Principles of algebraic language ASL

This paper discusses the problems and basic principles in the design of the algebraic language ASL/. A text of ASL/ is composed of a context‐free grammar and a set of (conditional, in general) axioms, and specifies the set of expressions and the congruence relation on the set. The set of expressions and the syntax of each expression are specified by the context‐free grammar. The congruence relation on the set of expressions is defined as the minimal equivalence relation, which satisfies the axioms and is closed under the “operations,” i. e., the substitution into a “subexpression.” The value of an expression and the concept of the realization are defined based on the congruence relation. The “projection” is a special case of the conditional axiom, which is a facility to include only the expressions satisfying the specified syntactical condition. Projection is useful for including primitive functions and procedures with parameter passing of call‐by‐value in a text, and also for description of a specification of a realization in a simple way.