Chapter 5 On the Orthogonality of Assignments andProcedures in

According to folklore, Algol is an orthogonall 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-calculus. To formalize Algol's notion of orthogonalityy, we deene an extended-calculus that models Algol. The calculus includes the full-reduction rule and reduction rules for assignment statements and commands. It has the usual Church-Rosser property and its recursion-free subset is strongly normalizing. In support of the orthogonalityy claim, we show that the proofs of the Church-Rosser and Strong-Normalization theorems are combinations of separate theorems for each sub-language. In addition, the calculus sat-isses a Postponement Theorem which operationally formalizes the idea that the evaluation of an Algol program has two distinct phases which correspond to the two sub-languages. The rst phase corresponds to an unrolling of the program according to the usual and xpoint reductions. The result of this phase is essentially an imperative program. The second phase corresponds to the execution of an imperative program on an ordinary stack machine.