On the Orthogonality of Assignments and Procedures in Algol

Abstract

According to folklore, Algol is an “orthogonal” extension of a simple imperative programming language with a call-by-name functional language. The former contains assignments, branching constructs, and compound statements; the latter is based on the typed λ-calculus. In an attempt to formalize the claim of “orthogonality”, we define a simple version of Algol and an extended λ-calculus. The calculus includes the full β-rule and rules for the reduction of assignment statements and commands. It has the usual properties, e.g., it satisfies a Church-Rosser and Strong Normalization Theorem. In support of the claim that the imperative and functional components are orthogonal to each other, we show that the proofs of these theorems are combinations of separate Church-Rosser and Strong Normalization theorems for each sublanguage.