The revised report on the syntactic theories of sequential control and state

Abstract

The syntactic theories of control and state are conservative extensions of the λ υ-calculus for equational reasoning about imperative programming facilities in higher-order languages. Unlike the simple λ υ-calculus, the extended theories are mixtures of equivalence relations and compatible congruence relations on the term language, which significantly complicates the reasoning process. In this paper we develop fully compatible equational theories of the same imperative higher-order programming languages. The new theories subsume the original calculi of control and state and satisfy the usual Church–Rosser and Standardization Theorems. With the new calculi, equational reasoning about imperative programs becomes as simple as reasoning about functional programs.