Prolog's clpfd (constrained logic programming over finite domains) is actually just a library - albeit one with very ergonomic bindings that mesh almost invisibly into the language.
Prolog's evaluator backtracks when it hits a conflict while trying to expand a predicate. It evaluates queries top-down, and tries predicate definitions/clauses in order. It's basically eager. This isn't a good fit for math, so CLPFD fixed this by making arithmetic constraints lazy. This works really well, but you're ultimately using Prolog to build a model, then (invisibly) solving the model separately.
Ultimately, the problem is that Prolog looks like a DSL but is Turing-complete. You can weave other solvers into the language, but there's a seam between the evaluators. I like the alternative, which is to sacrifice Prolog's Turing-completeness for a ridiculously powerful DSL. Answer Set Programming (clasp) and Datalog are fine examples of this.
Prolog's evaluator backtracks when it hits a conflict while trying to expand a predicate. It evaluates queries top-down, and tries predicate definitions/clauses in order. It's basically eager. This isn't a good fit for math, so CLPFD fixed this by making arithmetic constraints lazy. This works really well, but you're ultimately using Prolog to build a model, then (invisibly) solving the model separately.
Ultimately, the problem is that Prolog looks like a DSL but is Turing-complete. You can weave other solvers into the language, but there's a seam between the evaluators. I like the alternative, which is to sacrifice Prolog's Turing-completeness for a ridiculously powerful DSL. Answer Set Programming (clasp) and Datalog are fine examples of this.