[racket] Type of curry

I just pushed a generalization for the type of `curry'.

As Carl said, TR's type system can't fully describe the behavior of
`curry'. With its new type, `curry' works on n-ary functions, but the
returned function is limited to accepting its arguments in two steps,
the first one first, then all the others.

Vincent


At Mon, 25 Feb 2013 13:21:23 -0500,
Carl Eastlund wrote:
> 
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> The type of curry is correct, but imprecise.  It does not express all
> possible uses of curry.  The curry function can be used to split any
> function application into an arbitrary number of stages, each with an
> arbitrary number of arguments.  There is no way to write down that type.
> Typed Racket needs to know how many stages there are to the function
> application -- that's the nesting level of "->" -- and how many arguments
> all but the last step take -- because there can be only one "..." in the
> initial function type, and it must be at the end of the arguments.
> 
> Right now the type is specialized to two stages, each with one argument.
> It could be generalized a bit further -- perhaps to allow arbitrary
> arguments at the second stage, or to allow two arguments at the first
> stage, or to allow a three-stage case as well, or some combination
> thereof.  However, this specialization can only go to some arbitrary,
> finite degree without changing the type system, and each addition will
> complicate the type of curry used in error messages.
> 
> For now, that means you will have to define f1a explicitly, or write a more
> specific instantiation of curry for your uses.  In the future, perhaps the
> TR implementers can broaden the type of curry a bit.  Types for this kind
> of higher-order function are an area of open research for TR, so perhaps
> things will get better in the future.
> 
> Carl Eastlund
> 
> 
> On Sun, Feb 24, 2013 at 5:59 PM, Norman Gray <norman at astro.gla.ac.uk> wrote:
> 
> >
> > Greetings,
> >
> > Is the type of 'curry' correct?
> >
> > #lang typed/racket
> >
> > (: f2 (Boolean Integer Integer -> Integer))
> > (define (f2 add? i1 i2)
> >   (if add?
> >       (+ i1 i2)
> >       (- i1 i2)))
> >
> > (define f1a (curry f2 #t)) ; fails to typecheck
> >
> > (f2 #t 2 3)
> > (f2 #f 2 1)
> > ;(f1a 10 20)
> >
> > ===>
> >
> > Welcome to DrRacket, version 5.3.3 [3m].
> > Language: typed/racket; memory limit: 128 MB.
> > . Type Checker: Polymorphic function curry could not be applied to
> > arguments:
> > Domains: (a b -> c)
> >          (a b -> c) a
> > Arguments: (Boolean Integer Integer -> Integer) True
> >  in: (curry f2 #t)
> > >
> >
> > It works fine when currying a two-argument function.
> >
> > All the best,
> >
> > Norman
> > (I'll resist any vindaloo jokes)
> >
> >
> > --
> > Norman Gray  :  http://nxg.me.uk
> > SUPA School of Physics and Astronomy, University of Glasgow, UK
> >
> > ____________________
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