A Semantics for Logic Programs Based on Hereditary Harrop Formulas

We present a semantic framework for logic programs based on first-order hereditary Harrop formulas. The denotational and operational semantics are defined in a uniform way by characterizing some basic algebraic operators, which are directly related to the syntactic structure of the language. This allows us to address problems such as the relation between the operational semantics and the denotational semantics, the existence of a denotation of hereditary Harrop programs and their properties of compositionality, correctness and minimality. We define also an abstract interpretation framework based on the abstract interpretation theory. With this approach, the abstract denotational definition, the transition system and goal-independent denotations are systematically derived from the concrete ones, by replacing the concrete semantic operators by their abstract optimal versions. An extension to the higher-order context is considered. The adaptation of the first-order semantic framework to the higher-order language allows us the study of new properties such as abstraction and types.