Coinductive big-step operational semantics
Abstract
Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating evaluations. We formalize the connections between the coinductive big-step semantics and the standard small-step semantics, proving that both semantics are equivalent. We then study the use of coinductive big-step semantics in proofs of type soundness and proofs of semantic preservation for compilers. A methodological originality of this paper is that all results have been proved using the Coq proof assistant. We explain the proof-theoretic presentation of coinductive definitions and proofs offered by Coq, and show that it facilitates the discovery and the presentation of the results.
Keywords
Cite
@article{arxiv.0808.0586,
title = {Coinductive big-step operational semantics},
author = {Xavier Leroy and Hervé Grall},
journal= {arXiv preprint arXiv:0808.0586},
year = {2008}
}