Mechanizing UNITY in Isabelle

UNITY is an abstract formalism for proving properties of concurrent systems, which typically are expressed using guarded assignments [Chandy and Misra 1988]. UNITY has been mechanized in higher-order logic using Isabelle, a proof assistant. Safety and progress primitives, their weak forms (for the substitution axiom) and the program composition operator (union) have been formalized. To give a feel for the concrete syntax, the paper presents a few extracts from the Isabelle definitions and proofs. It discusses a small example, two-process mutual exclusion. A mechanical theory of unions of programs supports a degree of compositional reasoning. Original work on extending program states is presented and then illustrated through a simple example involving an array of processes