A direct semantic characterization of RELFUN

Abstract

This paper attempts a direct semantic formalization of first-order relational-functional languages (the characteristic RELFUN subset) in terms of a generalized model concept. Function-defining conditional equations (or, footed clauses) and active call-by-value expressions (in clause premises) are integrated into first-order theories. Herbrand models are accommodated to relational-functional programs by not only containing ground atoms but also ground molecules, i.e. specific function applications paired with values. Extending SLD-resolution toward innermost conditional narrowing of relational-functional clauses, SLV-resolution is introduced, which, e.g., flattens active expressions. The Tp-operator is generalized analogously, e.g. by unnesting ground-clause premises. Soundness and completeness proofs for SLV-resolution naturally extend the corresponding results in logic programming.