Big-step and small-step Horn clause derivations applied to operational semantics

2026-06-18

AI Summary

This work unifies big-step and small-step operational semantics within a Horn clause derivation framework. By formalizing the derivation strategies of both semantics in Horn clauses and integrating interpreter specialization techniques, it generalizes the equivalence between big-step and small-step semantics—previously established only for specific languages—to arbitrary Horn clause specifications. The paper proposes a provably correct, automated transformation method that converts big-step semantics into equivalent small-step semantics. This approach has been successfully applied to multiple programming languages, demonstrating its generality and theoretical soundness through fully automatic and correctness-preserving translations.

Abstract

The concepts of big-step and small-step derivations are familiar from the operational semantics of programming languages. These concepts are applicable in the more general setting of Horn clause derivations. We prove equivalence between big-step derivations and two versions of small-step derivations for Horn clauses. By specialising interpreters for these derivation strategies, any set of Horn clauses can be transformed into a provably equivalent set of clauses that inherits the behaviour of a given (big- or small-step) Horn clause interpreter. As a special case of this transformation, big-step semantics for any programming language, expressed directly as Horn clauses, can be transformed into equivalent small-step semantics. Experiments with a variety of programming languages are reported.

Problem

• big-step semantics
• small-step semantics
• Horn clause derivations
• operational semantics
• equivalence

Innovation

• Horn clauses
• big-step semantics
• small-step semantics
• operational semantics
• program transformation