🚀 go-pugleaf

In article <187@aucsv.UUCP>, ok@aucsv.UUCP (Richard Okeefe) writes:
> Note that having a predicate
> 	times(A,  B, A_times_B)
> is not all joy.  Successor and plus are ok, but times takes you out of the
> decidable fragment of arithmetic.

Of course using only successor and times is also ok (adding plus also 
takes you out of that decidable fragment of arithmetic).

> Note that
> 	times(X, 0, 0)
> has *infinitely* many solutions. 

Surely that's ok too if you have a way of representing that many
solutions without actually computing all of them (e.g. by imposing 
constraints on floating point intervals).  That doesn't necessarily
mean delaying the evaluation until X is sufficiently bound it means
evaluating

       times(X,[0,0],[0,0])

where X is initially [minfloat,maxfloat], and verifying that this
call to times remains true every time X gets narrowed, which in this
instance will always be the case.

With this kind of idea you can compute (with reasonable efficiency)
all kinds of arithmetic expressions that have infinte solutions. For
example, if range/2 defines interval-terms, the question

?- range(C, [-34,0]), range(F, [-40,14]), F is C * 9/5 + 32.

will narrow C to [-34,-10] and F to [-29.2, 14] (which, by the way,
is roughly the temperature range in Ottawa these days).

-- Andre Vellino
Bell-Northern Research
Computing Research Laboratory
% Standard disclaimers here, about my views being my own, etc.