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.arpis., On 14/08/2012 17:30:
> > Either I've misunderstood your response, or you've misunderstood the
> > challenge. The challenge is that the same bound variable need never
> > be repeated. Sure for any given single sentence containing n
> > different variables you can define an equivalent single predicate
> > with n arguments, but you can't do this for each of the infinitely
> > many sentences in a language.
>
> But you _can_!

Ah, so I did misunderstand your response.

> That's how you'd build up sentences if the language's mechanism for
> composing concepts involves uniting them into larger predicates.

I wish I'd been able to understand your worked example, then, because that'=
s the direction where I think the solution lies: iteratively uniting two pr=
edicates into one, with a method for indicating which argument-places merge=
 into a single argument-place, ideally without having lexicosyntactically *=
explicit* variables filling argument-places.

E.g. F(a,b) and G(c,d) merge into a compound predicate H(a,b=3Dc,d).

(My own unpublished solutiontakes this approach, with an inflectional machi=
nery for encoding how two argument lists (e.g. <a, b> & <c, d>) merge into =
one  (e.g. <a, b=3Dc, d>).)
 =20
> Combinatory logic provides a notation based on S and K (or another
> one based on B, C, K, and W) for expressing predicates without
> explicit reference.
>
> Concatenative programming uses the idea of a stack to avoid explicit
> reference.
>
> The J Programming Language uses ideas from the above to be very terse
> and linear without explicit variables.

Thanks for that, and I appreciate that you may well lack time or inclinatio=
n to explain further, but if I'm to understand these promising-looking idea=
s, I'd need a lot more handholding.

--And.

--=20
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