[plt-scheme] Y Combinator Exercise

From: John Clements (clements at brinckerhoff.org)
Date: Wed Nov 16 18:20:40 EST 2005

On Nov 16, 2005, at 12:59 PM, Matthias Felleisen wrote:

> In the monograph on reduction semantics [Felleisen & Flatt], we had  
> some sample calculations using the Y combinator along the lines of  
> what John points out. Use reductions to show ((Y mk-!) 2) is 2.  
> Then show them that the fixpoint equation helps. Reprove the first  
> one and wow it all gets easier. Then show them that you need a  
> calculus (=) and that reductions (->) are no longer enough for  
> this. Puzzle: can you design a cbv Y-like combinator that doesn't  
> use 'backwards' reductions. -- Matthias

Okay, now I'm confused.  Isn't cbv Y _itself_ a Y-like combinator  
that doesn't use 'backwards' reductions?


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