From: Matthias Blume (find@my.address.elsewhere)
Subject: Re: [OT] Finns and education 
Newsgroups: comp.lang.scheme
Date: 2004-09-07 19:12:10 PST 


richter@math.northwestern.edu (Bill Richter) writes:

> [ ... ]  On the 1st page of Will's
> RichterFAQ (which is short, not like his long links), he writes:
> 
>   Q: Why isn't his semantics compositional?
> 
>   Because his semantics is the totalization of the transitive
>   closure of beta-value reduction [requiring N to be a value]:
> 
>       ((lambda (x) M) N)  -->  M[N/x]
> 
>   Substituting N for x yields a term that is not a subterm of
>   the redex on the left side of that arrow. In a definition by
>   structural induction, the meaning of the redex must be
>   defined by a function of the meanings of its proper subterms.
> 
> I've refuted this several times here.  Will is not saying what you
> say: he's not saying the "whole shebang" is really OpS.  Will is
> giving a mathematical objection, and I only object that it's bad Math.
> Will's objection seems to be that my original definition of my E_i is
> not a compositional definition.  That's of course true.  But I proved
> that E_1 had a different definition that was compositional.

I can only conclude that you must be /really/, *really* dense!

For the last time: No, there is no "different" definition that is
compositional -- at least not the one you gave.  And the reason for
this is the simple fact that your supposedly compositional definition
_relies_ on an existing non-compositional definition.  You can't start
with a non-compositional definition, pile on some gratuituous identity
function in a compositional manner, and then claim the whole thing is
compositional!

> [ ... ] but I did at followup you,
> with a completely standard cls proof that my E_i have a compositional
> definition.  Nobody ever followuped my post.

Because it was complete bullshit.  See above.

> [ ... ]
> Correct.  Let me apologize again, and thank Gustavo for correcting me:
> Cartwright & Felleisen do not say this.  But that's only a "social"
> error, it's not a mathematical error.  I incorrectly cited C-F, but
> the definition I inferred from C-F makes perfect sense.

Right.  It's just a flesh wound.

> Sure, but maybe I'm the only here who understands what's meant by a
> mathematical definition.  Please show me I'm wrong!

You woundn't see it if it hit you.  You got me convinced of that by now.

Matthias