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arXiv · 2606.20944

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

John P. Gallagher·Manuel Hermenegildo·José Morales·Pedro Lopez-Garcia·Louis Rustenholz
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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.

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John P. Gallagher, Manuel Hermenegildo, José Morales, Pedro Lopez-Garcia, Louis Rustenholz. 2026-06-18. Big-step and small-step Horn clause derivations applied to operational semantics. https://arxiv.org/abs/2606.20944

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