From: Matthias Blume (find@my.address.elsewhere)
Subject: Re: [OT] Finns and education 
Newsgroups: comp.lang.scheme
Date: 2004-09-06 18:54:34 PST 


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

> I don't care why Will doesn't think my semantics is compositional.
> He's wrong.  My semantics was compositional, and so was his.  If you
> disagree with me, then put your Math where you mouth is.

The problem is that you think that a semantics is a mathematical
function alone. In reality it is a function and its definition.
Otherwise the predicate "compositional" does not make sense as it
refers to a property of definitions and not to a property of
functions.  (I don't care if you think you can define it as a property
of functions.  You didn't create this field, so you have to live with
the definitions that are already accepted.)

Your semantics consists of two parts.  One is a non-compositional
definition of a function over syntax (OpS).  The second is another
definition of a function over syntax.  This second definition is given
compositionally, using the first as a primitive.  The second
definition ends up defining the same mathematical function as the
first.  Together, the whole construction is non-compositional because
everything that's non-trivial about it is done non-compositionally.

>    first applying the identity function to E and subsequently running
>    the OpS on the result.
> 
> I don't think there's any mathematical meaning to `subsequently
> running the OpS on the result,' but let's not argue about it.

Well, I was speaking metaphorically -- intepreting the function
definition as a procedure.  To say it more "mathematically":

  Your semantics of ((lambda (x) E) 1) is defined as the composition
  of the identity function on E and the OpS.  This is precisely how
  the "add a new start symbol"-semantics is defined for E.

> Matthias Blume responds to me:
>    
>   THE C.L.S. WAY REQUIRES TO USE PHI FUNCTIONS THAT ARE NOT THEMSELVES
>    CONSTRUCTED USING THE E_i.
> 
> That's a serious error, Matthias.  You can't formulate notion this
> mathematically, and compositionality is a mathematical property.

See above.

>    [ ... ]  And the root of the problem is: YOU DON'T KNOW WHAT
>    C.L.S.-COMPOSITIONALITY IS.
> 
> I know the only possible mathematical definition of
> C.L.S.-COMPOSITIONALITY: the semantic functions E_i are defined via
> structural induction from the f_ij functions and Schmidt's equations.

See above.

> There is no mathematical meaning to the phrase "the f_ij are not
> themselves constructed using the E_i."  That's completely obvious to
> anyone who's fluent in the pure Math lingo of sets 'n functions.

Anyone familiar with formal languages and their intepretations (which,
incidentally, is the field of semantics) knows that this is complete
BS.  Remember, we are talking about definitions, not functions.

> Sets have a variety of definitions, and these definitions are not
> part of the sets themselves.  There's a point Will hasn't responded 
> to: Thus compositionality is a property only of the functions 
> themselves (as C-F declare), and not their definitions (because the
> defs aren't retrievable).

And here is, once again, your serious error.  As has been pointed out
to you, even "C-F" do not say that compositionality is a property of
the sets.

>    > 4) The main way in which you're correct (going back to your 1st
>    > para) is that these things Phi are not "simpler" than the sem
>    > function E_1 itself, but in fact defined by E_1.  That doesn't
>    > bother me at all.
>    
>    BUT IT BOTHERS EVERYBODY ELSE HERE.
> 
> It's fine for you dislike my style.  It's bad business for you to
> falsely claim that I'm violating a mathematical definition.  

It is even worse business to falsely claim someone is falsely claiming
you violated a mathematical definition if you didn't understand the
definition in question to begin with.

Matthias

PS: @felix:  I hate to see starving creatures, hence the feeding.