Can anyone tell me what's wrong with the following derivation?
Without going through your derivation completely, the problem is almost certainly polymorphic recursion. Vector is a nested datatype---its definition calls itself with different type arguments---and so, although
collect :: (v -> [a]) -> (w -> [a]) -> Vector v w -> [a]
the recursive call to collect in, for example, the second clause, has a different type, namely:
collect :: (v -> [a]) -> ((w,w) -> [a]) -> Vector v w -> [a]
However, in the absence of an explicit type signature, Haskell will assume that the types of the top-level and recursive occurrences of collect are equal, which they are not, so you'll get a type error.
Indeed, the error messages Dominic posted:
> ERROR "Test1.hs":23 - Type error in function binding
> *** Term : coal_
> *** Type : (a -> b) -> (c -> [d]) -> Vector_ a e -> b
> *** Does not match : (a -> b) -> ((c,c) -> [d]) -> Vector_ a (e,e) -> b
> *** Because : unification would give infinite type
>
> Test1.hs:25:
> Occurs check: cannot construct the infinite type: t = (t, t1)
> Expected type: (t, t1)
> Inferred type: t
> In the first argument of `coalw', namely `w1'
> In the first argument of `(++)', namely `(coalw w1)'
corroborate this argument.
Or, are you asking instead why it is that type inference does not work for polymorphic-recursive functions?
Regards, Frank
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