[Haskell-cafe] Find a point inside (x,y,z) -> Bool

[Levent Erkok]

This problem can be considered as an instance of the more general SAT
problem, in which you're trying to find a satisfying assignment to a
predicate. You might want to give that approach a try, though it does
require changes in representation. Here's a *very* simple example:

   Prelude> :m Data.SBV
   Prelude Data.SBV> let f (x, y, z) = 0 .<= x &&& y .>= 2 &&& z .<=
x+(y::SInteger)
   Prelude Data.SBV> sat f
   Satisfiable. Model:
     s0 = 0 :: Integer
     s1 = 2 :: Integer
     s2 = 2 :: Integer

Your "f" is probably going to be much more complicated, but if you can
afford to move to symbolic types, then SBV can bridge the gap and a SAT/SMT
solver can give you the required points. Or tell you if there isn't any,
like in the following example:

   Prelude Data.SBV> sat $ \x y -> x .> y &&& x .< (y::SInteger)
   Unsatisfiable

-Levent.

On Thu, Oct 29, 2015 at 2:01 AM, martin <martin.drautzburg at web.de> wrote:

> Hello all,
>
> I hope this is not a too silly question. It goes like this:
>
> Suppose I have a shape defined as
>
> (x,y,z) -> Bool
>
> how can I find a Point inside this shape? Obviously I could iterate
> through all possible x,y and z, but this appears
> very expensive.
>
> There may be no point at all at x=0. With brute force iteration I would
> have no clue that the False I am receiving with
> (0,1,1) is caused by x=0 and I may nedlessly try all combinations of y and
> z without ever receiving a True.
>
> Are there any alternative ways of finding points inside a shape?
>
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