Predicate Transformers for Infinite-State Automata in NuPRL Type Theory

This paper has two goals. The first is to present a formalization in Nuprl type theory of a very general methodology for system description, specification and verification. The method is especially suitable for describing distributed systems, and is based on a modification of the I/O automata of Lynch & Tuttle. By using infinite extendible records as the state spaces of automata we gain a key inheritance property that make modular verification tractible. The second goal is to show how we can state and prove meta-theorems about the method in Nuprl by a reflection procedure whereby we define syntax and semantics for both system descriptions and specifications within Nuprl type theory. We can then define a syntactic predicate transformation algorithm that generates syntactic verification conditions, and then prove the meta-theorem that shows that the truth of (the meanings of) the verification conditions implies that (the meaning of) the description satisfies (the meaning of) the specification.