Section: New Results

Hierarchy of Semantics by Abstract Interpretation and Formal Proofs

Participant : Jeremy Leconte.

Using the Coq proof assistant, we define a maximal trace semantics describing terminating and diverging computations of a simple functional language. This trace semantics is abstracted into a relational semantics which is in turn abstracted into a reduction semantics. The soundness of each abstraction is proved along with the equivalence between small steps and big steps of computation. An originality of the semantics is that it defines finite behaviors inductively and infinite behaviors coinductively while it avoids the duplication of rules common to the two behaviors. In consequence the semantics definition is simplified as well as some proofs that uses the definition.

This work is summarized in [61] .