Re: [boost] [mpl] Metafunction terminology - revival?

From: David Bergman (David.Bergman_at_[hidden])
Date: 2006-07-24 15:11:59

Joaquin wrote:

[snip]

> I've reread the referred page, and all I can take it to 
> define is: a lambda expression is a metafunction class or a 
> placeholder expression. Whether this is what the authors actually
> *meant* is debatable, of course.

What I think it literally means is that a lambda expression is either a
metafunction class or a placeholder expression, much like a woman is either
nice or mean. This does NOT imply that all nice people are women ;-) So, I
think even the literal reading of the refered sentence(s) leaves room for
non-lambda-expressive metafunction classes...

[snip]
 
> Personally, I favor your interpretation of what lambda 
> expressions and metafunction classes should be defined to be, 
> I was only sticking to the reference.
> 
> <pedantic digression>
> Just to play devil's advocate, what gives a lambda expression 
> its essence, at least in mathematical lambda calculus, is not 
> the presence of place holders, but the ability to apply to 
> actual arguments,

No, that is not true, actually, since that essence of applicability is best
captured by the notion of "function." A lambda expression is a special type
of function (or, rather, lambda expressions are isomorphic to a set of
functions...)

This is analogous to the MPL discussion we have, where I find that
"metafunctors" captures that notion better than the (more specific) "lambda
expression."

> and this ability  can be coded with 
> mechanisms other than placeholders. For instance, in 
> combinatorial calculus 
> (http://en.wikipedia.org/wiki/Combinatory_logic),
> all lambda expressions can be given equivalent formulations 
> using only the combinators S and K, thus effectively avoiding 
> the use of placeholders altogether.

Yes, but they all share the common element of abstracting a parameter into a
(concrete) expression, even though the parameters are not symbolically
present in the (super) combinatorial systems.

> It could be an 
> interesting investigation project to determine whether 
> combinatorial methods can be modelled into the 
> metaprogramming framework of C++ just the way lambda 
> expressions have been.

Yes, it could. In some sense, the mechanics of function adapters in C++
mirrors that parameter-less and beautiful world to some extent.

> </pedantic digression>

/David