Programming Language Semantics with Isabelle/HOL

Isabelle is a generic meta-logical framework for implementing logical formalisms, and Isabelle/HOL is the specialization of Isabelle for HOL, which stands for Higher Order Logic. In programming language theory, formal semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages. In this paper we develop a relational denotational semantics for a small imperative programming language and implement it as a theory in Isabelle/HOL. We give special attention to the specification of monotonic fix point functional for loops and provide non-trivialproofs of interesting lemmas and properties with the structured proof language Isar.