the class parameters. Each class parameter may only be used at most once per associated type, but some may be omitted and they may be in an order other than in the class head. Hence, the following contrived example is admissible:
class C a b c where
type T c a x :: *
Here c
and a
are class parameters, but the type is also indexed
on a third parameter x
.
9.8.3.1. Associated instances¶
When an associated data or type synonym family instance is declared
within a type class instance, we (optionally) may drop the instance
keyword in the family instance:
instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
...
instance Eq (Elem [e]) => Collects [e] where
type Elem [e] = e
...
Note the following points:
The type indexes corresponding to class parameters must have precisely the same shape the type given in the instance head. To have the same “shape” means that the two types are identical modulo renaming of type variables. For example:
instance Eq (Elem [e]) => Collects [e] where  Choose one of the following alternatives: type Elem [e] = e  OK type Elem [x] = x  OK type Elem x = x  BAD; shape of 'x' is different to '[e]' type Elem [Maybe x] = x  BAD: shape of '[Maybe x]' is different to '[e]'
An instances for an associated family can only appear as part of an instance declarations of the class in which the family was declared, just as with the equations of the methods of a class.
The instance for an associated type can be omitted in class instances. In that case, unless there is a default instance (see Associated type synonym defaults), the corresponding instance type is not inhabited; i.e., only diverging expressions, such as
undefined
, can assume the type.Although it is unusual, there (currently) can be multiple instances for an associated family in a single instance declaration. For example, this is legitimate:
instance GMapKey Flob where data GMap Flob [v] = G1 v data GMap Flob Int = G2 Int ...
Here we give two data instance declarations, one in which the last parameter is
[v]
, and one for which it isInt
. Since you cannot give any subsequent instances for(GMap Flob ...)
, this facility is most useful when the free indexed parameter is of a kind with a finite number of alternatives (unlike*
). WARNING: this facility may be withdrawn in the future.
9.8.3.2. Associated type synonym defaults¶
It is possible for the class defining the associated type to specify a default for associated type instances. So for example, this is OK:
class IsBoolMap v where
type Key v
type instance Key v = Int
lookupKey :: Key v > v > Maybe Bool
instance IsBoolMap [(Int, Bool)] where
lookupKey = lookup
In an instance
declaration for the class, if no explicit
type instance
declaration is given for the associated type, the
default declaration is used instead, just as with default class methods.
Note the following points:
 The
instance
keyword is optional.  There can be at most one default declaration for an associated type synonym.
 A default declaration is not permitted for an associated data type.
 The default declaration must mention only type variables on the left hand side, and the right hand side must mention only type variables bound on the left hand side. However, unlike the associated type family declaration itself, the type variables of the default instance are independent of those of the parent class.
Here are some examples:
class C a where
type F1 a :: *
type instance F1 a = [a]  OK
type instance F1 a = a>a  BAD; only one default instance is allowed
type F2 b a  OK; note the family has more type
 variables than the class
type instance F2 c d = c>d  OK; you don't have to use 'a' in the type instance
type F3 a
type F3 [b] = b  BAD; only type variables allowed on the LHS
type F4 a
type F4 b = a  BAD; 'a' is not in scope in the RHS
9.8.3.3. Scoping of class parameters¶
The visibility of class parameters in the righthand side of associated family instances depends solely on the parameters of the family. As an example, consider the simple class declaration
class C a b where
data T a
Only one of the two class parameters is a parameter to the data family. Hence, the following instance declaration is invalid:
instance C [c] d where
data T [c] = MkT (c, d)  WRONG!! 'd' is not in scope
Here, the righthand side of the data instance mentions the type
variable d
that does not occur in its lefthand side. We cannot
admit such data instances as they would compromise type safety.
9.8.3.4. Instance contexts and associated type and data instances¶
Associated type and data instance declarations do not inherit any
context specified on the enclosing instance. For type instance
declarations, it is unclear what the context would mean. For data
instance declarations, it is unlikely a user would want the context
repeated for every data constructor. The only place where the context
might likely be useful is in a deriving
clause of an associated data
instance. However, even here, the role of the outer instance context is
murky. So, for clarity, we just stick to the rule above: the enclosing
instance context is ignored. If you need to use a nontrivial context on
a derived instance, use a standalone
deriving clause (at the top level).
9.8.4. Import and export¶
The rules for export lists (Haskell Report Section 5.2) needs adjustment for type families:
 The form
T(..)
, whereT
is a data family, names the familyT
and all the inscope constructors (whether in scope qualified or unqualified) that are data instances ofT
.  The form
T(.., ci, .., fj, ..)
, whereT
is a data family, namesT
and the specified constructorsci
and fieldsfj
as usual. The constructors and field names must belong to some data instance ofT
, but are not required to belong to the same instance.  The form
C(..)
, whereC
is a class, names the classC
and all its methods and associated types.  The form
C(.., mi, .., type Tj, ..)
, whereC
is a class, names the classC
, and the specified methodsmi
and associated typesTj
. The types need a keyword “type
” to distinguish them from data constructors.  Whenever there is no export list and a data instance is defined, the corresponding data family type constructor is exported along with the new data constructors, regardless of whether the data family is defined locally or in another module.
9.8.4.1. Examples¶
Recall our running GMapKey
class example:
class GMapKey k where
data GMap k :: * > *
insert :: GMap k v > k > v > GMap k v
lookup :: GMap k v > k > Maybe v
empty :: GMap k v
instance (GMapKey a, GMapKey b) => GMapKey (Either a b) where
data GMap (Either a b) v = GMapEither (GMap a v) (GMap b v)
...method declarations...
Here are some export lists and their meaning:
module GMap( GMapKey )
Exports just the class name.
module GMap( GMapKey(..) )
Exports the class, the associated type
GMap
and the member functionsempty
,lookup
, andinsert
. The data constructors ofGMap
(in this caseGMapEither
) are not exported.module GMap( GMapKey( type GMap, empty, lookup, insert ) )
Same as the previous item. Note the “
type
” keyword.module GMap( GMapKey(..), GMap(..) )
Same as previous item, but also exports all the data constructors for
GMap
, namelyGMapEither
.module GMap ( GMapKey( empty, lookup, insert), GMap(..) )
Same as previous item.
module GMap ( GMapKey, empty, lookup, insert, GMap(..) )
Same as previous item.
Two things to watch out for:
You cannot write
GMapKey(type GMap(..))
— i.e., subcomponent specifications cannot be nested. To specifyGMap
‘s data constructors, you have to list it separately.Consider this example:
module X where data family D module Y where import X data instance D Int = D1  D2
Module
Y
exports all the entities defined inY
, namely the data constructorsD1
andD2
, and implicitly the data familyD
, even though it’s defined inX
. This means you can writeimport Y( D(D1,D2) )
without giving an explicit export list like this:module Y( D(..) ) where ... or module Y( module Y, D ) where ...
9.8.4.2. Instances¶
Family instances are implicitly exported, just like class instances. However, this applies only to the heads of instances, not to the data constructors an instance defines.
9.8.5. Type families and instance declarations¶
Type families require us to extend the rules for the form of instance heads, which are given in Relaxed rules for the instance head. Specifically:
 Data type families may appear in an instance head
 Type synonym families may not appear (at all) in an instance head
The reason for the latter restriction is that there is no way to check for instance matching. Consider
type family F a
type instance F Bool = Int
class C a
instance C Int
instance C (F a)
Now a constraint (C (F Bool))
would match both instances. The
situation is especially bad because the type instance for F Bool
might be in another module, or even in a module that is not yet written.
However, type class instances of instances of data families can be defined much like any other data type. For example, we can say
data instance T Int = T1 Int  T2 Bool
instance Eq (T Int) where
(T1 i) == (T1 j) = i==j
(T2 i) == (T2 j) = i==j
_ == _ = False
Note that class instances are always for particular instances of a data family and never for an entire family as a whole. This is for essentially the same reasons that we cannot define a toplevel function that performs pattern matching on the data constructors of different instances of a single type family. It would require a form of extensible case construct.
Data instance declarations can also have deriving
clauses. For
example, we can write
data GMap () v = GMapUnit (Maybe v)
deriving Show
which implicitly defines an instance of the form
instance Show v => Show (GMap () v) where ...
9.8.6. Injective type families¶
Starting with GHC 7.12 type families can be annotated with injectivity information. This information is then used by GHC during type checking to resolve type ambiguities in situations where a type variable appears only under type family applications.
For full details on injective type families refer to Haskell Symposium 2015 paper Injective type families for Haskell.
9.8.6.1. Syntax of injectivity annotation¶
Injectivity annotation is added after type family head and consists of two parts:
 a type variable that names the result of a type family. Syntax:
= tyvar
or= (tyvar :: kind)
. Type variable must be fresh.  an injectivity annotation of the form
 A > B
, whereA
is the result type variable (see previous bullet) andB
is a list of argument type and kind variables in which type family is injective. It is possible to omit some variables if type family is not injective in them.
Examples:
type family Id a = result  result > a where
type family F a b c = d  d > a c b
type family G (a :: k) b c = foo  foo > k b where
For open and closed type families it is OK to name the result but skip the injectivity annotation. This is not the case for associated type synonyms, where the named result without injectivity annotation will be interpreted as associated type synonym default.
9.8.6.2. Verifying injectivity annotation against type family equations¶
Once the user declares type family to be injective GHC must verify that this declaration is correct, ie. type family equations don’t violate the injectivity annotation. A general idea is that if at least one equation (bullets (1), (2) and (3) below) or a pair of equations (bullets (4) and (5) below) violates the injectivity annotation then a type family is not injective in a way user claims and an error is reported. In the bullets below RHS refers to the righthand side of the type family equation being checked for injectivity. LHS refers to the arguments of that type family equation. Below are the rules followed when checking injectivity of a type family:
If a RHS of a type family equation is a type family application GHC reports that the type family is not injective.
If a RHS of a type family equation is a bare type variable we require that all LHS variables (including implicit kind variables) are also bare. In other words, this has to be a sole equation of that type family and it has to cover all possible patterns. If the patterns are not covering GHC reports that the type family is not injective.
If a LHS type variable that is declared as injective is not mentioned on injective position in the RHS GHC reports that the type family is not injective. Injective position means either argument to a type constructor or injective argument to a type family.
Open type familiesOpen type families are typechecked incrementally. This means that when a module is imported type family instances contained in that module are checked against instances present in already imported modules.
A pair of an open type family equations is checked by attempting to unify their RHSs. If the RHSs don’t unify this pair does not violate injectivity annotation. If unification succeeds with a substitution then LHSs of unified equations must be identical under that substitution. If they are not identical then GHC reports that the type family is not injective.
In a closed type family all equations are ordered and in one place. Equations are also checked pairwise but this time an equation has to be paired with all the preceeding equations. Of course a singleequation closed type family is trivially injective (unless (1), (2) or (3) above holds).
When checking a pair of closed type family equations GHC tried to unify their RHSs. If they don’t unify this pair of equations does not violate injectivity annotation. If the RHSs can be unified under some substitution (possibly empty) then either the LHSs unify under the same substitution or the LHS of the latter equation is subsumed by earlier equations. If neither condition is met GHC reports that a type family is not injective.
Note that for the purpose of injectivity check in bullets (4) and (5) GHC uses a special variant of unification algorithm that treats type family applications as possibly unifying with anything.
9.9. Kind polymorphism¶
This section describes kind polymorphism, and extension enabled by
XPolyKinds
. It is described in more detail in the paper Giving
Haskell a Promotion, which
appeared at TLDI 2012.
9.9.1. Overview of kind polymorphism¶
Currently there is a lot of code duplication in the way Typeable
is
implemented (Deriving Typeable instances):
class Typeable (t :: *) where
typeOf :: t > TypeRep
class Typeable1 (t :: * > *) where
typeOf1 :: t a > TypeRep
class Typeable2 (t :: * > * > *) where
typeOf2 :: t a b > TypeRep
Kind polymorphism (with XPolyKinds
) allows us to merge all these
classes into one:
data Proxy t = Proxy
class Typeable t where
typeOf :: Proxy t > TypeRep
instance Typeable Int where typeOf _ = TypeRep
instance Typeable [] where typeOf _ = TypeRep
Note that the datatype Proxy
has kind forall k. k > *
(inferred
by GHC), and the new Typeable
class has kind
forall k. k > Constraint
.
Note the following specific points:
Generally speaking, with
XPolyKinds
, GHC will infer a polymorphic kind for undecorated declarations, whenever possible. For example, in GHCighci> :set XPolyKinds ghci> data T m a = MkT (m a) ghci> :k T T :: (k > *) > k > *
GHC does not usually print explicit
forall
s, including kindforall
s. You can make GHC show them explicitly withfprintexplicitforalls
(see Verbosity options):ghci> :set XPolyKinds ghci> :set fprintexplicitforalls ghci> data T m a = MkT (m a) ghci> :k T T :: forall (k :: BOX). (k > *) > k > *
Just as in the world of terms, you can restrict polymorphism using a kind signature (sometimes called a kind annotation)
data T m (a :: *) = MkT (m a)  GHC now infers kind T :: (* > *) > * > *
NB:
XPolyKinds
impliesXKindSignatures
(see Explicitlykinded quantification).The source language does not support an explicit
forall
for kind variables. Instead, when binding a type variable, you can simply mention a kind variable in a kind annotation for that typevariable binding, thus:data T (m :: k > *) a = MkT (m a)  GHC now infers kind T :: forall k. (k > *) > k > *
The (implicit) kind “forall” is placed just outside the outermost typevariable binding whose kind annotation mentions the kind variable. For example
f1 :: (forall a m. m a > Int) > Int  f1 :: forall (k::BOX).  (forall (a::k) (m::k>*). m a > Int)  > Int f2 :: (forall (a::k) m. m a > Int) > Int  f2 :: (forall (k::BOX) (a::k) (m::k>*). m a > Int)  > Int
Here in
f1
there is no kind annotation mentioning the polymorphic kind variable, sok
is generalised at the top level of the signature forf1
. But in the case of off2
we give a kind annotation in theforall (a:k)
binding, and GHC therefore puts the kindforall
right there too. This design decision makes default case (f1
) as polymorphic as possible; remember that a more polymorphic argument type (as inf2
makes the overall function less polymorphic, because there are fewer acceptable arguments.
Note
These rules are a bit indirect and clumsy. Perhaps GHC should allow explicit kind quantification. But the implicit quantification (e.g. in the declaration for data type T above) is certainly very convenient, and it is not clear what the syntax for explicit quantification should be.
9.9.2. Principles of kind inference¶
Generally speaking, when XPolyKinds
is on, GHC tries to infer the
most general kind for a declaration. For example:
data T f a = MkT (f a)  GHC infers:
 T :: forall k. (k>*) > k > *
In this case the definition has a righthand side to inform kind inference. But that is not always the case. Consider
type family F a
Type family declarations have no righthand side, but GHC must still
infer a kind for F
. Since there are no constraints, it could infer
F :: forall k1 k2. k1 > k2
, but that seems too polymorphic. So
GHC defaults those entirelyunconstrained kind variables to *
and we
get F :: * > *
. You can still declare F
to be kindpolymorphic
using kind signatures:
type family F1 a  F1 :: * > *
type family F2 (a :: k)  F2 :: forall k. k > *
type family F3 a :: k  F3 :: forall k. * > k
type family F4 (a :: k1) :: k  F4 :: forall k1 k2. k1 > k2
The general principle is this:
 When there is a righthand side, GHC infers the most polymorphic kind consistent with the righthand side. Examples: ordinary data type and GADT declarations, class declarations. In the case of a class declaration the role of “right hand side” is played by the class method signatures.
 When there is no right hand side, GHC defaults argument and result kinds to ``*``, except when directed otherwise by a kind signature. Examples: data and type family declarations.
This rule has occasionallysurprising consequences (see Trac #10132.
class C a where  Class declarations are generalised
 so C :: forall k. k > Constraint
data D1 a  No right hand side for these two family
type F1 a  declarations, but the class forces (a :: k)
 so D1, F1 :: forall k. k > *
data D2 a  No righthand side so D2 :: * > *
type F2 a  No righthand side so F2 :: * > *
The kindpolymorphism from the class declaration makes D1
kindpolymorphic, but not so D2
; and similarly F1
, F1
.
9.9.3. Polymorphic kind recursion and complete kind signatures¶
Just as in type inference, kind inference for recursive types can only use monomorphic recursion. Consider this (contrived) example:
data T m a = MkT (m a) (T Maybe (m a))
 GHC infers kind T :: (* > *) > * > *
The recursive use of T
forced the second argument to have kind
*
. However, just as in type inference, you can achieve polymorphic
recursion by giving a complete kind signature for T
. A complete
kind signature is present when all argument kinds and the result kind
are known, without any need for inference. For example:
data T (m :: k > *) :: k > * where
MkT :: m a > T Maybe (m a) > T m a
The complete usersupplied kind signature specifies the polymorphic kind
for T
, and this signature is used for all the calls to T
including the recursive ones. In particular, the recursive use of T
is at kind *
.
What exactly is considered to be a “complete usersupplied kind signature” for a type constructor? These are the forms:
For a datatype, every type variable must be annotated with a kind. In a GADTstyle declaration, there may also be a kind signature (with a toplevel
::
in the header), but the presence or absence of this annotation does not affect whether or not the declaration has a complete signature.data T1 :: (k > *) > k > * where ...  Yes T1 :: forall k. (k>*) > k > * data T2 (a :: k > *) :: k > * where ...  Yes T2 :: forall k. (k>*) > k > * data T3 (a :: k > *) (b :: k) :: * where ...  Yes T3 :: forall k. (k>*) > k > * data T4 (a :: k > *) (b :: k) where ...  Yes T4 :: forall k. (k>*) > k > * data T5 a (b :: k) :: * where ...  No kind is inferred data T6 a b where ...  No kind is inferred
For a class, every type variable must be annotated with a kind.
For a type synonym, every type variable and the result type must all be annotated with kinds.
type S1 (a :: k) = (a :: k)  Yes S1 :: forall k. k > k type S2 (a :: k) = a  No kind is inferred type S3 (a :: k) = Proxy a  No kind is inferred
Note that in
S2
andS3
, the kind of the righthand side is rather apparent, but it is still not considered to have a complete signature – no inference can be done before detecting the signature.An open type or data family declaration always has a complete userspecified kind signature; unannotated type variables default to kind
*
.data family D1 a  D1 :: * > * data family D2 (a :: k)  D2 :: forall k. k > * data family D3 (a :: k) :: *  D3 :: forall k. k > * type family S1 a :: k > *  S1 :: forall k. * > k > * class C a where  C :: k > Constraint type AT a b  AT :: k > * > *
In the last example, the variable
a
has an implicit kind variable annotation from the class declaration. It keeps its polymorphic kind in the associated type declaration. The variableb
, however, gets defaulted to*
.A closed type family has a complete signature when all of its type variables are annotated and a return kind (with a toplevel
::
) is supplied.
9.9.4. Kind inference in closed type families¶
Although all open type families are considered to have a complete userspecified kind signature, we can relax this condition for closed type families, where we have equations on which to perform kind inference. GHC will infer kinds for the arguments and result types of a closed type family.
GHC supports kindindexed type families, where the family matches both on the kind and type. GHC will not infer this behaviour without a complete usersupplied kind signature, as doing so would sometimes infer nonprincipal types.
For example:
type family F1 a where
F1 True = False
F1 False = True
F1 x = x
 F1 fails to compile: kindindexing is not inferred
type family F2 (a :: k) where
F2 True = False
F2 False = True
F2 x = x
 F2 fails to compile: no complete signature
type family F3 (a :: k) :: k where
F3 True = False
F3 False = True
F3 x = x
 OK
9.9.5. Kind inference in class instance declarations¶
Consider the following example of a polykinded class and an instance for it:
class C a where
type F a
instance C b where
type F b = b > b
In the class declaration, nothing constrains the kind of the type a
,
so it becomes a polykinded type variable (a :: k)
. Yet, in the
instance declaration, the righthand side of the associated type
instance b > b
says that b
must be of kind *
. GHC could
theoretically propagate this information back into the instance head,
and make that instance declaration apply only to type of kind *
, as
opposed to types of any kind. However, GHC does not do this.
In short: GHC does not propagate kind information from the members of a class instance declaration into the instance declaration head.
This lack of kind inference is simply an engineering problem within GHC,
but getting it to work would make a substantial change to the inference
infrastructure, and it’s not clear the payoff is worth it. If you want
to restrict b
‘s kind in the instance above, just use a kind
signature in the instance head.
9.10. Datatype promotion¶
This section describes data type promotion, an extension to the kind
system that complements kind polymorphism. It is enabled by
XDataKinds
, and described in more detail in the paper Giving
Haskell a Promotion, which
appeared at TLDI 2012.
9.10.1. Motivation¶
Standard Haskell has a rich type language. Types classify terms and
serve to avoid many common programming mistakes. The kind language,
however, is relatively simple, distinguishing only lifted types (kind
*
), type constructors (e.g. kind * > * > *
), and unlifted
types (Unboxed types). In particular when using advanced type
system features, such as type families (Type families) or GADTs
(Generalised Algebraic Data Types (GADTs)), this simple kind system is insufficient, and fails to
prevent simple errors. Consider the example of typelevel natural
numbers, and lengthindexed vectors:
data Ze
data Su n
data Vec :: * > * > * where
Nil :: Vec a Ze
Cons :: a > Vec a n > Vec a (Su n)
The kind of Vec
is * > * > *
. This means that eg.
Vec Int Char
is a wellkinded type, even though this is not what we
intend when defining lengthindexed vectors.
With XDataKinds
, the example above can then be rewritten to:
data Nat = Ze  Su Nat
data Vec :: * > Nat > * where
Nil :: Vec a Ze
Cons :: a > Vec a n > Vec a (Su n)
With the improved kind of Vec
, things like Vec Int Char
are now
illkinded, and GHC will report an error.
9.10.2. Overview¶
With XDataKinds
, GHC automatically promotes every suitable datatype
to be a kind, and its (value) constructors to be type constructors. The
following types
data Nat = Ze  Su Nat
data List a = Nil  Cons a (List a)
data Pair a b = Pair a b
data Sum a b = L a  R b
give rise to the following kinds and type constructors:
Nat :: BOX
Ze :: Nat
Su :: Nat > Nat
List k :: BOX
Nil :: List k
Cons :: k > List k > List k
Pair k1 k2 :: BOX
Pair :: k1 > k2 > Pair k1 k2
Sum k1 k2 :: BOX
L :: k1 > Sum k1 k2
R :: k2 > Sum k1 k2
where BOX
is the (unique) sort that classifies kinds. Note that
List
, for instance, does not get sort BOX > BOX
, because we do
not further classify kinds; all kinds have sort BOX
.
The following restrictions apply to promotion:
 We promote
data
types andnewtypes
, but not type synonyms, or type/data families (Type families).  We only promote types whose kinds are of the form
* > ... > * > *
. In particular, we do not promote higherkinded datatypes such asdata Fix f = In (f (Fix f))
, or datatypes whose kinds involve promoted types such asVec :: * > Nat > *
.  We do not promote data constructors that are kind polymorphic, involve constraints, mention type or data families, or involve types that are not promotable.
9.10.3. Distinguishing between types and constructors¶
Since constructors and types share the same namespace, with promotion you can get ambiguous type names:
data P  1
data Prom = P  2
type T = P  1 or promoted 2?
In these cases, if you want to refer to the promoted constructor, you should prefix its name with a quote:
type T1 = P  1
type T2 = 'P  promoted 2
Note that promoted datatypes give rise to named kinds. Since these can never be ambiguous, we do not allow quotes in kind names.
Just as in the case of Template Haskell (Syntax), there is no way to quote a data constructor or type constructor whose second character is a single quote.
9.10.4. Promoted list and tuple types¶
With XDataKinds
, Haskell’s list and tuple types are natively
promoted to kinds, and enjoy the same convenient syntax at the type
level, albeit prefixed with a quote:
data HList :: [*] > * where
HNil :: HList '[]
HCons :: a > HList t > HList (a ': t)
data Tuple :: (*,*) > * where
Tuple :: a > b > Tuple '(a,b)
foo0 :: HList '[]
foo0 = HNil
foo1 :: HList '[Int]
foo1 = HCons (3::Int) HNil
foo2 :: HList [Int, Bool]
foo2 = ...
(Note: the declaration for HCons
also requires XTypeOperators
because of infix type operator (:')
.) For typelevel lists of two
or more elements, such as the signature of foo2
above, the quote
may be omitted because the meaning is unambiguous. But for lists of one
or zero elements (as in foo0
and foo1
), the quote is required,
because the types []
and [Int]
have existing meanings in
Haskell.
9.10.5. Promoting existential data constructors¶
Note that we do promote existential data constructors that are otherwise suitable. For example, consider the following:
data Ex :: * where
MkEx :: forall a. a > Ex
Both the type Ex
and the data constructor MkEx
get promoted,
with the polymorphic kind 'MkEx :: forall k. k > Ex
. Somewhat
surprisingly, you can write a type family to extract the member of a
typelevel existential:
type family UnEx (ex :: Ex) :: k
type instance UnEx (MkEx x) = x
At first blush, UnEx
seems poorlykinded. The return kind k
is
not mentioned in the arguments, and thus it would seem that an instance
would have to return a member of k
for any k
. However, this is
not the case. The type family UnEx
is a kindindexed type family.
The return kind k
is an implicit parameter to UnEx
. The
elaborated definitions are as follows:
type family UnEx (k :: BOX) (ex :: Ex) :: k
type instance UnEx k (MkEx k x) = x
Thus, the instance triggers only when the implicit parameter to UnEx
matches the implicit parameter to MkEx
. Because k
is actually a
parameter to UnEx
, the kind is not escaping the existential, and the
above code is valid.
See also Trac #7347.
9.10.6. Promoting type operators¶
Type operators are not promoted to the kind level. Why not? Because
*
is a kind, parsed the way identifiers are. Thus, if a programmer
tried to write Either * Bool
, would it be Either
applied to
*
and Bool
? Or would it be *
applied to Either
and
Bool
. To avoid this quagmire, we simply forbid promoting type
operators to the kind level.
9.11. TypeLevel Literals¶
GHC supports numeric and string literals at the type level, giving
convenient access to a large number of predefined typelevel constants.
Numeric literals are of kind Nat
, while string literals are of kind
Symbol
. This feature is enabled by the XDataKinds
language
extension.
The kinds of the literals and all other lowlevel operations for this
feature are defined in module GHC.TypeLits
. Note that the module
defines some typelevel operators that clash with their valuelevel
counterparts (e.g. (+)
). Import and export declarations referring to
these operators require an explicit namespace annotation (see
Explicit namespaces in import/export).
Here is an example of using typelevel numeric literals to provide a safe interface to a lowlevel function:
import GHC.TypeLits
import Data.Word
import Foreign
newtype ArrPtr (n :: Nat) a = ArrPtr (Ptr a)
clearPage :: ArrPtr 4096 Word8 > IO ()
clearPage (ArrPtr p) = ...
Here is an example of using typelevel string literals to simulate simple record operations:
data Label (l :: Symbol) = Get
class Has a l b  a l > b where
from :: a > Label l > b
data Point = Point Int Int deriving Show
instance Has Point "x" Int where from (Point x _) _ = x
instance Has Point "y" Int where from (Point _ y) _ = y
example = from (Point 1 2) (Get :: Label "x")
9.11.1. Runtime Values for TypeLevel Literals¶
Sometimes it is useful to access the valuelevel literal associated with
a typelevel literal. This is done with the functions natVal
and
symbolVal
. For example:
GHC.TypeLits> natVal (Proxy :: Proxy 2)
2
These functions are overloaded because they need to return a different result, depending on the type at which they are instantiated.
natVal :: KnownNat n => proxy n > Integer
 instance KnownNat 0
 instance KnownNat 1
 instance KnownNat 2
 ...
GHC discharges the constraint as soon as it knows what concrete
typelevel literal is being used in the program. Note that this works
only for literals and not arbitrary type expressions. For example, a
constraint of the form KnownNat (a + b)
will not be simplified to
(KnownNat a, KnownNat b)
; instead, GHC will keep the constraint as
is, until it can simplify a + b
to a constant value.
It is also possible to convert a runtime integer or string value to the
corresponding typelevel literal. Of course, the resulting type literal
will be unknown at compiletime, so it is hidden in an existential type.
The conversion may be performed using someNatVal
for integers and
someSymbolVal
for strings:
someNatVal :: Integer > Maybe SomeNat
SomeNat :: KnownNat n => Proxy n > SomeNat
The operations on strings are similar.
9.11.2. Computing With TypeLevel Naturals¶
GHC 7.8 can evaluate arithmetic expressions involving typelevel natural
numbers. Such expressions may be constructed using the typefamilies
(+), (*), (^)
for addition, multiplication, and exponentiation.
Numbers may be compared using (<=?)
, which returns a promoted
boolean value, or (<=)
, which compares numbers as a constraint. For
example:
GHC.TypeLits> natVal (Proxy :: Proxy (2 + 3))
5
At present, GHC is quite limited in its reasoning about arithmetic: it
will only evaluate the arithmetic type functions and compare the
results— in the same way that it does for any other type function. In
particular, it does not know more general facts about arithmetic, such
as the commutativity and associativity of (+)
, for example.
However, it is possible to perform a bit of “backwards” evaluation. For example, here is how we could get GHC to compute arbitrary logarithms at the type level:
lg :: Proxy base > Proxy (base ^ pow) > Proxy pow
lg _ _ = Proxy
GHC.TypeLits> natVal (lg (Proxy :: Proxy 2) (Proxy :: Proxy 8))
3
9.12. Equality constraints¶
A type context can include equality constraints of the form t1 ~ t2
,
which denote that the types t1
and t2
need to be the same. In
the presence of type families, whether two types are equal cannot
generally be decided locally. Hence, the contexts of function signatures
may include equality constraints, as in the following example:
sumCollects :: (Collects c1, Collects c2, Elem c1 ~ Elem c2) => c1 > c2 > c2
where we require that the element type of c1
and c2
are the
same. In general, the types t1
and t2
of an equality constraint
may be arbitrary monotypes; i.e., they may not contain any quantifiers,
independent of whether higherrank types are otherwise enabled.
Equality constraints can also appear in class and instance contexts. The former enable a simple translation of programs using functional dependencies into programs using family synonyms instead. The general idea is to rewrite a class declaration of the form
class C a b  a > b
to
class (F a ~ b) => C a b where
type F a
That is, we represent every functional dependency (FD) a1 .. an > b
by an FD type family F a1 .. an
and a superclass context equality
F a1 .. an ~ b
, essentially giving a name to the functional
dependency. In class instances, we define the type instances of FD
families in accordance with the class head. Method signatures are not
affected by that process.
9.12.1. The Coercible
constraint¶
The constraint Coercible t1 t2
is similar to t1 ~ t2
, but
denotes representational equality between t1
and t2
in the sense
of Roles (Roles). It is exported by
Data.Coerce, which also
contains the documentation. More details and discussion can be found in
the paper
“Safe Coercions”.
9.13. The Constraint
kind¶
Normally, constraints (which appear in types to the left of the =>
arrow) have a very restricted syntax. They can only be:
 Class constraints, e.g.
Show a
 Implicit parameter constraints, e.g.
?x::Int
(with theXImplicitParams
flag)  Equality constraints, e.g.
a ~ Int
(with theXTypeFamilies
orXGADTs
flag)
With the XConstraintKinds
flag, GHC becomes more liberal in what it
accepts as constraints in your program. To be precise, with this flag
any type of the new kind Constraint
can be used as a constraint.
The following things have kind Constraint
:
Anything which is already valid as a constraint without the flag: saturated applications to type classes, implicit parameter and equality constraints.
Tuples, all of whose component types have kind
Constraint
. So for example the type(Show a, Ord a)
is of kindConstraint
.Anything whose form is not yet known, but the user has declared to have kind
Constraint
(for which they need to import it fromGHC.Exts
). So for exampletype Foo (f :: \* > Constraint) = forall b. f b => b > b
is allowed, as well as examples involving type families:type family Typ a b :: Constraint type instance Typ Int b = Show b type instance Typ Bool b = Num b func :: Typ a b => a > b > b func = ...
Note that because constraints are just handled as types of a particular kind, this extension allows type constraint synonyms:
type Stringy a = (Read a, Show a)
foo :: Stringy a => a > (String, String > a)
foo x = (show x, read)
Presently, only standard constraints, tuples and type synonyms for those two sorts of constraint are permitted in instance contexts and superclasses (without extra flags). The reason is that permitting more general constraints can cause type checking to loop, as it would with these two programs:
type family Clsish u a
type instance Clsish () a = Cls a
class Clsish () a => Cls a where
class OkCls a where
type family OkClsish u a
type instance OkClsish () a = OkCls a
instance OkClsish () a => OkCls a where
You may write programs that use exotic sorts of constraints in instance
contexts and superclasses, but to do so you must use
XUndecidableInstances
to signal that you don’t mind if the type
checker fails to terminate.
9.14. Other type system extensions¶
9.14.1. Explicit universal quantification (forall)¶
Haskell type signatures are implicitly quantified. When the language
option XExplicitForAll
is used, the keyword forall
allows us to
say exactly what this means. For example:
g :: b > b
means this:
g :: forall b. (b > b)
The two are treated identically.
Of course forall
becomes a keyword; you can’t use forall
as a
type variable any more!
9.14.2. The context of a type signature¶
The XFlexibleContexts
flag lifts the Haskell 98 restriction that
the typeclass constraints in a type signature must have the form
(class typevariable) or (class (typevariable type1 type2 ...
typen)). With XFlexibleContexts
these type signatures are
perfectly okay
g :: Eq [a] => ...
g :: Ord (T a ()) => ...
The flag XFlexibleContexts
also lifts the corresponding restriction
on class declarations (The superclasses of a class declaration) and instance
declarations (Relaxed rules for instance contexts).
9.14.3. Ambiguous types and the ambiguity check¶
Each userwritten type signature is subjected to an ambiguity check. The ambiguity check rejects functions that can never be called; for example:
f :: C a => Int
The idea is there can be no legal calls to f
because every call will
give rise to an ambiguous constraint. Indeed, the only purpose of the
ambiguity check is to report functions that cannot possibly be called.
We could soundly omit the ambiguity check on type signatures entirely,
at the expense of delaying ambiguity errors to call sites. Indeed, the
language extension XAllowAmbiguousTypes
switches off the ambiguity
check.
Ambiguity can be subtle. Consider this example which uses functional dependencies:
class D a b  a > b where ..
h :: D Int b => Int
The Int
may well fix b
at the call site, so that signature
should not be rejected. Moreover, the dependencies might be hidden.
Consider
class X a b where ...
class D a b  a > b where ...
instance D a b => X [a] b where...
h :: X a b => a > a
Here h
‘s type looks ambiguous in b
, but here’s a legal call:
...(h [True])...
That gives rise to a (X [Bool] beta)
constraint, and using the
instance means we need (D Bool beta)
and that fixes beta
via
D
‘s fundep!
Behind all these special cases there is a simple guiding principle. Consider
f :: type
f = ...blah...
g :: type
g = f
You would think that the definition of g
would surely typecheck!
After all f
has exactly the same type, and g=f
. But in fact
f
‘s type is instantiated and the instantiated constraints are solved
against the constraints bound by g
‘s signature. So, in the case an
ambiguous type, solving will fail. For example, consider the earlier
definition f :: C a => Int
:
f :: C a => Int
f = ...blah...
g :: C a => Int
g = f
In g
‘s definition, we’ll instantiate to (C alpha)
and try to
deduce (C alpha)
from (C a)
, and fail.
So in fact we use this as our definition of ambiguity: a type ty
is ambiguous if and only if ((undefined :: ty) :: ty)
would fail to
typecheck. We use a very similar test for inferred types, to ensure
that they too are unambiguous.
Switching off the ambiguity check. Even if a function is has an ambiguous type according the “guiding principle”, it is possible that the function is callable. For example:
class D a b where ...
instance D Bool b where ...
strange :: D a b => a > a
strange = ...blah...
foo = strange True
Here strange
‘s type is ambiguous, but the call in foo
is OK
because it gives rise to a constraint (D Bool beta)
, which is
soluble by the (D Bool b)
instance. So the language extension
XAllowAmbiguousTypes
allows you to switch off the ambiguity check.
But even with ambiguity checking switched off, GHC will complain about a
function that can never be called, such as this one:
f :: (Int ~ Bool) => a > a
Note
A historical note. GHC used to impose some more restrictive and less
principled conditions on type signatures. For type type
forall tv1..tvn (c1, ...,cn) => type
GHC used to require (a) that
each universally quantified type variable tvi
must be “reachable”
from type
, and (b) that every constraint ci
mentions at least
one of the universally quantified type variables tvi
. These adhoc
restrictions are completely subsumed by the new ambiguity check.
9.14.4. Implicit parameters¶
Implicit parameters are implemented as described in “Implicit parameters: dynamic scoping with static types”, J Lewis, MB Shields, E Meijer, J Launchbury, 27th ACM Symposium on Principles of Programming Languages (POPL‘00), Boston, Jan 2000. (Most of the following, still rather incomplete, documentation is due to Jeff Lewis.)
Implicit parameter support is enabled with the option
XImplicitParams
.
A variable is called dynamically bound when it is bound by the calling context of a function and statically bound when bound by the callee’s context. In Haskell, all variables are statically bound. Dynamic binding of variables is a notion that goes back to Lisp, but was later discarded in more modern incarnations, such as Scheme. Dynamic binding can be very confusing in an untyped language, and unfortunately, typed languages, in particular HindleyMilner typed languages like Haskell, only support static scoping of variables.
However, by a simple extension to the type class system of Haskell, we
can support dynamic binding. Basically, we express the use of a
dynamically bound variable as a constraint on the type. These
constraints lead to types of the form (?x::t') => t
, which says
“this function uses a dynamicallybound variable ?x
of type t'
”.
For example, the following expresses the type of a sort function,
implicitly parameterised by a comparison function named cmp
.
sort :: (?cmp :: a > a > Bool) => [a] > [a]
The dynamic binding constraints are just a new form of predicate in the type class system.
An implicit parameter occurs in an expression using the special form
?x
, where x
is any valid identifier (e.g. ord ?x
is a valid
expression). Use of this construct also introduces a new dynamicbinding
constraint in the type of the expression. For example, the following
definition shows how we can define an implicitly parameterised sort
function in terms of an explicitly parameterised sortBy
function:
sortBy :: (a > a > Bool) > [a] > [a]
sort :: (?cmp :: a > a > Bool) => [a] > [a]
sort = sortBy ?cmp
9.14.4.1. Implicitparameter type constraints¶
Dynamic binding constraints behave just like other type class
constraints in that they are automatically propagated. Thus, when a
function is used, its implicit parameters are inherited by the function
that called it. For example, our sort
function might be used to pick
out the least value in a list:
least :: (?cmp :: a > a > Bool) => [a] > a
least xs = head (sort xs)
Without lifting a finger, the ?cmp
parameter is propagated to become
a parameter of least
as well. With explicit parameters, the default
is that parameters must always be explicit propagated. With implicit
parameters, the default is to always propagate them.
An implicitparameter type constraint differs from other type class
constraints in the following way: All uses of a particular implicit
parameter must have the same type. This means that the type of
(?x, ?x)
is (?x::a) => (a,a)
, and not
(?x::a, ?x::b) => (a, b)
, as would be the case for type class
constraints.
You can’t have an implicit parameter in the context of a class or instance declaration. For example, both these declarations are illegal:
class (?x::Int) => C a where ...
instance (?x::a) => Foo [a] where ...
Reason: exactly which implicit parameter you pick up depends on exactly where you invoke a function. But the “invocation” of instance declarations is done behind the scenes by the compiler, so it’s hard to figure out exactly where it is done. Easiest thing is to outlaw the offending types.
Implicitparameter constraints do not cause ambiguity. For example, consider:
f :: (?x :: [a]) => Int > Int
f n = n + length ?x
g :: (Read a, Show a) => String > String
g s = show (read s)
Here, g
has an ambiguous type, and is rejected, but f
is fine.
The binding for ?x
at f
‘s call site is quite unambiguous, and
fixes the type a
.
9.14.4.2. Implicitparameter bindings¶
An implicit parameter is bound using the standard let
or where
binding forms. For example, we define the min
function by binding
cmp
.
min :: [a] > a
min = let ?cmp = (<=) in least
A group of implicitparameter bindings may occur anywhere a normal group
of Haskell bindings can occur, except at top level. That is, they can
occur in a let
(including in a list comprehension, or donotation,
or pattern guards), or a where
clause. Note the following points:
An implicitparameter binding group must be a collection of simple bindings to implicitstyle variables (no functionstyle bindings, and no type signatures); these bindings are neither polymorphic or recursive.
You may not mix implicitparameter bindings with ordinary bindings in a single
let
expression; use two nestedlet
s instead. (In the case ofwhere
you are stuck, since you can’t nestwhere
clauses.)You may put multiple implicitparameter bindings in a single binding group; but they are not treated as a mutually recursive group (as ordinary
let
bindings are). Instead they are treated as a nonrecursive group, simultaneously binding all the implicit parameter. The bindings are not nested, and may be reordered without changing the meaning of the program. For example, consider:f t = let { ?x = t; ?y = ?x+(1::Int) } in ?x + ?y
The use of
?x
in the binding for?y
does not “see” the binding for?x
, so the type off
isf :: (?x::Int) => Int > Int
9.14.4.3. Implicit parameters and polymorphic recursion¶
Consider these two definitions:
len1 :: [a] > Int
len1 xs = let ?acc = 0 in len_acc1 xs
len_acc1 [] = ?acc
len_acc1 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc1 xs

len2 :: [a] > Int
len2 xs = let ?acc = 0 in len_acc2 xs
len_acc2 :: (?acc :: Int) => [a] > Int
len_acc2 [] = ?acc
len_acc2 (x:xs) = let ?acc = ?acc + (1::Int) in len_acc2 xs
The only difference between the two groups is that in the second group
len_acc
is given a type signature. In the former case, len_acc1
is monomorphic in its own righthand side, so the implicit parameter
?acc
is not passed to the recursive call. In the latter case,
because len_acc2
has a type signature, the recursive call is made to
the polymorphic version, which takes ?acc
as an implicit
parameter. So we get the following results in GHCi:
Prog> len1 "hello"
0
Prog> len2 "hello"
5
Adding a type signature dramatically changes the result! This is a rather counterintuitive phenomenon, worth watching out for.
9.14.4.4. Implicit parameters and monomorphism¶
GHC applies the dreaded Monomorphism Restriction (section 4.5.5 of the Haskell Report) to implicit parameters. For example, consider:
f :: Int > Int
f v = let ?x = 0 in
let y = ?x + v in
let ?x = 5 in
y
Since the binding for y
falls under the Monomorphism Restriction it
is not generalised, so the type of y
is simply Int
, not
(?x::Int) => Int
. Hence, (f 9)
returns result 9
. If you add
a type signature for y
, then y
will get type
(?x::Int) => Int
, so the occurrence of y
in the body of the
let
will see the inner binding of ?x
, so (f 9)
will return
14
.
9.14.4.5. Special implicit parameters¶
GHC treats implicit parameters of type GHC.Types.CallStack
specially, by resolving them to the current location in the program.
Consider:
f :: String
f = show (?loc :: CallStack)
GHC will automatically resolve ?loc
to its source location. If
another implicit parameter with type CallStack
is in scope, GHC will
append the two locations, creating an explicit callstack. For example:
f :: (?stk :: CallStack) => String
f = show (?stk :: CallStack)
will produce the location of ?stk
, followed by f
‘s callsite.
Note that the name of the implicit parameter does not matter (we used
?loc
above), GHC will solve any implicit parameter with the right
type. The name does, however, matter when pushing new locations onto
existing stacks. Consider:
f :: (?stk :: CallStack) => String
f = show (?loc :: CallStack)
When we call f
, the stack will include the use of ?loc
, but not
the call to f
; in this case the names must match.
CallStack
is kept abstract, but GHC provides a function
getCallStack :: CallStack > [(String, SrcLoc)]
to access the individual callsites in the stack. The String
is the
name of the function that was called, and the SrcLoc
provides the
package, module, and file name, as well as the line and column numbers.
The stack will never be empty, as the first callsite will be the
location at which the implicit parameter was used. GHC will also never
infer ?loc :: CallStack
as a type constraint, which means that
functions must explicitly ask to be told about their callsites.
A potential “gotcha” when using implicit CallStack
s is that the
:type
command in GHCi will not report the ?loc :: CallStack
constraint, as the typechecker will immediately solve it. Use :info
instead to print the unsolved type.
9.14.5. Explicitlykinded quantification¶
Haskell infers the kind of each type variable. Sometimes it is nice to be able to give the kind explicitly as (machinechecked) documentation, just as it is nice to give a type signature for a function. On some occasions, it is essential to do so. For example, in his paper “Restricted Data Types in Haskell” (Haskell Workshop 1999) John Hughes had to define the data type:
data Set cxt a = Set [a]
 Unused (cxt a > ())
The only use for the Unused
constructor was to force the correct
kind for the type variable cxt
.
GHC now instead allows you to specify the kind of a type variable
directly, wherever a type variable is explicitly bound, with the flag
XKindSignatures
.
This flag enables kind signatures in the following places:
data
declarations:data Set (cxt :: * > *) a = Set [a]
type
declarations:type T (f :: * > *) = f Int
class
declarations:class (Eq a) => C (f :: * > *) a where ...
forall
‘s in type signatures:f :: forall (cxt :: * > *). Set cxt Int
The parentheses are required. Some of the spaces are required too, to
separate the lexemes. If you write “(f::*>*)
” you will get a parse
error, because “::*>*
” is a single lexeme in Haskell.
As part of the same extension, you can put kind annotations in types as well. Thus:
f :: (Int :: *) > Int
g :: forall a. a > (a :: *)
The syntax is
atype ::= '(' ctype '::' kind ')
The parentheses are required.
9.14.6. Arbitraryrank polymorphism¶
GHC’s type system supports arbitraryrank explicit universal quantification in types. For example, all the following types are legal:
f1 :: forall a b. a > b > a
g1 :: forall a b. (Ord a, Eq b) => a > b > a
f2 :: (forall a. a>a) > Int > Int
g2 :: (forall a. Eq a => [a] > a > Bool) > Int > Int
f3 :: ((forall a. a>a) > Int) > Bool > Bool
f4 :: Int > (forall a. a > a)
Here, f1
and g1
are rank1 types, and can be written in standard
Haskell (e.g. f1 :: a>b>a
). The forall
makes explicit the
universal quantification that is implicitly added by Haskell.
The functions f2
and g2
have rank2 types; the forall
is on
the left of a function arrow. As g2
shows, the polymorphic type on
the left of the function arrow can be overloaded.
The function f3
has a rank3 type; it has rank2 types on the left
of a function arrow.
The language option XRankNTypes
(which implies
XExplicitForAll
, Explicit universal quantification (forall)) enables higherrank
types. That is, you can nest forall
s arbitrarily deep in function
arrows. For example, a foralltype (also called a “type scheme”),
including a typeclass context, is legal:
 On the left or right (see
f4
, for example) of a function arrow  As the argument of a constructor, or type of a field, in a data type
declaration. For example, any of the
f1, f2, f3, g1, g2
above would be valid field type signatures.  As the type of an implicit parameter
 In a pattern type signature (see Lexically scoped type variables)
The XRankNTypes
option is also required for any type with a
forall
or context to the right of an arrow (e.g.
f :: Int > forall a. a>a
, or g :: Int > Ord a => a > a
).
Such types are technically rank 1, but are clearly not Haskell98, and
an extra flag did not seem worth the bother.
In particular, in data
and newtype
declarations the constructor
arguments may be polymorphic types of any rank; see examples in
Examples. Note that the declared types are nevertheless always
monomorphic. This is important because by default GHC will not
instantiate type variables to a polymorphic type
(Impredicative polymorphism).
The obsolete language options XPolymorphicComponents
and
XRank2Types
are synonyms for XRankNTypes
. They used to specify
finer distinctions that GHC no longer makes. (They should really elicit
a deprecation warning, but they don’t, purely to avoid the need to
library authors to change their old flags specifications.)
9.14.6.1. Examples¶
These are examples of data
and newtype
declarations whose data
constructors have polymorphic argument types:
data T a = T1 (forall b. b > b > b) a
data MonadT m = MkMonad { return :: forall a. a > m a,
bind :: forall a b. m a > (a > m b) > m b
}
newtype Swizzle = MkSwizzle (forall a. Ord a => [a] > [a])
The constructors have rank2 types:
T1 :: forall a. (forall b. b > b > b) > a > T a
MkMonad :: forall m. (forall a. a > m a)
> (forall a b. m a > (a > m b) > m b)
> MonadT m
MkSwizzle :: (forall a. Ord a => [a] > [a]) > Swizzle
In earlier versions of GHC, it was possible to omit the forall
in
the type of the constructor if there was an explicit context. For
example:
newtype Swizzle' = MkSwizzle' (Ord a => [a] > [a])
As of GHC 7.10, this is deprecated. The
fwarncontextquantification
flag detects this situation and issues
a warning. In GHC 7.12, declarations such as MkSwizzle'
will cause
an outofscope error.
As for type signatures, implicit quantification happens for nonoverloaded types too. So if you write this:
f :: (a > a) > a
it’s just as if you had written this:
f :: forall a. (a > a) > a
That is, since the type variable a
isn’t in scope, it’s implicitly
universally quantified.
You construct values of types T1, MonadT, Swizzle
by applying the
constructor to suitable values, just as usual. For example,
a1 :: T Int
a1 = T1 (\xy>x) 3
a2, a3 :: Swizzle
a2 = MkSwizzle sort
a3 = MkSwizzle reverse
a4 :: MonadT Maybe
a4 = let r x = Just x
b m k = case m of
Just y > k y
Nothing > Nothing
in
MkMonad r b
mkTs :: (forall b. b > b > b) > a > [T a]
mkTs f x y = [T1 f x, T1 f y]
The type of the argument can, as usual, be more general than the type
required, as (MkSwizzle reverse)
shows. (reverse
does not need
the Ord
constraint.)
When you use pattern matching, the bound variables may now have polymorphic types. For example:
f :: T a > a > (a, Char)
f (T1 w k) x = (w k x, w 'c' 'd')
g :: (Ord a, Ord b) => Swizzle > [a] > (a > b) > [b]
g (MkSwizzle s) xs f = s (map f (s xs))
h :: MonadT m > [m a] > m [a]
h m [] = return m []
h m (x:xs) = bind m x $ \y >
bind m (h m xs) $ \ys >
return m (y:ys)
In the function h
we use the record selectors return
and
bind
to extract the polymorphic bind and return functions from the
MonadT
data structure, rather than using pattern matching.
9.14.6.2. Type inference¶
In general, type inference for arbitraryrank types is undecidable. GHC uses an algorithm proposed by Odersky and Laufer (“Putting type annotations to work”, POPL‘96) to get a decidable algorithm by requiring some help from the programmer. We do not yet have a formal specification of “some help” but the rule is this:
For a lambdabound or casebound variable, x, either the programmer provides an explicit polymorphic type for x, or GHC’s type inference will assume that x’s type has no foralls in it.
What does it mean to “provide” an explicit type for x? You can do that by giving a type signature for x directly, using a pattern type signature (Lexically scoped type variables), thus:
\ f :: (forall a. a>a) > (f True, f 'c')
Alternatively, you can give a type signature to the enclosing context, which GHC can “push down” to find the type for the variable:
(\ f > (f True, f 'c')) :: (forall a. a>a) > (Bool,Char)
Here the type signature on the expression can be pushed inwards to give a type signature for f. Similarly, and more commonly, one can give a type signature for the function itself:
h :: (forall a. a>a) > (Bool,Char)
h f = (f True, f 'c')
You don’t need to give a type signature if the lambda bound variable is a constructor argument. Here is an example we saw earlier:
f :: T a > a > (a, Char)
f (T1 w k) x = (w k x, w 'c' 'd')
Here we do not need to give a type signature to w
, because it is an
argument of constructor T1
and that tells GHC all it needs to know.
9.14.6.3. Implicit quantification¶
GHC performs implicit quantification as follows. At the top level
(only) of userwritten types, if and only if there is no explicit
forall
, GHC finds all the type variables mentioned in the type that
are not already in scope, and universally quantifies them. For example,
the following pairs are equivalent:
f :: a > a
f :: forall a. a > a
g (x::a) = let
h :: a > b > b
h x y = y
in ...
g (x::a) = let
h :: forall b. a > b > b
h x y = y
in ...
Notice that GHC does not find the innermost possible quantification point. For example:
f :: (a > a) > Int
 MEANS
f :: forall a. (a > a) > Int
 NOT
f :: (forall a. a > a) > Int
g :: (Ord a => a > a) > Int
 MEANS the illegal type
g :: forall a. (Ord a => a > a) > Int
 NOT
g :: (forall a. Ord a => a > a) > Int
The latter produces an illegal type, which you might think is silly, but
at least the rule is simple. If you want the latter type, you can write
your forall
s explicitly. Indeed, doing so is strongly advised for
rank2 types.
9.14.7. Impredicative polymorphism¶
In general, GHC will only instantiate a polymorphic function at a monomorphic type (one with no foralls). For example,
runST :: (forall s. ST s a) > a
id :: forall b. b > b
foo = id runST  Rejected
The definition of foo
is rejected because one would have to
instantiate id
‘s type with b := (forall s. ST s a) > a
, and
that is not allowed. Instanting polymorpic type variables with
polymorphic types is called impredicative polymorphism.
GHC has extremely flaky support for impredicative polymorphism,
enabled with XImpredicativeTypes
. If it worked, this would mean
that you could call a polymorphic function at a polymorphic type, and
parameterise data structures over polymorphic types. For example:
f :: Maybe (forall a. [a] > [a]) > Maybe ([Int], [Char])
f (Just g) = Just (g [3], g "hello")
f Nothing = Nothing
Notice here that the Maybe
type is parameterised by the
polymorphic type (forall a. [a] > [a])
. However the extension
should be considered highly experimental, and certainly unsupported.
You are welcome to try it, but please don’t rely on it working
consistently, or working the same in subsequent releases. See
this wiki page for more details.
If you want impredicative polymorphism, the main workaround is to use a
newtype wrapper. The id runST
example can be written using theis
workaround like this:
runST :: (forall s. ST s a) > a
id :: forall b. b > b
nwetype Wrap a = Wrap { unWrap :: (forall s. ST s a) > a }
foo :: (forall s. ST s a) > a
foo = unWrap (id (Wrap runST))
 Here id is called at monomorphic type (Wrap a)
9.14.8. Lexically scoped type variables¶
GHC supports lexically scoped type variables, without which some type signatures are simply impossible to write. For example:
f :: forall a. [a] > [a]
f xs = ys ++ ys
where
ys :: [a]
ys = reverse xs
The type signature for f
brings the type variable a
into scope,
because of the explicit forall
(Declaration type signatures). The type
variables bound by a forall
scope over the entire definition of the
accompanying value declaration. In this example, the type variable a
scopes over the whole definition of f
, including over the type
signature for ys
. In Haskell 98 it is not possible to declare a type
for ys
; a major benefit of scoped type variables is that it becomes
possible to do so.
Lexicallyscoped type variables are enabled by
XScopedTypeVariables
. This flag implies XRelaxedPolyRec
.
9.14.8.1. Overview¶
The design follows the following principles
 A scoped type variable stands for a type variable, and not for a type. (This is a change from GHC’s earlier design.)
 Furthermore, distinct lexical type variables stand for distinct type variables. This means that every programmerwritten type signature (including one that contains free scoped type variables) denotes a rigid type; that is, the type is fully known to the type checker, and no inference is involved.
 Lexical type variables may be alpharenamed freely, without changing the program.
A lexically scoped type variable can be bound by:
 A declaration type signature (Declaration type signatures)
 An expression type signature (Expression type signatures)
 A pattern type signature (Pattern type signatures)
 Class and instance declarations (Class and instance declarations)
In Haskell, a programmerwritten type signature is implicitly quantified
over its free type variables (Section
4.1.2 of
the Haskell Report). Lexically scoped type variables affect this
implicit quantification rules as follows: any type variable that is in
scope is not universally quantified. For example, if type variable
a
is in scope, then
(e :: a > a) means (e :: a > a)
(e :: b > b) means (e :: forall b. b>b)
(e :: a > b) means (e :: forall b. a>b)
9.14.8.2. Declaration type signatures¶
A declaration type signature that has explicit quantification (using
forall
) brings into scope the explicitlyquantified type variables,
in the definition of the named function. For example:
f :: forall a. [a] > [a]
f (x:xs) = xs ++ [ x :: a ]
The “forall a
” brings “a
” into scope in the definition of
“f
”.
This only happens if:
The quantification in
f
‘s type signature is explicit. For example:g :: [a] > [a] g (x:xs) = xs ++ [ x :: a ]
This program will be rejected, because “
a
” does not scope over the definition of “g
”, so “x::a
” means “x::forall a. a
” by Haskell’s usual implicit quantification rules.The signature gives a type for a function binding or a bare variable binding, not a pattern binding. For example:
f1 :: forall a. [a] > [a] f1 (x:xs) = xs ++ [ x :: a ]  OK f2 :: forall a. [a] > [a] f2 = \(x:xs) > xs ++ [ x :: a ]  OK f3 :: forall a. [a] > [a] Just f3 = Just (\(x:xs) > xs ++ [ x :: a ])  Not OK!
The binding for
f3
is a pattern binding, and so its type signature does not bringa
into scope. Howeverf1
is a function binding, andf2
binds a bare variable; in both cases the type signature bringsa
into scope.
9.14.8.3. Expression type signatures¶
An expression type signature that has explicit quantification (using
forall
) brings into scope the explicitlyquantified type variables,
in the annotated expression. For example:
f = runST ( (op >>= \(x :: STRef s Int) > g x) :: forall s. ST s Bool )
Here, the type signature forall s. ST s Bool
brings the type
variable s
into scope, in the annotated expression
(op >>= \(x :: STRef s Int) > g x)
.
9.14.8.4. Pattern type signatures¶
A type signature may occur in any pattern; this is a pattern type signature. For example:
 f and g assume that 'a' is already in scope
f = \(x::Int, y::a) > x
g (x::a) = x
h ((x,y) :: (Int,Bool)) = (y,x)
In the case where all the type variables in the pattern type signature are already in scope (i.e. bound by the enclosing context), matters are simple: the signature simply constrains the type of the pattern in the obvious way.
Unlike expression and declaration type signatures, pattern type signatures are not implicitly generalised. The pattern in a pattern binding may only mention type variables that are already in scope. For example:
f :: forall a. [a] > (Int, [a])
f xs = (n, zs)
where
(ys::[a], n) = (reverse xs, length xs)  OK
zs::[a] = xs ++ ys  OK
Just (v::b) = ...  Not OK; b is not in scope
Here, the pattern signatures for ys
and zs
are fine, but the one
for v
is not because b
is not in scope.
However, in all patterns other than pattern bindings, a pattern type signature may mention a type variable that is not in scope; in this case, the signature brings that type variable into scope. This is particularly important for existential data constructors. For example:
data T = forall a. MkT [a]
k :: T > T
k (MkT [t::a]) = MkT t3
where
t3::[a] = [t,t,t]
Here, the pattern type signature (t::a)
mentions a lexical type
variable that is not already in scope. Indeed, it cannot already be in
scope, because it is bound by the pattern match. GHC’s rule is that in
this situation (and only then), a pattern type signature can mention a
type variable that is not already in scope; the effect is to bring it
into scope, standing for the existentiallybound type variable.
When a pattern type signature binds a type variable in this way, GHC insists that the type variable is bound to a rigid, or fullyknown, type variable. This means that any userwritten type signature always stands for a completely known type.
If all this seems a little odd, we think so too. But we must have some way to bring such type variables into scope, else we could not name existentiallybound type variables in subsequent type signatures.
This is (now) the only situation in which a pattern type signature is
allowed to mention a lexical variable that is not already in scope. For
example, both f
and g
would be illegal if a
was not already
in scope.
9.14.8.5. Class and instance declarations¶
The type variables in the head of a class
or instance
declaration scope over the methods defined in the where
part. You do
not even need an explicit forall
. For example:
class C a where
op :: [a] > a
op xs = let ys::[a]
ys = reverse xs
in
head ys
instance C b => C [b] where
op xs = reverse (head (xs :: [[b]]))
9.14.9. Bindings and generalisation¶
9.14.9.1. Switching off the dreaded Monomorphism Restriction¶
Haskell’s monomorphism restriction (see Section
4.5.5 of
the Haskell Report) can be completely switched off by
XNoMonomorphismRestriction
. Since GHC 7.8.1, the monomorphism
restriction is switched off by default in GHCi’s interactive options
(see Setting options for interactive evaluation only).
9.14.9.2. Generalised typing of mutually recursive bindings¶
The Haskell Report specifies that a group of bindings (at top level, or
in a let
or where
) should be sorted into stronglyconnected
components, and then typechecked in dependency order
(Haskell Report, Section
4.5.1). As
each group is typechecked, any binders of the group that have an
explicit type signature are put in the type environment with the
specified polymorphic type, and all others are monomorphic until the
group is generalised (Haskell Report, Section
4.5.2).
Following a suggestion of Mark Jones, in his paper Typing Haskell in
Haskell, GHC implements a
more general scheme. If XRelaxedPolyRec
is specified: the
dependency analysis ignores references to variables that have an
explicit type signature. As a result of this refined dependency
analysis, the dependency groups are smaller, and more bindings will
typecheck. For example, consider:
f :: Eq a => a > Bool
f x = (x == x)  g True  g "Yes"
g y = (y <= y)  f True
This is rejected by Haskell 98, but under Jones’s scheme the definition
for g
is typechecked first, separately from that for f
, because
the reference to f
in g
‘s right hand side is ignored by the
dependency analysis. Then g
‘s type is generalised, to get
g :: Ord a => a > Bool
Now, the definition for f
is typechecked, with this type for g
in the type environment.
The same refined dependency analysis also allows the type signatures of
mutuallyrecursive functions to have different contexts, something that
is illegal in Haskell 98 (Section 4.5.2, last sentence). With
XRelaxedPolyRec
GHC only insists that the type signatures of a
refined group have identical type signatures; in practice this means
that only variables bound by the same pattern binding must have the same
context. For example, this is fine:
f :: Eq a => a > Bool
f x = (x == x)  g True
g :: Ord a => a > Bool
g y = (y <= y)  f True
9.14.9.3. Letgeneralisation¶
An MLstyle language usually generalises the type of any let
bound or
where
bound variable, so that it is as polymorphic as possible. With the
flag XMonoLocalBinds
GHC implements a slightly more conservative
policy, using the following rules:
 A variable is closed if and only if
 the variable is letbound
 one of the following holds:
 the variable has an explicit type signature that has no free type variables, or
 its binding group is fully generalised (see next bullet)
 A binding group is fully generalised if and only if
 each of its free variables is either imported or closed, and
 the binding is not affected by the monomorphism restriction (Haskell Report, Section 4.5.5)
For example, consider
f x = x + 1
g x = let h y = f y * 2
k z = z+x
in h x + k x
Here f
is generalised because it has no free variables; and its
binding group is unaffected by the monomorphism restriction; and hence
f
is closed. The same reasoning applies to g
, except that it has
one closed free variable, namely f
. Similarly h
is closed, even
though it is not bound at top level, because its only free variable
f
is closed. But k
is not closed, because it mentions x
which is not closed (because it is not letbound).
Notice that a toplevel binding that is affected by the monomorphism restriction is not closed, and hence may in turn prevent generalisation of bindings that mention it.
The rationale for this more conservative strategy is given in the papers “Let should not be generalised” and “Modular type inference with local assumptions”, and a related blog post.
The flag XMonoLocalBinds
is implied by XTypeFamilies
and
XGADTs
. You can switch it off again with XNoMonoLocalBinds
but
type inference becomes less predicatable if you do so. (Read the
papers!)
9.15. Typed Holes¶
Typed holes are a feature of GHC that allows special placeholders
written with a leading underscore (e.g., “_
”, “_foo
”,
“_bar
”), to be used as expressions. During compilation these holes
will generate an error message that describes which type is expected at
the hole’s location, information about the origin of any free type
variables, and a list of local bindings that might help fill the hole
with actual code. Typed holes are always enabled in GHC.
The goal of typed holes is to help with writing Haskell code rather than to change the type system. Typed holes can be used to obtain extra information from the type checker, which might otherwise be hard to get. Normally, using GHCi, users can inspect the (inferred) type signatures of all toplevel bindings. However, this method is less convenient with terms that are not defined on toplevel or inside complex expressions. Holes allow the user to check the type of the term they are about to write.
For example, compiling the following module with GHC:
f :: a > a
f x = _
will fail with the following error:
hole.hs:2:7:
Found hole `_' with type: a
Where: `a' is a rigid type variable bound by
the type signature for f :: a > a at hole.hs:1:6
Relevant bindings include
f :: a > a (bound at hole.hs:2:1)
x :: a (bound at hole.hs:2:3)
In the expression: _
In an equation for `f': f x = _
Here are some more details:
A “
Found hole
” error usually terminates compilation, like any other type error. After all, you have omitted some code from your program. Nevertheless, you can run and test a piece of code containing holes, by using thefdefertypedholes
flag. This flag defers errors produced by typed holes until runtime, and converts them into compiletime warnings. These warnings can in turn be suppressed entirely byfnowarntypedholes
).The result is that a hole will behave like
undefined
, but with the added benefits that it shows a warning at compile time, and will show the same message if it gets evaluated at runtime. This behaviour follows that of thefdefertypeerrors
option, which impliesfdefertypedholes
. See Deferring type errors to runtime.All unbound identifiers are treated as typed holes, whether or not they start with an underscore. The only difference is in the error message:
cons z = z : True : _x : y
yields the errors
Foo.hs:5:15: error: Found hole: _x :: Bool Relevant bindings include p :: Bool (bound at Foo.hs:3:6) cons :: Bool > [Bool] (bound at Foo.hs:3:1) Foo.hs:5:20: error: Variable not in scope: y :: [Bool]
More information is given for explicit holes (i.e. ones that start with an underscore), than for outofscope variables, because the latter are often unintended typos, so the extra information is distracting. If you the detailed information, use a leading underscore to make explicit your intent to use a hole.
Unbound identifiers with the same name are never unified, even within the same function, but shown individually. For example:
cons = _x : _x
results in the following errors:
unbound.hs:1:8: Found hole '_x' with type: a Where: `a' is a rigid type variable bound by the inferred type of cons :: [a] at unbound.hs:1:1 Relevant bindings include cons :: [a] (bound at unbound.hs:1:1) In the first argument of `(:)', namely `_x' In the expression: _x : _x In an equation for `cons': cons = _x : _x unbound.hs:1:13: Found hole '_x' with type: [a] Arising from: an undeclared identifier `_x' at unbound.hs:1:1314 Where: `a' is a rigid type variable bound by the inferred type of cons :: [a] at unbound.hs:1:1 Relevant bindings include cons :: [a] (bound at unbound.hs:1:1) In the second argument of `(:)', namely `_x' In the expression: _x : _x In an equation for `cons': cons = _x : _x
Notice the two different types reported for the two different occurrences of
_x
.No language extension is required to use typed holes. The lexeme “
_
” was previously illegal in Haskell, but now has a more informative error message. The lexeme “_x
” is a perfectly legal variable, and its behaviour is unchanged when it is in scope. For examplef _x = _x + 1
does not elict any errors. Only a variable that is not in scope (whether or not it starts with an underscore) is treated as an error (which it always was), albeit now with a more informative error message.
Unbound data constructors used in expressions behave exactly as above. However, unbound data constructors used in patterns cannot be deferred, and instead bring compilation to a halt. (In implementation terms, they are reported by the renamer rather than the type checker.)
9.16. Partial Type Signatures¶
A partial type signature is a type signature containing special
placeholders written with a leading underscore (e.g., “_
”,
“_foo
”, “_bar
”) called wildcards. Partial type signatures are
to type signatures what Typed Holes are to expressions. During
compilation these wildcards or holes will generate an error message that
describes which type was inferred at the hole’s location, and
information about the origin of any free type variables. GHC reports
such error messages by default.
Unlike Typed Holes, which make the program incomplete and will generate errors when they are evaluated, this needn’t be the case for holes in type signatures. The type checker is capable (in most cases) of typechecking a binding with or without a type signature. A partial type signature bridges the gap between the two extremes, the programmer can choose which parts of a type to annotate and which to leave over to the typechecker to infer.
By default, the typechecker will report an error message for each hole
in a partial type signature, informing the programmer of the inferred
type. When the XPartialTypeSignatures
flag is enabled, the
typechecker will accept the inferred type for each hole, generating
warnings instead of errors. Additionally, these warnings can be silenced
with the fnowarnpartialtypesignatures
flag.
9.16.1. Syntax¶
A (partial) type signature has the following form:
forall a b .. . (C1, C2, ..) => tau
. It consists of three parts:
 The type variables:
a b ..
 The constraints:
(C1, C2, ..)
 The (mono)type:
tau
We distinguish three kinds of wildcards.
9.16.1.1. Type Wildcards¶
Wildcards occurring within the monotype (tau) part of the type signature
are type wildcards (“type” is often omitted as this is the default
kind of wildcard). Type wildcards can be instantiated to any monotype
like Bool
or Maybe [Bool]
, including functions and higherkinded
types like (Int > Bool)
or Maybe
.
not' :: Bool > _
not' x = not x
 Inferred: Bool > Bool
maybools :: _
maybools = Just [True]
 Inferred: Maybe [Bool]
just1 :: _ Int
just1 = Just 1
 Inferred: Maybe Int
filterInt :: _ > _ > [Int]
filterInt = filter  has type forall a. (a > Bool) > [a] > [a]
 Inferred: (Int > Bool) > [Int] > [Int]
For instance, the first wildcard in the type signature not'
would
produce the following error message:
Test.hs:4:17:
Found hole ‘_’ with type: Bool
To use the inferred type, enable PartialTypeSignatures
In the type signature for ‘not'’: Bool > _
When a wildcard is not instantiated to a monotype, it will be
generalised over, i.e. replaced by a fresh type variable (of which the
name will often start with w_
), e.g.
foo :: _ > _
foo x = x
 Inferred: forall w_. w_ > w_
filter' :: _
filter' = filter  has type forall a. (a > Bool) > [a] > [a]
 Inferred: (a > Bool) > [a] > [a]
9.16.1.2. Named Wildcards¶
Type wildcards can also be named by giving the underscore an identifier
as suffix, i.e. _a
. These are called named wildcards. All
occurrences of the same named wildcard within one type signature will
unify to the same type. For example:
f :: _x > _x
f ('c', y) = ('d', error "Urk")
 Inferred: forall t. (Char, t) > (Char, t)
The named wildcard forces the argument and result types to be the same.
Lacking a signature, GHC would have inferred
forall a b. (Char, a) > (Char, b)
. A named wildcard can be
mentioned in constraints, provided it also occurs in the monotype part
of the type signature to make sure that it unifies with something:
somethingShowable :: Show _x => _x > _
somethingShowable x = show x
 Inferred type: Show w_x => w_x > String
somethingShowable' :: Show _x => _x > _
somethingShowable' x = show (not x)
 Inferred type: Bool > String
Besides an extraconstraints wildcard (see
ExtraConstraints Wildcard), only named wildcards can occur in
the constraints, e.g. the _x
in Show _x
.
Named wildcards should not be confused with type variables. Even though syntactically similar, named wildcards can unify with monotypes as well as be generalised over (and behave as type variables).
In the first example above, _x
is generalised over (and is
effectively replaced by a fresh type variable w_x
). In the second
example, _x
is unified with the Bool
type, and as Bool
implements the Show
type class, the constraint Show Bool
can be
simplified away.
By default, GHC (as the Haskell 2010 standard prescribes) parses
identifiers starting with an underscore in a type as type variables. To
treat them as named wildcards, the XNamedWildCards
flag should be
enabled. The example below demonstrated the effect.
foo :: _a > _a
foo _ = False
Compiling this program without enabling XNamedWildCards
produces
the following error message complaining about the type variable _a
no matching the actual type Bool
.
Test.hs:5:9:
Couldn't match expected type ‘_a’ with actual type ‘Bool’
‘_a’ is a rigid type variable bound by
the type signature for foo :: _a > _a at Test.hs:4:8
Relevant bindings include foo :: _a > _a (bound at Test.hs:4:1)
In the expression: False
In an equation for ‘foo’: foo _ = False
Compiling this program with XNamedWildCards
enabled produces the
following error message reporting the inferred type of the named
wildcard _a
.
Test.hs:4:8: Warning:
Found hole ‘_a’ with type: Bool
In the type signature for ‘foo’: _a > _a
9.16.1.3. ExtraConstraints Wildcard¶
The third kind of wildcard is the extraconstraints wildcard. The presence of an extraconstraints wildcard indicates that an arbitrary number of extra constraints may be inferred during type checking and will be added to the type signature. In the example below, the extraconstraints wildcard is used to infer three extra constraints.
arbitCs :: _ => a > String
arbitCs x = show (succ x) ++ show (x == x)
 Inferred:
 forall a. (Enum a, Eq a, Show a) => a > String
 Error:
Test.hs:5:12:
Found hole ‘_’ with inferred constraints: (Enum a, Eq a, Show a)
To use the inferred type, enable PartialTypeSignatures
In the type signature for ‘arbitCs’: _ => a > String
An extraconstraints wildcard shouldn’t prevent the programmer from already listing the constraints he knows or wants to annotate, e.g.
 Also a correct partial type signature:
arbitCs' :: (Enum a, _) => a > String
arbitCs' x = arbitCs x
 Inferred:
 forall a. (Enum a, Show a, Eq a) => a > String
 Error:
Test.hs:9:22:
Found hole ‘_’ with inferred constraints: (Eq a, Show a)
To use the inferred type, enable PartialTypeSignatures
In the type signature for ‘arbitCs'’: (Enum a, _) => a > String
An extraconstraints wildcard can also lead to zero extra constraints to be inferred, e.g.
noCs :: _ => String
noCs = "noCs"
 Inferred: String
 Error:
Test.hs:13:9:
Found hole ‘_’ with inferred constraints: ()
To use the inferred type, enable PartialTypeSignatures
In the type signature for ‘noCs’: _ => String
As a single extraconstraints wildcard is enough to infer any number of constraints, only one is allowed in a type signature and it should come last in the list of constraints.
Extraconstraints wildcards cannot be named.
9.16.2. Where can they occur?¶
Partial type signatures are allowed for bindings, pattern and expression signatures. In all other contexts, e.g. type class or type family declarations, they are disallowed. In the following example a wildcard is used in each of the three possible contexts. Extraconstraints wildcards are not supported in pattern or expression signatures.
{# LANGUAGE ScopedTypeVariables #}
foo :: _
foo (x :: _) = (x :: _)
 Inferred: forall w_. w_ > w_
Anonymous wildcards can occur in type or data instance declarations. However, these declarations are not partial type signatures and different rules apply. See Data instance declarations for more details.
Partial type signatures can also be used in Template Haskell splices.
Declaration splices: partial type signature are fully supported.
{# LANGUAGE TemplateHaskell, NamedWildCards #} $( [d foo :: _ => _a > _a > _ foo x y = x == y] )
Expression splices: anonymous and named wildcards can be used in expression signatures. Extraconstraints wildcards are not supported, just like in regular expression signatures.
{# LANGUAGE TemplateHaskell, NamedWildCards #} $( [e foo = (Just True :: _m _) ] )
Typed expression splices: the same wildcards as in (untyped) expression splices are supported.
Pattern splices: Template Haskell doesn’t support type signatures in pattern splices. Consequently, partial type signatures are not supported either.
Type splices: only anonymous wildcards are supported in type splices. Named and extraconstraints wildcards are not.
{# LANGUAGE TemplateHaskell #} foo :: $( [t _ ] ) > a foo x = x
9.17. Deferring type errors to runtime¶
While developing, sometimes it is desirable to allow compilation to succeed even if there are type errors in the code. Consider the following case:
module Main where
a :: Int
a = 'a'
main = print "b"
Even though a
is illtyped, it is not used in the end, so if all
that we’re interested in is main
it can be useful to be able to
ignore the problems in a
.
For more motivation and details please refer to the Wiki page or the original paper.
9.17.1. Enabling deferring of type errors¶
The flag fdefertypeerrors
controls whether type errors are
deferred to runtime. Type errors will still be emitted as warnings, but
will not prevent compilation. You can use
fnowarndeferredtypeerrors
to suppress these warnings.
This flag implies the fdefertypedholes
flag, which enables this
behaviour for typed holes. Should you so wish, it is
possible to enable fdefertypeerrors
without enabling
fdefertypedholes
, by explicitly specifying
fnodefertypedholes
on the commandline after the
fdefertypeerrors
flag.
At runtime, whenever a term containing a type error would need to be
evaluated, the error is converted into a runtime exception of type
TypeError
. Note that type errors are deferred as much as possible
during runtime, but invalid coercions are never performed, even when
they would ultimately result in a value of the correct type. For
example, given the following code:
x :: Int
x = 0
y :: Char
y = x
z :: Int
z = y
evaluating z
will result in a runtime TypeError
.
9.17.2. Deferred type errors in GHCi¶
The flag fdefertypeerrors
works in GHCi as well, with one
exception: for “naked” expressions typed at the prompt, type errors
don’t get delayed, so for example:
Prelude> fst (True, 1 == 'a')
<interactive>:2:12:
No instance for (Num Char) arising from the literal `1'
Possible fix: add an instance declaration for (Num Char)
In the first argument of `(==)', namely `1'
In the expression: 1 == 'a'
In the first argument of `fst', namely `(True, 1 == 'a')'
Otherwise, in the common case of a simple type error such as typing
reverse True
at the prompt, you would get a warning and then an
immediatelyfollowing type error when the expression is evaluated.
This exception doesn’t apply to statements, as the following example demonstrates:
Prelude> let x = (True, 1 == 'a')
<interactive>:3:16: Warning:
No instance for (Num Char) arising from the literal `1'
Possible fix: add an instance declaration for (Num Char)
In the first argument of `(==)', namely `1'
In the expression: 1 == 'a'
In the expression: (True, 1 == 'a')
Prelude> fst x
True
9.18. Template Haskell¶
Template Haskell allows you to do compiletime metaprogramming in Haskell. The background to the main technical innovations is discussed in “Template Metaprogramming for Haskell” (Proc Haskell Workshop 2002).
There is a Wiki page about Template Haskell at
http://www.haskell.org/haskellwiki/Template_Haskell, and that is the
best place to look for further details. You may also consult the online
Haskell library reference
material
(look for module Language.Haskell.TH
). Many changes to the original
design are described in Notes on Template Haskell version
2.
Not all of these changes are in GHC, however.
The first example from that paper is set out below (A Template Haskell Worked Example) as a worked example to help get you started.
The documentation here describes the realisation of Template Haskell in GHC. It is not detailed enough to understand Template Haskell; see the Wiki page.
9.18.1. Syntax¶
Template Haskell has the following new syntactic constructions. You
need to use the flag XTemplateHaskell
to switch these syntactic
extensions on. Alternatively, the XTemplateHaskellQuotes
flag can
be used to enable the quotation subset of Template Haskell
(i.e. without splice syntax). The XTemplateHaskellQuotes
extension is considered safe under Safe Haskell while
XTemplateHaskell
is not.
A splice is written
$x
, wherex
is an identifier, or$(...)
, where the ”...” is an arbitrary expression. There must be no space between the “$” and the identifier or parenthesis. This use of “$” overrides its meaning as an infix operator, just as “M.x” overrides the meaning of ”.” as an infix operator. If you want the infix operator, put spaces around it.A splice can occur in place of
 an expression; the spliced expression must have type
Q Exp
 a pattern; the spliced pattern must have type
Q Pat
 a type; the spliced expression must have type
Q Type
 a list of declarations at top level; the spliced expression must
have type
Q [Dec]
Inside a splice you can only call functions defined in imported modules, not functions defined elsewhere in the same module. Note that declaration splices are not allowed anywhere except at top level (outside any other declarations).
 an expression; the spliced expression must have type
A expression quotation is written in Oxford brackets, thus:
[ ... ]
, or[e ... ]
, where the ”...” is an expression; the quotation has typeQ Exp
.[d ... ]
, where the ”...” is a list of toplevel declarations; the quotation has typeQ [Dec]
.[t ... ]
, where the ”...” is a type; the quotation has typeQ Type
.[p ... ]
, where the ”...” is a pattern; the quotation has typeQ Pat
.
See Where can they occur? for using partial type signatures in quotations.
A typed expression splice is written
$$x
, wherex
is an identifier, or$$(...)
, where the ”...” is an arbitrary expression.A typed expression splice can occur in place of an expression; the spliced expression must have type
Q (TExp a)
A typed expression quotation is written as
[ ... ]
, or[e ... ]
, where the ”...” is an expression; if the ”...” expression has typea
, then the quotation has typeQ (TExp a)
.Values of type
TExp a
may be converted to values of typeExp
using the functionunType :: TExp a > Exp
.A quasiquotation can appear in a pattern, type, expression, or declaration context and is also written in Oxford brackets:
[varid ... ]
, where the ”...” is an arbitrary string; a full description of the quasiquotation facility is given in Template Haskell Quasiquotation.
A name can be quoted with either one or two prefix single quotes:
'f
has typeName
, and names the functionf
. Similarly'C
has typeName
and names the data constructorC
. In general'
⟨thing⟩ interprets ⟨thing⟩ in an expression context.A name whose second character is a single quote (sadly) cannot be quoted in this way, because it will be parsed instead as a quoted character. For example, if the function is called
f'7
(which is a legal Haskell identifier), an attempt to quote it as'f'7
would be parsed as the character literal'f'
followed by the numeric literal7
. There is no current escape mechanism in this (unusual) situation.''T
has typeName
, and names the type constructorT
. That is,''
⟨thing⟩ interprets ⟨thing⟩ in a type context.
These
Names
can be used to construct Template Haskell expressions, patterns, declarations etc. They may also be given as an argument to thereify
function.It is possible for a splice to expand to an expression that contain names which are not in scope at the site of the splice. As an example, consider the following code:
module Bar where import Language.Haskell.TH add1 :: Int > Q Exp add1 x = [ x + 1 ]
Now consider a splice using <literal>add1</literal> in a separate module:
module Foo where import Bar two :: Int two = $(add1 1)
Template Haskell cannot know what the argument to
add1
will be at the function’s definition site, so a lifting mechanism is used to promotex
into a value of typeQ Exp
. This functionality is exposed to the user as theLift
typeclass in theLanguage.Haskell.TH.Syntax
module. If a type has aLift
instance, then any of its values can be lifted to a Template Haskell expression:class Lift t where lift :: t > Q Exp
In general, if GHC sees an expression within Oxford brackets (e.g.,
[ foo bar ]
, then GHC looks up each name within the brackets. If a name is global (e.g., supposefoo
comes from an import or a toplevel declaration), then the fully qualified name is used directly in the quotation. If the name is local (e.g., supposebar
is bound locally in the function definitionmkFoo bar = [ foo bar ]
), then GHC useslift
on it (so GHC pretends[ foo bar ]
actually contains[ foo $(lift bar) ]
). Local names, which are not in scope at splice locations, are actually evaluated when the quotation is processed.The
templatehaskell
library providesLift
instances for many common data types. Furthermore, it is possible to deriveLift
instances automatically by using theXDeriveLift
language extension. See Deriving Lift instances for more information.You may omit the
$(...)
in a toplevel declaration splice. Simply writing an expression (rather than a declaration) implies a splice. For example, you can writemodule Foo where import Bar f x = x $(deriveStuff 'f)  Uses the $(...) notation g y = y+1 deriveStuff 'g  Omits the $(...) h z = z1
This abbreviation makes toplevel declaration slices quieter and less intimidating.
Pattern splices introduce variable binders but scoping of variables in expressions inside the pattern’s scope is only checked when a splice is run. Note that pattern splices that occur outside of any quotation brackets are run at compile time. Pattern splices occurring inside a quotation bracket are not run at compile time; they are run when the bracket is spliced in, sometime later. For example,
mkPat :: Q Pat mkPat = [p (x, y) ]  in another module: foo :: (Char, String) > String foo $(mkPat) = x : z bar :: Q Exp bar = [ \ $(mkPat) > x : w ]
will fail with
z
being out of scope in the definition offoo
but it will not fail withw
being out of scope in the definition ofbar
. That will only happen whenbar
is spliced.A pattern quasiquoter may generate binders that scope over the righthand side of a definition because these binders are in scope lexically. For example, given a quasiquoter
haskell
that parses Haskell, in the following code, they
in the righthand side off
refers to they
bound by thehaskell
pattern quasiquoter, not the toplevely = 7
.y :: Int y = 7 f :: Int > Int > Int f n = \ [haskelly] > y+n
Toplevel declaration splices break up a source file into declaration groups. A declaration group is the group of declarations created by a toplevel declaration splice, plus those following it, down to but not including the next toplevel declaration splice. The first declaration group in a module includes all toplevel definitions down to but not including the first toplevel declaration splice.
Each declaration group is mutually recursive only within the group. Declaration groups can refer to definitions within previous groups, but not later ones.
Accordingly, the type environment seen by
reify
includes all the toplevel declarations up to the end of the immediately preceding declaration group, but no more.Unlike normal declaration splices, declaration quasiquoters do not cause a break. These quasiquoters are expanded before the rest of the declaration group is processed, and the declarations they generate are merged into the surrounding declaration group. Consequently, the type environment seen by
reify
from a declaration quasiquoter will not include anything from the quasiquoter’s declaration group.Concretely, consider the following code
module M where import ... f x = x $(th1 4) h y = k y y $(blah1) [qqblah] k x y = x + y $(th2 10) w z = $(blah2)
In this example
The body of
h
would be unable to refer to the functionw
.A
reify
inside the splice$(th1 ..)
would see the definition off
.A
reify
inside the splice$(blah1)
would see the definition off
, but would not see the definition ofh
.A
reify
inside the splice$(th2..)
would see the definition off
, all the bindings created by$(th1..)
, and the definition ofh
.A
reify
inside the splice$(blah2)
would see the same definitions as the splice$(th2...)
.The body of
h
is able to refer to the functionk
appearing on the other side of the declaration quasiquoter, as quasiquoters never cause a declaration group to be broken up.A
reify
inside theqq
quasiquoter would be able to see the definition off
from the preceding declaration group, but not the definitions ofh
ork
, or any definitions from subsequent declaration groups.
Expression quotations accept most Haskell language constructs. However, there are some GHCspecific extensions which expression quotations currently do not support, including
 Recursive
do
statements (see Trac #1262)  Pattern synonyms (see Trac #8761)
 Typed holes (see Trac #10267)
 Recursive
(Compared to the original paper, there are many differences of detail.
The syntax for a declaration splice uses “$
” not “splice
”. The type of
the enclosed expression must be Q [Dec]
, not [Q Dec]
. Typed expression
splices and quotations are supported.)
9.18.2. Using Template Haskell¶
The data types and monadic constructor functions for Template Haskell are in the library
Language.Haskell.THSyntax
.You can only run a function at compile time if it is imported from another module. That is, you can’t define a function in a module, and call it from within a splice in the same module. (It would make sense to do so, but it’s hard to implement.)
You can only run a function at compile time if it is imported from another module that is not part of a mutuallyrecursive group of modules that includes the module currently being compiled. Furthermore, all of the modules of the mutuallyrecursive group must be reachable by nonSOURCE imports from the module where the splice is to be run.
For example, when compiling module A, you can only run Template Haskell functions imported from B if B does not import A (directly or indirectly). The reason should be clear: to run B we must compile and run A, but we are currently typechecking A.
If you are building GHC from source, you need at least a stage2 bootstrap compiler to run Template Haskell splices and quasiquotes. A stage1 compiler will only accept regular quotes of Haskell. Reason: TH splices and quasiquotes compile and run a program, and then looks at the result. So it’s important that the program it compiles produces results whose representations are identical to those of the compiler itself.
Template Haskell works in any mode (make
, interactive
, or
fileatatime). There used to be a restriction to the former two, but
that restriction has been lifted.
9.18.3. Viewing Template Haskell generated code¶
The flag ddumpsplices
shows the expansion of all toplevel
declaration splices, both typed and untyped, as they happen. As with all
dump flags, the default is for this output to be sent to stdout. For a
nontrivial program, you may be interested in combining this with the
ddumptofile flag
(see Dumping out compiler intermediate structures. For each file using
Template Haskell, this will show the output in a .dumpsplices
file.
The flag dthdecfile
shows the expansions of all toplevel TH
declaration splices, both typed and untyped, in the file M.th.hs
where M is the name of the module being compiled. Note that other types
of splices (expressions, types, and patterns) are not shown. Application
developers can check this into their repository so that they can grep
for identifiers that were defined in Template Haskell. This is similar
to using ddumptofile
with ddumpsplices
but it always
generates a file instead of being coupled to ddumptofile
. The
format is also different: it does not show code from the original file,
instead it only shows generated code and has a comment for the splice
location of the original file.
Below is a sample output of ddumpsplices
TH_pragma.hs:(6,4)(8,26): Splicing declarations
[d foo :: Int > Int
foo x = x + 1 ]
======>
foo :: Int > Int
foo x = (x + 1)
Below is the output of the same sample using dthdecfile
 TH_pragma.hs:(6,4)(8,26): Splicing declarations
foo :: Int > Int
foo x = (x + 1)
9.18.4. A Template Haskell Worked Example¶
To help you get over the confidence barrier, try out this skeletal worked example. First cut and paste the two modules below into “Main.hs” and “Printf.hs”:
{ Main.hs }
module Main where
 Import our template "pr"
import Printf ( pr )
 The splice operator $ takes the Haskell source code
 generated at compile time by "pr" and splices it into
 the argument of "putStrLn".
main = putStrLn ( $(pr "Hello") )
{ Printf.hs }
module Printf where
 Skeletal printf from the paper.
 It needs to be in a separate module to the one where
 you intend to use it.
 Import some Template Haskell syntax
import Language.Haskell.TH
 Describe a format string
data Format = D  S  L String
 Parse a format string. This is left largely to you
 as we are here interested in building our first ever
 Template Haskell program and not in building printf.
parse :: String > [Format]
parse s = [ L s ]
 Generate Haskell source code from a parsed representation
 of the format string. This code will be spliced into
 the module which calls "pr", at compile time.
gen :: [Format] > Q Exp
gen [D] = [ \n > show n ]
gen [S] = [ \s > s ]
gen [L s] = stringE s
 Here we generate the Haskell code for the splice
 from an input format string.
pr :: String > Q Exp
pr s = gen (parse s)
Now run the compiler (here we are a Cygwin prompt on Windows):
$ ghc make XTemplateHaskell main.hs o main.exe
Run “main.exe” and here is your output:
$ ./main
Hello
9.18.5. Using Template Haskell with Profiling¶
Template Haskell relies on GHC’s builtin bytecode compiler and interpreter to run the splice expressions. The bytecode interpreter runs the compiled expression on top of the same runtime on which GHC itself is running; this means that the compiled code referred to by the interpreted expression must be compatible with this runtime, and in particular this means that object code that is compiled for profiling cannot be loaded and used by a splice expression, because profiled object code is only compatible with the profiling version of the runtime.
This causes difficulties if you have a multimodule program containing Template Haskell code and you need to compile it for profiling, because GHC cannot load the profiled object code and use it when executing the splices. Fortunately GHC provides a workaround. The basic idea is to compile the program twice:
Compile the program or library first the normal way, without
prof
.Then compile it again with
prof
, and additionally useosuf p_o
to name the object files differently (you can choose any suffix that isn’t the normal object suffix here). GHC will automatically load the object files built in the first step when executing splice expressions. If you omit theosuf
flag when building withprof
and Template Haskell is used, GHC will emit an error message.
9.18.6. Template Haskell Quasiquotation¶
Quasiquotation allows patterns and expressions to be written using programmerdefined concrete syntax; the motivation behind the extension and several examples are documented in “Why It’s Nice to be Quoted: Quasiquoting for Haskell” (Proc Haskell Workshop 2007). The example below shows how to write a quasiquoter for a simple expression language.
Here are the salient features
A quasiquote has the form
[quoter string ]
. The ⟨quoter⟩ must be the name of an imported quoter, either qualified or unqualified; it cannot be an arbitrary expression.
 The ⟨quoter⟩ cannot be “
e
”, “t
”, “d
”, or “p
”, since those overlap with Template Haskell quotations.  There must be no spaces in the token
[quoter
.  The quoted ⟨string⟩ can be arbitrary, and may contain newlines.
 The quoted ⟨string⟩ finishes at the first occurrence of the
twocharacter sequence
"]"
. Absolutely no escaping is performed. If you want to embed that character sequence in the string, you must invent your own escape convention (such as, say, using the string"~]"
instead), and make your quoter function interpret"~]"
as"]"
. One way to implement this is to compose your quoter with a preprocessing pass to perform your escape conversion. See the discussion in Trac #5348 for details.
A quasiquote may appear in place of
 An expression
 A pattern
 A type
 A toplevel declaration
(Only the first two are described in the paper.)
A quoter is a value of type
Language.Haskell.TH.Quote.QuasiQuoter
, which is defined thus:data QuasiQuoter = QuasiQuoter { quoteExp :: String > Q Exp, quotePat :: String > Q Pat, quoteType :: String > Q Type, quoteDec :: String > Q [Dec] }
That is, a quoter is a tuple of four parsers, one for each of the contexts in which a quasiquote can occur.
A quasiquote is expanded by applying the appropriate parser to the string enclosed by the Oxford brackets. The context of the quasiquote (expression, pattern, type, declaration) determines which of the parsers is called.
Unlike normal declaration splices of the form
$(...)
, declaration quasiquotes do not cause a declaration group break. See Syntax for more information.
The example below shows quasiquotation in action. The quoter expr
is bound to a value of type QuasiQuoter
defined in module Expr
.
The example makes use of an antiquoted variable n
, indicated by the
syntax 'int:n
(this syntax for antiquotation was defined by the
parser’s author, not by GHC). This binds n
to the integer value
argument of the constructor IntExpr
when pattern matching. Please
see the referenced paper for further details regarding antiquotation as
well as the description of a technique that uses SYB to leverage a
single parser of type String > a
to generate both an expression
parser that returns a value of type Q Exp
and a pattern parser that
returns a value of type Q Pat
.
Quasiquoters must obey the same stage restrictions as Template Haskell,
e.g., in the example, expr
cannot be defined in Main.hs
where it
is used, but must be imported.
{  file Main.hs  }
module Main where
import Expr
main :: IO ()
main = do { print $ eval [expr1 + 2]
; case IntExpr 1 of
{ [expr'int:n] > print n
; _ > return ()
}
}
{  file Expr.hs  }
module Expr where
import qualified Language.Haskell.TH as TH
import Language.Haskell.TH.Quote
data Expr = IntExpr Integer
 AntiIntExpr String
 BinopExpr BinOp Expr Expr
 AntiExpr String
deriving(Show, Typeable, Data)
data BinOp = AddOp
 SubOp
 MulOp
 DivOp
deriving(Show, Typeable, Data)
eval :: Expr > Integer
eval (IntExpr n) = n
eval (BinopExpr op x y) = (opToFun op) (eval x) (eval y)
where
opToFun AddOp = (+)
opToFun SubOp = ()
opToFun MulOp = (*)
opToFun DivOp = div
expr = QuasiQuoter { quoteExp = parseExprExp, quotePat = parseExprPat }
 Parse an Expr, returning its representation as
 either a Q Exp or a Q Pat. See the referenced paper
 for how to use SYB to do this by writing a single
 parser of type String > Expr instead of two
 separate parsers.
parseExprExp :: String > Q Exp
parseExprExp ...
parseExprPat :: String > Q Pat
parseExprPat ...
Now run the compiler:
$ ghc make XQuasiQuotes Main.hs o main
Run “main” and here is your output:
$ ./main
3
1
9.19. Arrow notation¶
Arrows are a generalisation of monads introduced by John Hughes. For more details, see
 “Generalising Monads to Arrows”, John Hughes, in Science of Computer Programming 37, pp. 67–111, May 2000. The paper that introduced arrows: a friendly introduction, motivated with programming examples.
 “A New Notation for Arrows”, Ross Paterson, in ICFP, Sep 2001. Introduced the notation described here.
 “Arrows and Computation”, Ross Paterson, in The Fun of Programming, Palgrave, 2003.
 “Programming with Arrows”, John Hughes, in 5th International Summer School on Advanced Functional Programming, Lecture Notes in Computer Science vol. 3622, Springer, 2004. This paper includes another introduction to the notation, with practical examples.
 “Type and Translation Rules for Arrow Notation in GHC”, Ross Paterson and Simon Peyton Jones, September 16, 2004. A terse enumeration of the formal rules used (extracted from comments in the source code).
 The arrows web page at
http://www.haskell.org/arrows/
<http://www.haskell.org/arrows/>`__.
With the XArrows
flag, GHC supports the arrow notation described in
the second of these papers, translating it using combinators from the
Control.Arrow module.
What follows is a brief introduction to the notation; it won’t make much
sense unless you’ve read Hughes’s paper.
The extension adds a new kind of expression for defining arrows:
exp10 ::= ...
 proc apat > cmd
where proc
is a new keyword. The variables of the pattern are bound
in the body of the proc
expression, which is a new sort of thing
called a command. The syntax of commands is as follows:
cmd ::= exp10 < exp
 exp10 << exp
 cmd0
with ⟨cmd⟩^{0} up to ⟨cmd⟩^{9} defined using infix operators as for expressions, and
cmd10 ::= \ apat ... apat > cmd
 let decls in cmd
 if exp then cmd else cmd
 case exp of { calts }
 do { cstmt ; ... cstmt ; cmd }
 fcmd
fcmd ::= fcmd aexp
 ( cmd )
 ( aexp cmd ... cmd )
cstmt ::= let decls
 pat < cmd
 rec { cstmt ; ... cstmt [;] }
 cmd
where ⟨calts⟩ are like ⟨alts⟩ except that the bodies are commands instead of expressions.
Commands produce values, but (like monadic computations) may yield more than one value, or none, and may do other things as well. For the most part, familiarity with monadic notation is a good guide to using commands. However the values of expressions, even monadic ones, are determined by the values of the variables they contain; this is not necessarily the case for commands.
A simple example of the new notation is the expression
proc x > f < x+1
We call this a procedure or arrow abstraction. As with a lambda
expression, the variable x
is a new variable bound within the
proc
expression. It refers to the input to the arrow. In the above
example, <
is not an identifier but an new reserved symbol used for
building commands from an expression of arrow type and an expression to
be fed as input to that arrow. (The weird look will make more sense
later.) It may be read as analogue of application for arrows. The above
example is equivalent to the Haskell expression
arr (\ x > x+1) >>> f
That would make no sense if the expression to the left of <
involves the bound variable x
. More generally, the expression to the
left of <
may not involve any local variable, i.e. a variable bound
in the current arrow abstraction. For such a situation there is a
variant <<
, as in
proc x > f x << x+1
which is equivalent to
arr (\ x > (f x, x+1)) >>> app
so in this case the arrow must belong to the ArrowApply
class. Such
an arrow is equivalent to a monad, so if you’re using this form you may
find a monadic formulation more convenient.
9.19.1. donotation for commands¶
Another form of command is a form of do
notation. For example, you
can write
proc x > do
y < f < x+1
g < 2*y
let z = x+y
t < h < x*z
returnA < t+z
You can read this much like ordinary do
notation, but with commands
in place of monadic expressions. The first line sends the value of
x+1
as an input to the arrow f
, and matches its output against
y
. In the next line, the output is discarded. The arrow returnA
is defined in the Control.Arrow module as arr
id
. The above example is treated as an abbreviation for
arr (\ x > (x, x)) >>>
first (arr (\ x > x+1) >>> f) >>>
arr (\ (y, x) > (y, (x, y))) >>>
first (arr (\ y > 2*y) >>> g) >>>
arr snd >>>
arr (\ (x, y) > let z = x+y in ((x, z), z)) >>>
first (arr (\ (x, z) > x*z) >>> h) >>>
arr (\ (t, z) > t+z) >>>
returnA
Note that variables not used later in the composition are projected out. After simplification using rewrite rules (see Rewrite rules) defined in the Control.Arrow module, this reduces to
arr (\ x > (x+1, x)) >>>
first f >>>
arr (\ (y, x) > (2*y, (x, y))) >>>
first g >>>
arr (\ (_, (x, y)) > let z = x+y in (x*z, z)) >>>
first h >>>
arr (\ (t, z) > t+z)
which is what you might have written by hand. With arrow notation, GHC keeps track of all those tuples of variables for you.
Note that although the above translation suggests that let
bound
variables like z
must be monomorphic, the actual translation
produces Core, so polymorphic variables are allowed.
It’s also possible to have mutually recursive bindings, using the new
rec
keyword, as in the following example:
counter :: ArrowCircuit a => a Bool Int
counter = proc reset > do
rec output < returnA < if reset then 0 else next
next < delay 0 < output+1
returnA < output
The translation of such forms uses the loop
combinator, so the arrow
concerned must belong to the ArrowLoop
class.
9.19.2. Conditional commands¶
In the previous example, we used a conditional expression to construct the input for an arrow. Sometimes we want to conditionally execute different commands, as in
proc (x,y) >
if f x y
then g < x+1
else h < y+2
which is translated to
arr (\ (x,y) > if f x y then Left x else Right y) >>>
(arr (\x > x+1) >>> g)  (arr (\y > y+2) >>> h)
Since the translation uses 
, the arrow concerned must belong to
the ArrowChoice
class.
There are also case
commands, like
case input of
[] > f < ()
[x] > g < x+1
x1:x2:xs > do
y < h < (x1, x2)
ys < k < xs
returnA < y:ys
The syntax is the same as for case
expressions, except that the
bodies of the alternatives are commands rather than expressions. The
translation is similar to that of if
commands.
9.19.3. Defining your own control structures¶
As we’re seen, arrow notation provides constructs, modelled on those for
expressions, for sequencing, value recursion and conditionals. But
suitable combinators, which you can define in ordinary Haskell, may also
be used to build new commands out of existing ones. The basic idea is
that a command defines an arrow from environments to values. These
environments assign values to the free local variables of the command.
Thus combinators that produce arrows from arrows may also be used to
build commands from commands. For example, the ArrowPlus
class
includes a combinator
ArrowPlus a => (<+>) :: a b c > a b c > a b c
so we can use it to build commands:
expr' = proc x > do
returnA < x
<+> do
symbol Plus < ()
y < term < ()
expr' < x + y
<+> do
symbol Minus < ()
y < term < ()
expr' < x  y
(The do
on the first line is needed to prevent the first <+> ...
from being interpreted as part of the expression on the previous line.)
This is equivalent to
expr' = (proc x > returnA < x)
<+> (proc x > do
symbol Plus < ()
y < term < ()
expr' < x + y)
<+> (proc x > do
symbol Minus < ()
y < term < ()
expr' < x  y)
We are actually using <+>
here with the more specific type
ArrowPlus a => (<+>) :: a (e,()) c > a (e,()) c > a (e,()) c
It is essential that this operator be polymorphic in e
(representing
the environment input to the command and thence to its subcommands) and
satisfy the corresponding naturality property
arr (first k) >>> (f <+> g) = (arr (first k) >>> f) <+> (arr (first k) >>> g)
at least for strict k
. (This should be automatic if you’re not using
seq
.) This ensures that environments seen by the subcommands are
environments of the whole command, and also allows the translation to
safely trim these environments. (The second component of the input pairs
can contain unnamed input values, as described in the next section.) The
operator must also not use any variable defined within the current arrow
abstraction.
We could define our own operator
untilA :: ArrowChoice a => a (e,s) () > a (e,s) Bool > a (e,s) ()
untilA body cond = proc x >
b < cond < x
if b then returnA < ()
else do
body < x
untilA body cond < x
and use it in the same way. Of course this infix syntax only makes sense for binary operators; there is also a more general syntax involving special brackets:
proc x > do
y < f < x+1
(untilA (increment < x+y) (within 0.5 < x))
9.19.4. Primitive constructs¶
Some operators will need to pass additional inputs to their subcommands. For example, in an arrow type supporting exceptions, the operator that attaches an exception handler will wish to pass the exception that occurred to the handler. Such an operator might have a type
handleA :: ... => a (e,s) c > a (e,(Ex,s)) c > a (e,s) c
where Ex
is the type of exceptions handled. You could then use this
with arrow notation by writing a command
body `handleA` \ ex > handler
so that if an exception is raised in the command body
, the variable
ex
is bound to the value of the exception and the command
handler
, which typically refers to ex
, is entered. Though the
syntax here looks like a functional lambda, we are talking about
commands, and something different is going on. The input to the arrow
represented by a command consists of values for the free local variables
in the command, plus a stack of anonymous values. In all the prior
examples, we made no assumptions about this stack. In the second
argument to handleA
, the value of the exception has been added to
the stack input to the handler. The command form of lambda merely gives
this value a name.
More concretely, the input to a command consists of a pair of an
environment and a stack. Each value on the stack is paired with the
remainder of the stack, with an empty stack being ()
. So operators
like handleA
that pass extra inputs to their subcommands can be
designed for use with the notation by placing the values on the stack
paired with the environment in this way. More precisely, the type of
each argument of the operator (and its result) should have the form
a (e, (t1, ... (tn, ())...)) t
where ⟨e⟩ is a polymorphic variable (representing the environment) and ⟨ti⟩ are the types of the values on the stack, with ⟨t1⟩ being the “top”. The polymorphic variable ⟨e⟩ must not occur in ⟨a⟩, ⟨ti⟩ or ⟨t⟩. However the arrows involved need not be the same. Here are some more examples of suitable operators:
bracketA :: ... => a (e,s) b > a (e,(b,s)) c > a (e,(c,s)) d > a (e,s) d
runReader :: ... => a (e,s) c > a' (e,(State,s)) c
runState :: ... => a (e,s) c > a' (e,(State,s)) (c,State)
We can supply the extra input required by commands built with the last two by applying them to ordinary expressions, as in
proc x > do
s < ...
(runReader (do { ... })) s
which adds s
to the stack of inputs to the command built using
runReader
.
The command versions of lambda abstraction and application are analogous
to the expression versions. In particular, the beta and eta rules
describe equivalences of commands. These three features (operators,
lambda abstraction and application) are the core of the notation;
everything else can be built using them, though the results would be
somewhat clumsy. For example, we could simulate do
notation by
defining
bind :: Arrow a => a (e,s) b > a (e,(b,s)) c > a (e,s) c
u `bind` f = returnA &&& u >>> f
bind_ :: Arrow a => a (e,s) b > a (e,s) c > a (e,s) c
u `bind_` f = u `bind` (arr fst >>> f)
We could simulate if
by defining
cond :: ArrowChoice a => a (e,s) b > a (e,s) b > a (e,(Bool,s)) b
cond f g = arr (\ (e,(b,s)) > if b then Left (e,s) else Right (e,s)) >>> f  g
9.19.5. Differences with the paper¶
 Instead of a single form of arrow application (arrow tail) with two
translations, the implementation provides two forms “
<
” (firstorder) and “<<
” (higherorder).  Userdefined operators are flagged with banana brackets instead of a
new
form
keyword.  In the paper and the previous implementation, values on the stack were paired to the right of the environment in a single argument, but now the environment and stack are separate arguments.
9.19.6. Portability¶
Although only GHC implements arrow notation directly, there is also a preprocessor (available from the arrows web page) that translates arrow notation into Haskell 98 for use with other Haskell systems. You would still want to check arrow programs with GHC; tracing type errors in the preprocessor output is not easy. Modules intended for both GHC and the preprocessor must observe some additional restrictions:
 The module must import Control.Arrow.
 The preprocessor cannot cope with other Haskell extensions. These would have to go in separate modules.
 Because the preprocessor targets Haskell (rather than Core),
let
bound variables are monomorphic.
9.20. Bang patterns¶
GHC supports an extension of pattern matching called bang patterns,
written !pat
. Bang patterns are under consideration for Haskell
Prime. The Haskell prime feature
description
contains more discussion and examples than the material below.
The key change is the addition of a new rule to the semantics of
pattern matching in the Haskell 98
report. Add
new bullet 10, saying: Matching the pattern !
⟨pat⟩ against a value
⟨v⟩ behaves as follows:
 if ⟨v⟩ is bottom, the match diverges
 otherwise, ⟨pat⟩ is matched against ⟨v⟩
Bang patterns are enabled by the flag XBangPatterns
.
9.20.1. Informal description of bang patterns¶
The main idea is to add a single new production to the syntax of patterns:
pat ::= !pat
Matching an expression e
against a pattern !p
is done by first
evaluating e
(to WHNF) and then matching the result against p
.
Example:
f1 !x = True
This definition makes f1
is strict in x
, whereas without the
bang it would be lazy. Bang patterns can be nested of course:
f2 (!x, y) = [x,y]
Here, f2
is strict in x
but not in y
. A bang only really has
an effect if it precedes a variable or wildcard pattern:
f3 !(x,y) = [x,y]
f4 (x,y) = [x,y]
Here, f3
and f4
are identical; putting a bang before a pattern
that forces evaluation anyway does nothing.
There is one (apparent) exception to this general rule that a bang only
makes a difference when it precedes a variable or wildcard: a bang at
the top level of a let
or where
binding makes the binding
strict, regardless of the pattern. (We say “apparent” exception because
the Right Way to think of it is that the bang at the top of a binding is
not part of the pattern; rather it is part of the syntax of the
binding, creating a “bangpattern binding”.) See Strict recursive and
polymorphic let bindings for
how bangpattern bindings are compiled.
However, nested bangs in a pattern binding behave uniformly with all other forms of pattern matching. For example
let (!x,[y]) = e in b
is equivalent to this:
let { t = case e of (x,[y]) > x `seq` (x,y)
x = fst t
y = snd t }
in b
The binding is lazy, but when either x
or y
is evaluated by
b
the entire pattern is matched, including forcing the evaluation of
x
.
Bang patterns work in case
expressions too, of course:
g5 x = let y = f x in body
g6 x = case f x of { y > body }
g7 x = case f x of { !y > body }
The functions g5
and g6
mean exactly the same thing. But g7
evaluates (f x)
, binds y
to the result, and then evaluates
body
.
9.20.2. Syntax and semantics¶
We add a single new production to the syntax of patterns:
pat ::= !pat
There is one problem with syntactic ambiguity. Consider:
f !x = 3
Is this a definition of the infix function “(!)
”, or of the “f
”
with a bang pattern? GHC resolves this ambiguity in favour of the
latter. If you want to define (!)
with bangpatterns enabled, you
have to do so using prefix notation:
(!) f x = 3
The semantics of Haskell pattern matching is described in Section 3.17.2 of the Haskell Report. To this description add one extra item 10, saying:
 Matching the pattern
!pat
against a valuev
behaves as follows: if
v
is bottom, the match diverges  otherwise,
pat
is matched againstv
 if
Similarly, in Figure 4 of Section 3.17.3, add a new case (t):
case v of { !pat > e; _ > e' }
= v `seq` case v of { pat > e; _ > e' }
That leaves let expressions, whose translation is given in Section
3.12 of the
Haskell Report. In the translation box, first apply the following
transformation: for each pattern pi
that is of form !qi = ei
,
transform it to (xi,!qi) = ((),ei)
, and replace e0
by
(xi `seq` e0)
. Then, when none of the lefthandside patterns have a
bang at the top, apply the rules in the existing box.
The effect of the let rule is to force complete matching of the pattern
qi
before evaluation of the body is begun. The bang is retained in
the translated form in case qi
is a variable, thus:
let !y = f x in b
The letbinding can be recursive. However, it is much more common for
the letbinding to be nonrecursive, in which case the following law
holds: (let !p = rhs in body)
is equivalent to
(case rhs of !p > body)
A pattern with a bang at the outermost level is not allowed at the top level of a module.
9.21. Assertions¶
If you want to make use of assertions in your standard Haskell code, you could define a function like the following:
assert :: Bool > a > a
assert False x = error "assertion failed!"
assert _ x = x
which works, but gives you back a less than useful error message – an assertion failed, but which and where?
One way out is to define an extended assert
function which also
takes a descriptive string to include in the error message and perhaps
combine this with the use of a preprocessor which inserts the source
location where assert
was used.
GHC offers a helping hand here, doing all of this for you. For every use
of assert
in the user’s source:
kelvinToC :: Double > Double
kelvinToC k = assert (k >= 0.0) (k+273.15)
GHC will rewrite this to also include the source location where the assertion was made,
assert pred val ==> assertError "Main.hs15" pred val
The rewrite is only performed by the compiler when it spots applications
of Control.Exception.assert
, so you can still define and use your
own versions of assert
, should you so wish. If not, import
Control.Exception
to make use assert
in your code.
GHC ignores assertions when optimisation is turned on with the
O
flag. That is, expressions of the form assert pred e
will be rewritten to e
. You can also disable assertions using the
fignoreasserts
option. The option fnoignoreasserts
allows enabling
assertions even when optimisation is turned on.
Assertion failures can be caught, see the documentation for the
Control.Exception
library for the details.
9.22. Static pointers¶
The language extension XStaticPointers
adds a new syntactic form
static e
, which stands for a reference to the closed expression ⟨e⟩.
This reference is stable and portable, in the sense that it remains
valid across different processes on possibly different machines. Thus, a
process can create a reference and send it to another process that can
resolve it to ⟨e⟩.
With this extension turned on, static
is no longer a valid
identifier.
Static pointers were first proposed in the paper Towards Haskell in the cloud, Jeff Epstein, Andrew P. Black and Simon PeytonJones, Proceedings of the 4th ACM Symposium on Haskell, pp. 118129, ACM, 2011.
9.22.1. Using static pointers¶
Each reference is given a key which can be used to locate it at runtime with unsafeLookupStaticPtr which uses a global and immutable table called the Static Pointer Table. The compiler includes entries in this table for all static forms found in the linked modules. The value can be obtained from the reference via deRefStaticPtr.
The body e
of a static e
expression must be a closed expression.
That is, there can be no free variables occurring in e
, i.e. lambda
or letbound variables bound locally in the context of the expression.
All of the following are permissible:
inc :: Int > Int
inc x = x + 1
ref1 = static 1
ref2 = static inc
ref3 = static (inc 1)
ref4 = static ((\x > x + 1) (1 :: Int))
ref5 y = static (let x = 1 in x)
While the following definitions are rejected:
ref6 = let x = 1 in static x
ref7 y = static (let x = 1 in y)
9.22.2. Static semantics of static pointers¶
Informally, if we have a closed expression
e :: forall a_1 ... a_n . t
the static form is of type
static e :: (Typeable a_1, ... , Typeable a_n) => StaticPtr t
Furthermore, type t
is constrained to have a Typeable
instance.
The following are therefore illegal:
static show  No Typeable instance for (Show a => a > String)
static Control.Monad.ST.runST  No Typeable instance for ((forall s. ST s a) > a)
That being said, with the appropriate use of wrapper datatypes, the above limitations induce no loss of generality:
{# LANGUAGE ConstraintKinds #}
{# LANGUAGE DeriveDataTypeable #}
{# LANGUAGE ExistentialQuantification #}
{# LANGUAGE Rank2Types #}
{# LANGUAGE StandaloneDeriving #}
{# LANGUAGE StaticPointers #}
import Control.Monad.ST
import Data.Typeable
import GHC.StaticPtr
data Dict c = c => Dict
deriving Typeable
g1 :: Typeable a => StaticPtr (Dict (Show a) > a > String)
g1 = static (\Dict > show)
data Rank2Wrapper f = R2W (forall s. f s)
deriving Typeable
newtype Flip f a s = Flip { unFlip :: f s a }
deriving Typeable
g2 :: Typeable a => StaticPtr (Rank2Wrapper (Flip ST a) > a)
g2 = static (\(R2W f) > runST (unFlip f))
9.23. Pragmas¶
GHC supports several pragmas, or instructions to the compiler placed in the source code. Pragmas don’t normally affect the meaning of the program, but they might affect the efficiency of the generated code.
Pragmas all take the form {# word ... #}
where ⟨word⟩ indicates
the type of pragma, and is followed optionally by information specific
to that type of pragma. Case is ignored in ⟨word⟩. The various values
for ⟨word⟩ that GHC understands are described in the following sections;
any pragma encountered with an unrecognised ⟨word⟩ is ignored. The
layout rule applies in pragmas, so the closing #}
should start in a
column to the right of the opening {#
.
Certain pragmas are fileheader pragmas:
 A fileheader pragma must precede the
module
keyword in the file.  There can be as many fileheader pragmas as you please, and they can be preceded or followed by comments.
 Fileheader pragmas are read once only, before preprocessing the file (e.g. with cpp).
 The fileheader pragmas are:
{# LANGUAGE #}
,{# OPTIONS_GHC #}
, and{# INCLUDE #}
.
9.23.1. LANGUAGE pragma¶
The LANGUAGE
pragma allows language extensions to be enabled in a
portable way. It is the intention that all Haskell compilers support the
LANGUAGE
pragma with the same syntax, although not all extensions
are supported by all compilers, of course. The LANGUAGE
pragma
should be used instead of OPTIONS_GHC
, if possible.
For example, to enable the FFI and preprocessing with CPP:
{# LANGUAGE ForeignFunctionInterface, CPP #}
LANGUAGE
is a fileheader pragma (see Pragmas).
Every language extension can also be turned into a commandline flag by
prefixing it with “X
”; for example XForeignFunctionInterface
.
(Similarly, all “X
” flags can be written as LANGUAGE
pragmas.)
A list of all supported language extensions can be obtained by invoking
ghc supportedextensions
(see Modes of operation).
Any extension from the Extension
type defined in
Language.Haskell.Extension
may be used. GHC will report an error if any of the requested extensions
are not supported.
9.23.2. OPTIONS_GHC
pragma¶
The OPTIONS_GHC
pragma is used to specify additional options that
are given to the compiler when compiling this source file. See
Command line options in source files for details.
Previous versions of GHC accepted OPTIONS
rather than
OPTIONS_GHC
, but that is now deprecated.
OPTIONS_GHC
is a fileheader pragma (see Pragmas).
9.23.3. INCLUDE
pragma¶
The INCLUDE
used to be necessary for specifying header files to be
included when using the FFI and compiling via C. It is no longer
required for GHC, but is accepted (and ignored) for compatibility with
other compilers.
9.23.4. WARNING
and DEPRECATED
pragmas¶
The WARNING
pragma allows you to attach an arbitrary warning to a
particular function, class, or type. A DEPRECATED
pragma lets you
specify that a particular function, class, or type is deprecated. There
are two ways of using these pragmas.
You can work on an entire module thus:
module Wibble {# DEPRECATED "Use Wobble instead" #} where ...
Or:
module Wibble {# WARNING "This is an unstable interface." #} where ...
When you compile any module that import
Wibble
, GHC will print the specified message.You can attach a warning to a function, class, type, or data constructor, with the following toplevel declarations:
{# DEPRECATED f, C, T "Don't use these" #} {# WARNING unsafePerformIO "This is unsafe; I hope you know what you're doing" #}
When you compile any module that imports and uses any of the specified entities, GHC will print the specified message.
You can only attach to entities declared at top level in the module being compiled, and you can only use unqualified names in the list of entities. A capitalised name, such as
T
refers to either the type constructorT
or the data constructorT
, or both if both are in scope. If both are in scope, there is currently no way to specify one without the other (c.f. fixities Infix type constructors, classes, and type variables).
Warnings and deprecations are not reported for (a) uses within the defining module, (b) defining a method in a class instance, and (c) uses in an export list. The latter reduces spurious complaints within a library in which one module gathers together and reexports the exports of several others.
You can suppress the warnings with the flag
fnowarnwarningsdeprecations
.
9.23.5. MINIMAL pragma¶
The MINIMAL
pragma is used to specify the minimal complete definition of
a class, i.e. specify which methods must be implemented by all
instances. If an instance does not satisfy the minimal complete
definition, then a warning is generated. This can be useful when a class
has methods with circular defaults. For example
class Eq a where
(==) :: a > a > Bool
(/=) :: a > a > Bool
x == y = not (x /= y)
x /= y = not (x == y)
{# MINIMAL (==)  (/=) #}
Without the MINIMAL
pragma no warning would be generated for an instance
that implements neither method.
The syntax for minimal complete definition is:
mindef ::= name
 '(' mindef ')'
 mindef '' mindef
 mindef ',' mindef
A vertical bar denotes disjunction, i.e. one of the two sides is required. A comma denotes conjunction, i.e. both sides are required. Conjunction binds stronger than disjunction.
If no MINIMAL
pragma is given in the class declaration, it is just as if
a pragma {# MINIMAL op1, op2, ..., opn #}
was given, where the
opi
are the methods (a) that lack a default method in the class
declaration, and (b) whose name that does not start with an underscore
(c.f. fwarnmissingmethods
, Warnings and sanitychecking).
This warning can be turned off with the flag
fnowarnmissingmethods
.
9.23.6. INLINE and NOINLINE pragmas¶
These pragmas control the inlining of function definitions.
9.23.6.1. INLINE pragma¶
GHC (with O
, as always) tries to inline (or “unfold”)
functions/values that are “small enough,” thus avoiding the call
overhead and possibly exposing other morewonderful optimisations. GHC
has a set of heuristics, tuned over a long period of time using many
benchmarks, that decide when it is beneficial to inline a function at
its call site. The heuristics are designed to inline functions when it
appears to be beneficial to do so, but without incurring excessive code
bloat. If a function looks too big, it won’t be inlined, and functions
larger than a certain size will not even have their definition exported
in the interface file. Some of the thresholds that govern these
heuristic decisions can be changed using flags, see f*: platformindependent flags.
Normally GHC will do a reasonable job of deciding by itself when it is a good idea to inline a function. However, sometimes you might want to override the default behaviour. For example, if you have a key function that is important to inline because it leads to further optimisations, but GHC judges it to be too big to inline.
The sledgehammer you can bring to bear is the INLINE
pragma, used thusly:
key_function :: Int > String > (Bool, Double)
{# INLINE key_function #}
The major effect of an INLINE
pragma is to declare a function’s
“cost” to be very low. The normal unfolding machinery will then be very
keen to inline it. However, an INLINE
pragma for a function “f
”
has a number of other effects:
While GHC is keen to inline the function, it does not do so blindly. For example, if you write
map key_function xs
there really isn’t any point in inlining
key_function
to getmap (\x > body) xs
In general, GHC only inlines the function if there is some reason (no matter how slight) to suppose that it is useful to do so.
Moreover, GHC will only inline the function if it is fully applied, where “fully applied” means applied to as many arguments as appear (syntactically) on the LHS of the function definition. For example:
comp1 :: (b > c) > (a > b) > a > c {# INLINE comp1 #} comp1 f g = \x > f (g x) comp2 :: (b > c) > (a > b) > a > c {# INLINE comp2 #} comp2 f g x = f (g x)
The two functions
comp1
andcomp2
have the same semantics, butcomp1
will be inlined when applied to two arguments, whilecomp2
requires three. This might make a big difference if you saymap (not `comp1` not) xs
which will optimise better than the corresponding use of
comp2
.It is useful for GHC to optimise the definition of an INLINE function
f
just like any other nonINLINE function, in case the noninlined version off
is ultimately called. But we don’t want to inline the optimised version off
; a major reason for INLINE pragmas is to expose functions inf
‘s RHS that have rewrite rules, and it’s no good if those functions have been optimised away.So GHC guarantees to inline precisely the code that you wrote, no more and no less. It does this by capturing a copy of the definition of the function to use for inlining (we call this the “inlineRHS”), which it leaves untouched, while optimising the ordinarily RHS as usual. For externallyvisible functions the inlineRHS (not the optimised RHS) is recorded in the interface file.
An INLINE function is not worker/wrappered by strictness analysis. It’s going to be inlined wholesale instead.
GHC ensures that inlining cannot go on forever: every mutuallyrecursive group is cut by one or more loop breakers that is never inlined (see Secrets of the GHC inliner, JFP 12(4) July 2002). GHC tries not to select a function with an INLINE pragma as a loop breaker, but when there is no choice even an INLINE function can be selected, in which case the INLINE pragma is ignored. For example, for a selfrecursive function, the loop breaker can only be the function itself, so an INLINE pragma is always ignored.
Syntactically, an INLINE
pragma for a function can be put anywhere
its type signature could be put.
INLINE
pragmas are a particularly good idea for the
then
/return
(or bind
/unit
) functions in a monad. For
example, in GHC’s own UniqueSupply
monad code, we have:
{# INLINE thenUs #}
{# INLINE returnUs #}
See also the NOINLINE
(NOINLINE pragma) and INLINABLE
(INLINABLE pragma) pragmas.
9.23.6.2. INLINABLE pragma¶
An {# INLINABLE f #}
pragma on a function f
has the following
behaviour:
 While
INLINE
says “please inline me”, theINLINABLE
says “feel free to inline me; use your discretion”. In other words the choice is left to GHC, which uses the same rules as for pragmafree functions. UnlikeINLINE
, that decision is made at the call site, and will therefore be affected by the inlining threshold, optimisation level etc.  Like
INLINE
, theINLINABLE
pragma retains a copy of the original RHS for inlining purposes, and persists it in the interface file, regardless of the size of the RHS.  One way to use
INLINABLE
is in conjunction with the special functioninline
(Special builtin functions). The callinline f
tries very hard to inlinef
. To make sure thatf
can be inlined, it is a good idea to mark the definition off
asINLINABLE
, so that GHC guarantees to expose an unfolding regardless of how big it is. Moreover, by annotatingf
asINLINABLE
, you ensure thatf
‘s original RHS is inlined, rather than whatever random optimised version off
GHC’s optimiser has produced.  The
INLINABLE
pragma also works withSPECIALISE
: if you mark functionf
asINLINABLE
, then you can subsequentlySPECIALISE
in another module (see SPECIALIZE pragma).  Unlike