6.11.2. Ambiguous types and the ambiguity check¶
Allow type signatures which appear that they would result in an unusable binding.
Each user-written 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
AllowAmbiguousTypes switches off the ambiguity
Ambiguity can be subtle. Consider this example which uses functional dependencies:
class D a b | a -> b where .. h :: D Int b => Int
Int may well fix
b at the call site, so that signature
should not be rejected. Moreover, the dependencies might be hidden.
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
h’s type looks ambiguous in
b, but here’s a legal call:
That gives rise to a
(X [Bool] beta) constraint, and using the
instance means we need
(D Bool beta) and that fixes
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!
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
f :: C a => Int:
f :: C a => Int f = ...blah... g :: C a => Int g = f
g’s definition, we’ll instantiate to
(C alpha) and try to
(C alpha) from
(C a), and fail.
So in fact we use this as our definition of ambiguity: a type
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 has an ambiguous type according to 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
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.
Another way of getting rid of the ambiguity at the call site is to use
TypeApplications extension to specify the types. For example:
class D a b where h :: b instance D Int Int where ... main = print (h @Int @Int)
a is ambiguous in the definition of
D but later specified
to be Int using type applications.
AllowAmbiguousTypes allows you to switch off the ambiguity check.
However, 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
foo :: forall r. (forall i. (KnownNat i) => r) -> r foo f = f @1 boo :: forall j. (KnownNat j) => Int boo = .... h :: Int h = foo boo
This program will be rejected as ambiguous because GHC will not unify the type variables j and i.
Unlike the previous examples, it is not currently possible
to resolve the ambiguity manually by using
A historical note. GHC used to impose some more restrictive and less
principled conditions on type signatures. For type
forall tv1..tvn (c1, ...,cn) => type GHC used to require
- that each universally quantified type variable
tvimust be “reachable” from
- that every constraint
cimentions at least one of the universally quantified type variables
tvi. These ad-hoc restrictions are completely subsumed by the new ambiguity check.