Peter Berry:
{-# LANGUAGE TypeFamilies, TypeSynonymInstances,
ScopedTypeVariables #-}
The following is a class of memo tries indexed by d:
class Fun d where
type Memo d :: * -> *
abst :: (d -> a) -> Memo d a
appl :: Memo d a -> (d -> a)
-- Law: abst . appl = id
-- Law: appl . abst = id (denotationally)
Any such type Memo d is naturally a functor:
memo_fmap f x = abst (f . appl x)
The type of memo_fmap (as given by ghci) is (Fun d) => (a -> c) ->
Memo d a -> Memo d c. (Obviously this would also be the type of fmap
for Memo d, so we could declare a Functor instance in principle.) If
we add this signature:
memo_fmap' :: Fun d => (a -> b) -> Memo d a -> Memo d b
memo_fmap' f x = abst (f . appl x)
it doesn't type check:
TypeSynonymTest.hs:14:17:
Couldn't match expected type `Memo d1 b'
against inferred type `Memo d b'
In the expression: abst (f . appl x)
In the definition of `memo_fmap'':
memo_fmap' f x = abst (f . appl x)
TypeSynonymTest.hs:14:32:
Couldn't match expected type `Memo d a'
against inferred type `Memo d1 a'
In the first argument of `appl', namely `x'
In the second argument of `(.)', namely `appl x'
In the first argument of `abst', namely `(f . appl x)'
Failed, modules loaded: none.
As I understand it, the type checker's thought process should be along
these lines:
1) the type signature dictates that x has type Memo d a.
2) appl has type Memo d1 a -> d1 -> a for some d1.
3) we apply appl to x, so Memo d1 a = Memo d a. unify d = d1
But for some reason, step 3 fails.
Step 3 is invalid - cf, <http://www.haskell.org/pipermail/haskell-cafe/2009-April/059196.html
>.
More generally, the signature of memo_fmap is ambiguous, and hence,
correctly rejected. We need to improve the error message, though.
Here is a previous discussion of the subject:
http://www.mail-archive.com/haskell-cafe@haskell.org/msg39673.html
Manuel
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