comparing/intersecting compare criteria

Question

If there's any open source code that does this already I'm interested in hearing about it. But I haven't seen it yet so I'm trying to roll my own.

Example:

variable x = compareCriteriaBetween 3 and 6
variable y = compareCriteriaLesserThanOrEqual 5

The difficult part for me is finding an elegant way to compare the compareCriteria and create an intersection. In the example the intersection between the two is 'between 3 and 5'.

How can I implement this in a 'tell don't ask' manner? Note that compareCriteria can be completely unrelated (eg startsWithLetter versus betweenNumber).

Answer 1

If you are just interested in simple criteria like less equal or between on integers/floats, you can rewrite between 3 and 6 as (greater equal 3 and less equal 6). If you combine this with a logical and with less equal 5 you can use Boolean algebra to obtain (greater equal 3 and (less equal 6 and less equal 5)) before simplifying the inner parenthesis to just less equal 5 and rewriting the result as between 3 and 5.

Answer 2

If you only have constants in your expressions you should be safe from undecidability (I think!). Problems arise as soon as you can express e.g. general statements about integers with +-*/ (see Peano arithmetic).

Even if you stay within the realm of decidability, there exists no algorithm that can take arbitrary statements P(x) and Q(x) and compute a statement R(x) equivalent to P(x) & Q(x) for all x, where x can range over any domain (integers, strings, matrices, real numbers, complex numbers, logical statements [whoops, back into undecidable territory!], ...). You need domain specific tricks to get there, and strictly delimited languages in which P, Q and R are formulated. There exist software products for certain domains -- one of them is called Mathematica...

Try to get back to basics: what problem are you trying to solve?