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.

Authors

• Xavier Leroy
• Hervé Grall

Keywords

• Coinduction
• Operational semantics
• Big-step semantics
• Natural semantics
• Small-step semantics
• Reduction semantics
• Type soundness
• Compiler correctness
• Mechanized proofs
• The Coq proof assistant