Observational Logic, Constructor-Based Logic, and Their Duality

Document Type

Article

Publication Date

2003

Abstract

Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability. Then we develop in a completely analogous way the constructor-based logic institution which formalizes a novel treatment of reachability. Both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view. We show that there is a methodological and even formal duality between both frameworks. In particular, we establish a correspondence between observer operations and datatype constructors, observational and constructor-based algebras, fully abstract and reachable algebras, and observational and inductive consequences of specifications. The formal duality between the observability and reachability concepts is established in a category-theoretic setting.

Comments

This article was originally published in Theoretical Computer Science, volume 298, number 3, in 2003. DOI: 10.1016/S0304-3975(02)00865-4

Copyright

Elsevier

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