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From: "Pascal J. Bourguignon" <p...@informatimago.com>
Newsgroups: comp.lang.functional,comp.lang.lisp,comp.lang.scheme,comp.programming,comp.emacs
Subject: Re: Associativity paradox in functional expressions
Date: Tue, 06 Nov 2012 07:28:47 +0100
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Rivka Miller <rivkaumil...@gmail.com> writes:

> Are you saying that the Late Dr McCarthy, after thinking of lisp in
> terms of lambda calculus (and its associated currying), nevertheless
> implemented it in terms of variadic non-curried functions? Thus the
> turing machine replacement that lambda calculus is supposed to be,
> does not need any currying to be a replacement of turing machine - in
> the sense of computability?

Yes.  John McCarthy didn't understand lambda calculus at the time. He
just used the lambda notation for his functions, but they differed
greately, notably  in that he used dynamic binding instead of lexical
binding.


> How would the "(funcall g g n)"  and  "(funcall f f (1- n))" in the
> function advanced by the OP supposed to be associated if currying were
> available?
>
> ((lambda(g n) (funcall g g n))
>  (lambda(f n)
>    (if (zerop n) 1
>      (* n (funcall f f (1- n)))))
>  4 )

Well, in lisp there are parentheses to imply the order of evaluation…

-- 
__Pascal Bourguignon__
http://www.informatimago.com