Algebraic Properties of Idempotent Substitutions

This paper presents an algebra of idempotent substitutions whose operations have many properties. We provide an algorithm to compute these operations and we show how they are related to the standard composition. The theory of Logic Programming can be rewritten in terms of these new operations. The advantages are that both the operational and the declarative semantics of Horn Clause Logic can be formalized in a compositional way and the proofs of standard results, like the switching lemma, get easier and more intuitive. Moreover, this formalization can be naturally extended to a parallel computational model, and therefore it can be regarded as a basis for a theory of concurrent logic programming.