LaPeL: a Logic Programming Language

Where ~t is a sequence of terms, ~x is a sequence of variables, and ~a is a sequence of assumptions. In the assumptions we write implication in the opposite direction than we normally do (i.e., “p(~t ) ⊂ g” rather than “g ⊃ p(~t )”). This is a standard convention in logic programming (e.g., Prolog) because it makes it easier for the programmer to understand the program; the meaning of implication is unchanged. A program consists of an ordered sequence of assumptions followed by a goal (also known as the query). Think of the assumptions as the hypotheses in a judgement, and the query as the proposition that is supposed to be proved. The computation consists of attempting to prove the truth of the goal g given the hypotheses ~a. The LaPeL syntax is an extension of definite Horn clauses; the added features are (1) the goal g1∨g2, which allows for disjunction; (2) the goal r ⊃ g, which allows for hypothetical implication; and (3) the goal output, which outputs the values of all the variables currently in scope. These extensions preserve the primary benefit of definite Horn clauses: goal-directed execution, allowing for tractable computation—e.g., as with definite Horn clauses, the implications given in the assumptions ~a have exactly one predicate as the succedent of the implication, thus when trying to prove a predicate goal p(~t ) we know exactly which assumptions to apply.