On Coevaluation Behavior and Equivalence

Abstract

Coevaluation, the coinductive interpretation of standard big-step evaluation rules, is a concise form of semantics, with the same number of rules as in evaluation, which intends to simultaneously describe , finite and infinite computations. However, it is known that it is only able to express an infinite computations subset, and, to date, it remains unknown exactly what this subset is. More precisely, coevaluation behavior has several unusual features: there are terms whose for which evaluation is infinite but that do not coevaluate, it is not deterministic in the sense that there are terms which coevaluate to any value v, and there are terms whose for which evaluation is infinite but that coevaluate to only one value. In this work, we describe what the infinite computations subset which is able to be expressed by coevaluation is able to express is. More importantly, we introduce a coevaluation extension which that is well-behaved in the sense that the finite computations coevaluate exactly as in evaluation and the infinite computations coevaluate exactly as in divergence. In consequence Consequently, it does not present unusual features no unusual features are presented; in particular, this extension captures all infinite computations (not only a subset of them). In addition, as a consequence of thiswell-behavior,we present the expected equivalence between (extended) coevaluation and evaluation union divergence.

A Machine Proof System of Point Geometry Based on Coq

“…It provides an efficient, reliable, and automated proof environment. In the field of computer science, Coq has been widely used for program verification, language design, formal semantics, security protocol analysis, program repair, and many other applications, as documented in various research studies [17][18][19][20][21]. Coq is also widely used in mathematics to formalize [22,23] and verify theorems and lemmas.…”