wren ng thornton wrote:
On 9/13/10 6:22 AM, Michael Lazarev wrote:
Thanks for examples and pointers.
Since I came from Lisp, it never occurred to me that let and lambda are different constructs in Haskell. I thought that let x = y in f is really (\x -> f) y It turns out that let is about declarations which are not the same as function applications above.
Right. This is a common mistake for people coming from Lisp, Scheme, and other untyped lambda calculi. In the untyped world it's fine to conflate let and lambda, because they only differ in how they're typed (and if you have no types...).
The difference is that, for let-bindings, once you've figured out a type of the variable being bound, then that type can be "generalized". The exact process of generalization has some subtle details to watch out for, but suffice it to say that certain type variables are allowed to become universally quantified. Which means that you're allowed to use x at different types within f, provided all those different types are consistent with the generalized type.
Whereas, lambda-bindings don't get generalized, and so they'll always be monomorphic (assuming Hindley--Milner inference without extensions like -XRankNTypes). This is necessary in order to catch numerous type errors,
Disclaimer: I am not a type system expert. Anyway, I thought the reason was that type inference for rank-n types (n>1) is undecidable. And therefore:
though Haskell lets you override this behavior by giving an explicitly polymorphic type signature if you have -XRankNTypes enabled.
...so that polymorphic types for arguments don't have to be inferred. I think it was in Milner's original paper where he tries to give some intuition why let and lambda are treated differently: even though we always have (\x -> e) y == let x = y in e which means that let can be translated to lambda, the converse is not true, since a lambda expression can appear in contexts other than (as the left hand side of) an application. Thus, let is syntactically more restrictive than lambda, which means we can be more liberal when typing it. In principle, the type-checker *could* be extended to infer polymorphic types for those lambda-bound variables where the lambda expression immediately gets applied to some other expression. In practice this would be of little use as these are exactly the situations where a let can (and should!) be used instead of a lambda. Cheers Ben