6.11.7. Partial Type Signatures¶
-
PartialTypeSignatures
¶ Since: 7.10.1 Type checker will allow inferred types for holes.
A partial type signature is a type signature containing special
placeholders called wildcards. A wildcard is written as an underscore (e.g. “_
”)
or, if NamedWildCards
is enabled, any identifier with a leading
underscore (e.g. “_foo
”, “_bar
”). 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 type-checking 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 type-checker to infer.
By default, the type-checker will report an error message for each hole
in a partial type signature, informing the programmer of the inferred
type. When the PartialTypeSignatures
extension is enabled, the
type-checker will accept the inferred type for each hole, generating
warnings instead of errors. Additionally, these warnings can be silenced
with the -Wno-partial-type-signatures
flag.
However, because GHC must infer the type when part of a type is left out, it is unable to use polymorphic recursion. The same restriction takes place when the type signature is omitted completely.
6.11.7.1. 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.
6.11.7.1.1. 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 higher-kinded
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: error:
• Found type wildcard ‘_’ standing for ‘Bool’
To use the inferred type, enable PartialTypeSignatures
• In the type signature:
not' :: Bool -> _
• Relevant bindings include
not' :: Bool -> Bool (bound at Test.hs:5:1)
When a wildcard is not instantiated to a monotype, it will be generalised over, i.e. replaced by a fresh type variable, e.g.
foo :: _ -> _
foo x = x
-- Inferred: forall t. t -> t
filter' :: _
filter' = filter -- has type forall a. (a -> Bool) -> [a] -> [a]
-- Inferred: (a -> Bool) -> [a] -> [a]
6.11.7.1.2. Named Wildcards¶
-
NamedWildCards
¶ Since: 7.10.1 Allow naming of wildcards (e.g.
_x
) in type signatures.
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 a => a -> String
somethingShowable' :: Show _x => _x -> _
somethingShowable' x = show (not x)
-- Inferred type: Bool -> String
Besides an extra-constraints wildcard (see
Extra-Constraints 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 a
). 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 NamedWildCards
extension should be
enabled. The example below demonstrated the effect.
foo :: _a -> _a
foo _ = False
Compiling this program without enabling NamedWildCards
produces
the following error message complaining about the type variable _a
no matching the actual type Bool
.
Test.hs:5:9: error:
• Couldn't match expected type ‘_a’ with actual type ‘Bool’
‘_a’ is a rigid type variable bound by
the type signature for:
foo :: forall _a. _a -> _a
at Test.hs:4:8
• In the expression: False
In an equation for ‘foo’: foo _ = False
• Relevant bindings include foo :: _a -> _a (bound at Test.hs:5:1)
Compiling this program with NamedWildCards
(as well as
PartialTypeSignatures
) enabled produces the following error
message reporting the inferred type of the named wildcard _a
.
Test.hs:4:8: warning: [-Wpartial-type-signatures]
• Found type wildcard ‘_a’ standing for ‘Bool’
• In the type signature:
foo :: _a -> _a
• Relevant bindings include
foo :: Bool -> Bool (bound at Test.hs:5:1)
6.11.7.1.3. Extra-Constraints Wildcard¶
The third kind of wildcard is the extra-constraints wildcard. The presence of an extra-constraints 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 extra-constraints 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: error:
Found constraint wildcard ‘_’ standing for ‘(Show a, Eq a, Enum a)’
To use the inferred type, enable PartialTypeSignatures
In the type signature:
arbitCs :: _ => a -> String
An extra-constraints 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: error:
Found constraint wildcard ‘_’ standing for ‘()’
To use the inferred type, enable PartialTypeSignatures
In the type signature:
arbitCs' :: (Enum a, _) => a -> String
An extra-constraints wildcard can also lead to zero extra constraints to be inferred, e.g.
noCs :: _ => String
noCs = "noCs"
-- Inferred: String
-- Error:
Test.hs:13:9: error:
Found constraint wildcard ‘_’ standing for ‘()’
To use the inferred type, enable PartialTypeSignatures
In the type signature:
noCs :: _ => String
As a single extra-constraints 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.
Extra-constraints wildcards cannot be named.
6.11.7.2. Where can they occur?¶
Partial type signatures are allowed for bindings, pattern and expression signatures, except that extra-constraints wildcards are not supported in pattern or expression signatures. In the following example a wildcard is used in each of the three possible contexts.
{-# LANGUAGE ScopedTypeVariables #-}
foo :: _
foo (x :: _) = (x :: _)
-- Inferred: forall w_. w_ -> w_
Anonymous and named wildcards can occur on the left hand side of a type or data instance declaration; see Wildcards on the LHS of data and type family instances.
Anonymous wildcards are also allowed in visible type applications/ visible kind
applications (Visible type application). If you want to specify only the
second type argument to wurble
, then you can say wurble @_ @Int
where
the first argument is a wildcard.
Standalone deriving
declarations permit the use of a single,
extra-constraints wildcard, like so:
deriving instance _ => Eq (Foo a)
This denotes a derived Eq (Foo a)
instance where the context is inferred,
in much the same way that ordinary deriving
clauses do. Any other use of
wildcards in a standalone deriving
declaration is prohibited.
In all other contexts, type wildcards are disallowed, and a named wildcard is treated as an ordinary type variable. For example:
class C _ where ... -- Illegal
instance Eq (T _) -- Illegal (currently; would actually make sense)
instance Eq _a => Eq (T _a) -- Perfectly fine, same as Eq a => Eq (T a)
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. Extra-constraints 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: anonymous and named wildcards can be used in pattern signatures. Note that
ScopedTypeVariables
has to be enabled to allow pattern signatures. Extra-constraints wildcards are not supported, just like in regular pattern signatures.{-# LANGUAGE TemplateHaskell, ScopedTypeVariables #-} foo $( [p| (x :: _) |] ) = x
Type splices: only anonymous wildcards are supported in type splices. Named and extra-constraints wildcards are not.
{-# LANGUAGE TemplateHaskell #-} foo :: $( [t| _ |] ) -> a foo x = x