6.11.3. Ambiguous types and the ambiguity check¶

AllowAmbiguousTypes
¶ Since: 7.8.1 Allow type signatures which appear that they would result in an unusable binding.
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 AllowAmbiguousTypes
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 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.
Another way of getting rid of the ambiguity at the call site is to use
the 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)
Here 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
Sometimes AllowAmbiguousTypes
does not mix well with RankNTypes
.
For example:
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 TypeApplications
.
Note
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
tvi
must be “reachable” fromtype
, and that every constraint
ci
mentions at least one of the universally quantified type variablestvi
. These adhoc restrictions are completely subsumed by the new ambiguity check.