Computational Soundness of a Call by Name Calculus of Recursively-scoped Records

The paper presents a calculus of recursively-scoped records: a two-level calculus with a traditional call-by-name λ-calculus at a lower level and unordered collections of labeled λ-calculus terms at a higher level. Terms in records may reference each other, possibly in a mutually recursive manner, by means of labels. We define two relations: a rewriting relation that models program transformations and an evaluation relation that defines a small-step operational semantics of records. Both relations follow a call-by-name strategy. We use a special symbol called a black hole to model cyclic dependencies that lead to infinite substitution. Computational soundness is a property of a calculus that connects the rewriting relation and the evaluation relation: it states that any sequence of rewriting steps (in either direction) preserves the meaning of a record as defined by the evaluation relation. The computational soundness property implies that any program transformation that can be represented as a sequence of forward and backward rewriting steps preserves the meaning of a record as defined by the small step operational semantics. In this paper we describe the computational soundness framework and prove computational soundness of the calculus. The proof is based on a novel inductive context-based argument for meaning preservation of substituting one component into another.