A PROLOG Interpreter for First-Order Intuitionistic Logic

What does it mean to write an “efficient” theorem prover for first-order intuitionistic logic? This paper suggests a possible answer to the question, following the philosophy of logic programming. We decompose intuitionistic logic into two syntactically restricted subsets: (i) the class of simple embedded implications and (ii) the class of disjunctive and existential assertions. Each of these subsets has been studied previously as a possible logic programming language, and we show how to write a simple interpreter (in PROLOG) for each one. We then combine the two interpreters into a single PROLOG interpreter for full first-order intuitionistic logic, and analyze its performance on several benchmark examples.