Document Type

Article

Publication Date

2007

Abstract

The paper presents a calculus of recursively-scoped records: a two-level calculus with a traditional call-by-name lambda-calculus at a lower level and unordered collections of labeled lambda-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.

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