Combinator evaluation of functional programs with logical variables

Abstract

A technique is presented that brings logical variables into the scope of the well-known Turner method for normal order evaluation of functional programs by S, K, I combinator graph reduction. This extension is illustrated by SASL+LV, an extension of Turner's language SASL in which arbitrary expressions serve as formal parameters, and parameter passage is done by unification. The conceptual and practical advantages of such an extension are discussed, as well as semantic pitfalls that arise from the attendant weakening of referential transparency. Only five new combinators (LV, BY, FN, FB and UNIFY) are introduced. The resulting object code is fully upward compatible in the sense that previously compiled SASL programs remain executable with unchanged semantics. However, read-only variable usage in SASL+LV programs requires a multitasking extension of the customary stack-based evaluation method. Mechanisms are presented for managing this multitasking on both single and multiprocessor systems. Finally, directions are mentioned for applying this technique to implementations involving larger granularity combinators, and fuller semantic treatment of logical variables (e.g. accommodation of failing unifications).