Talk:Fixed-point combinator: Difference between revisions

Revision as of 10:58, 10 December 2008

Revision as of 06:23, 29 January 2009

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[[User:Subwy|Subwy]] ([[User talk:Subwy|talk]]) 10:58, 10 December 2008 (UTC)

== Some material ==

One really good demonstration of how the Y combinator works (it has enough hand waving to make the general principles accessible to the layman), is this:

let Y = (lambda (f)

((lambda (g) (f (g g)))

(lambda (g) (f (g g)))))

let H = (lambda (g) (f (g g))) for convenience

let fact = (Y fact-h)

fact

=> (Y fact-h)

=> (H H) ; with f = fact-h

=> (fact-h (g g))

=> (fact-h (H H))

= (fact-h (Y fact-h))

= (fact-h fact)

;; => indicates a substitution step, while = indicates an equivalence

;; which is not actually a substitution

Unfortunately, this uses a lispy syntax, which most people are not familiar with. We should work this into something that could go into the article. &mdash; <span style="font-variant:small-caps;font-family:sans-serif;">[[User:Edward Z. Yang|Edward Z. Yang]]</span><sup style="font-family:serif;">([[User talk:Edward Z. Yang|Talk]])</sup> 06:23, 29 January 2009 (UTC)