Coinductive Big-Step Operational Semantics

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. Key words: Coinduction, Operational semantics, Big-step semantics, Natural semantics, Small-step semantics, Reduction semantics, Type soundness, Compiler correctness, Mech...

• Type: Conference
• Year: 2006
• Where: ESOP
• Authors: Xavier Leroy
• Keywords: Coinductive Big-step Semantics, ESOP 2006, Operational Semantics, Programming Languages, Small-step Semantics