2009/10/9 wren ng thornton
Cristiano Paris wrote:
On Thu, Oct 8, 2009 at 12:48 PM, Lennart Augustsson wrote:
The reason a gets a single type is the monomorphism restriction (read the report). Using NoMonomorphismRestriction your example with a works fine.
Could you explain why, under NoMonomorphismRestriction, this typechecks:
let a = 1 in (a + (1 :: Int),a + (1 :: Float))
while this not:
foo :: Num a => a -> (Int,Float) foo k = (k + (1 :: Int), k + (1.0 :: Float))
Because lambda-binding is always[1] monomorphic, whereas let-binding can be polymorphic. This distinction is the reason for introducing let-binding in the first place. If let-bindings weren't allowed to be polymorphic (or if lambda-bindings were allowed to be) then we could desugar "let x = e in f" into "(\x -> f) $ e" and simplify the core language.[2]
As it turns out, section 31.6 Why Let and not Lambda of PLAI [*] explains why lambda-bindings are treated monomorphically. [*] http://www.cs.brown.edu/~sk/Publications/Books/ProgLangs/
Milner's original paper[3] on the topic is still a good introduction to the field. He couldn't take advantage of subsequent work, so his notation is a bit outdated (though still understandable). If you're familiar with the details behind System F, etc. then you should be able to massage the paper into more modern notation in order to discuss issues like where and how Rank-2 polymorphism fits in.
[1] That is, under the Hindley--Milner type system. If we add Rank-2 (or Rank-N) polymorphism then lambdas can bind polymorphic values.
[2] There's a wrinkle with simplifying the core here. Let-binding is often introduced in tandem with a special form for declaring recursive values and mutually recursive groups. Usually this form is simplified somewhat as in ML's "let rec" or Haskell's invisible laziness recursion. If we remove "let" then we'll want to use the general version of "rec" and will need to be explicit about it.
[3] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.5276
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