Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is A(X,Y) :- X+Y>0, B(X), C(Y). In this clause, X+Y>0 is a constraint; A(X,Y), B(X), and C(Y) are literals as in regular logic programming. This clause states one condition under which the statement A(X,Y) holds: X+Y is greater than zero and both B(X) and C(Y) are true.

As in regular logic programming, programs are queried about the provability of a goal, which itself may contain constraints in addition to literals. A proof for a goal is composed of clauses whose bodies are satisfiable constraints and literals that can in turn be proved using other clauses. Execution is performed by an interpreter, which starts from the goal and recursively scans the clauses trying to prove the goal. Constraints encountered during this scan are placed in a set called the constraint store. If this set is found out to be unsatisfiable, the interpreter backtracks, trying to use other clauses for proving the goal. In practice, satisfiability of the constraint store may be checked using an incomplete algorithm, which does not always detect inconsistency.

Formally, constraint logic programs are like regular logic programs, but the body of clauses can contain constraints, in addition to the regular logic programming literals. As an example, X>0 is a constraint, and is included in the last clause of the following constraint logic program.

Like in regular logic programming, evaluating a goal such as A(X,1) requires evaluating the body of the last clause with Y=1. Like in regular logic programming, this in turn requires proving the goal B(X,1). Contrary to regular logic programming, this also requires a constraint to be satisfied: X>0, the constraint in the body of the last clause. (In regular logic programming, X>0 cannot be proved unless X is bound to a fully ground term and execution of the program will fail if that is not the case.)

Whether a constraint is satisfied cannot always be determined when the constraint is encountered. In this case, for example, the value of X is not determined when the last clause is evaluated. As a result, the constraint X>0 is neither satisfied nor violated at this point. Rather than proceeding in the evaluation of B(X,1) and then checking whether the resulting value of X is positive afterwards, the interpreter stores the constraint X>0 and then proceeds in the evaluation of B(X,1); this way, the interpreter can detect violation of the constraint X>0 during the evaluation of B(X,1), and backtrack immediately if this is the case, rather than waiting for the evaluation of B(X,1) to conclude.

In general, the evaluation of a constraint logic program proceeds as does a regular logic program. However, constraints encountered during evaluation are placed in a set called a constraint store. As an example, the evaluation of the goal A(X,1) proceeds by evaluating the body of the first clause with Y=1; this evaluation adds X>0 to the constraint store and requires the goal B(X,1) to be proven. While trying to prove this goal, the first clause is applied but its evaluation adds X<0 to the constraint store. This addition makes the constraint store unsatisfiable. The interpreter then backtracks, removing the last addition from the constraint store. The evaluation of the second clause adds X=1 and Y>0 to the constraint store. Since the constraint store is satisfiable and no other literal is left to prove, the interpreter stops with the solution X=1, Y=1.

The semantics of constraint logic programs can be defined in terms of a virtual interpreter that maintains a pair ${\displaystyle \langle G,S\rangle }$ during execution. The first element of this pair is called current goal; the second element is called constraint store. The current goal contains the literals the interpreter is trying to prove and may also contain some constraints it is trying to satisfy; the constraint store contains all constraints the interpreter has assumed satisfiable so far.

Initially, the current goal is the goal and the constraint store is empty. The interpreter proceeds by removing the first element from the current goal and analyzing it. The details of this analysis are explained below, but in the end this analysis may produce a successful termination or a failure. This analysis may involve recursive calls and addition of new literals to the current goal and new constraint to the constraint store. The interpreter backtracks if a failure is generated. A successful termination is generated when the current goal is empty and the constraint store is satisfiable.