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Re: [Caml-list] Lambda-Term (f x) (x f) translated to Ocaml?
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Date: 2006-03-28 (00:56)
From: Marius Nita <marius@c...>
Subject: Re: [Caml-list] Lambda-Term (f x) (x f) translated to Ocaml?
yoann padioleau wrote:
>> Hello,
>> I'm not firm in lambda calculus, what is the lambda-term
>> in the subject translated to OCaml?
>> Is this possible?
> the ocaml interpreter dont want this definition
> let g f x = (f x) (x f)
> and shout: 
>   this expression has type ('a -> 'b) -> 'c -> 'd but is here used with type 'a
> I guess that this is not a lambda term that can be typed.
> There are many of them. A famous one is the Y combinator.
> The _typed_ lambda calculus does not allow all the lambda terms
> of the (normal) lambda calculus.

g can't be written, but (f x) (x f) works for suitable values for f and 
x :) Namely if f = x = id. There's probably some deep parametricity 
property at the heart of it.