type declarations & inference in Haskell or ML?

[gusl]

Does Haskell or ML support code like the following?


>> a : p;
a : p

>> b : q;
b : q

>> c : p -> q -> r;
c : p -> q -> r

>> d = (c a);
d : q -> r

>> f : r -> s;
f : r -> s

>> e = lambda(x) (f(d x));
e : q -> s


Note that I get these inferences even though the variables were not instantiated, and the functions were not implemented.