Composing Programs in a Rewriting Logic for Declarative Programming

TL;DR

This paper introduces a modular framework for declarative programming based on rewriting logic, enabling flexible composition and semantic analysis of program modules with various semantics.

Contribution

It proposes a simple, expressive set of operations for program modularization within rewriting logic and studies their semantic properties for compositionality and abstraction.

Findings

Defines a notion of open program modules and composition mechanisms.

Introduces an immediate consequence operator for semantic analysis.

Explores multiple semantics for modules ensuring compositionality.

Abstract

Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this formalism, we introduce a simple notion of program module as an open program which can be extended together with several mechanisms to combine them. These mechanisms are based on a reduced set of operations. However, the high expressiveness of these operations enable us to model typical constructs for program modularization like hiding, export/import, genericity/instantiation, and inheritance in a simple way. We also deal with the semantic aspects of the proposal by introducing an immediate consequence operator, and studying several alternative semantics for a program module, based on this operator, in the line of logic programming: the operator itself, its least fixpoint (the least model of the module), the set of its pre-fixpoints (term models of the module), and some other variations in order to find a compositional and fully abstract semantics wrt the set of operations and a natural notion of observability.