This site is devoted to solve such puzzles with CLP(FD). But the full power of CLP(FD) is overkill here: your assignment can be solved effectively searching the entire solution space when you have adequately described the constraints.
The solution will be composed of 5 houses, where each attribute satisfy all constraints imposed by description.
Be aware to use the very same symbol for each attribute (i.e. green and green_house is wrong, choose one of them).
Also next_to seems wrong: if you number from 1 to 5, this can be computed or enumerated, but refers to the immediate neighbour.
So complete the ‘solution search space’ data representation, something like
Problem = [
house(1, Nationality1, Color1, Pet1, Drinks1, Smokes1),
house(2, Nationality2, Color2, Pet2, Drinks2, Smokes2),
...
],
% place constraints
member(house(_, englishman, red, _, _, _), Problem),
member(house(_, spaniard, _, dog, _, _), Problem),
...
member/2 it’s the simpler Prolog builtin, but in this case suffices to solve the problem: when all constraints have been posted, the variables will bind to appropriate values. The key is the ability of member to non deterministically select a member (duh) of the solution.
So when you need to express a constraint between 2 different elements, invoke 2 times member, and place the constraints between appropriate variables: i.e.
the man who smokes Chesterelds lives in the house next to the man with the fox
will be translated to
....,
member(house(N, _, _, _, _, chesterelds), Problem),
member(house(M, _, _, fox, _, _), Problem),
next_to(N, M),
...
When expressing many constraints in such way, beware to symbols identity: could be useful to code each predicate in a separate procedure, to avoid undue aliasing. But the couterpart
is also true: if the same symbol is involved in more than a constraint, will be necessary to pass around the symbol, to narrow down the search.
I will let you to think about the right representation of ‘geometric’ predicates: next_to and right_of could be enumerated, or expressed by means of arithmetic.