Results 1  10
of
11
Institution Morphisms
, 2001
"... Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces ..."
Abstract

Cited by 58 (18 self)
 Add to MetaCart
Institutions formalize the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasizes the natural way that institutions can support deduction on sentences, and inclusions of signatures, theories, etc.; it also introduces terminology to clearly distinguish several levels of generality of the institution concept. A surprising number of different notions of morphism have been suggested for forming categories with institutions as objects, and an amazing variety of names have been proposed for them. One goal of this paper is to suggest a terminology that is uniform and informative to replace the current chaotic nomenclature; another goal is to investigate the properties and interrelations of these notions in a systematic way. Following brief expositions of indexed categories, diagram categories, twisted relations, and Kan extensions, we demonstrate and then exploit the duality between institution morphisms in the original sense of Goguen and Burstall, and the "plain maps" of Meseguer, obtaining simple uniform proofs of completeness and cocompleteness for both resulting categories. Because of this duality, we prefer the name "comorphism" over "plain map;" moreover, we argue that morphisms are more natural than comorphisms in many cases. We also consider "theoroidal" morphisms and comorphisms, which generalize signatures to theories, based on a theoroidal institution construction, finding that the "maps" of Meseguer are theoroidal comorphisms, while theoroidal morphisms are a new concept. We introduce "forward" and "seminatural" morphisms, and develop some of their properties. Appendices discuss institutions for partial algebra, a variant of order sorted algebra, two versions of hidden algebra, and...
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], a ..."
Abstract

Cited by 27 (18 self)
 Add to MetaCart
This paper presents some techniques of this kind in the area called hidden algebra, clustered around the central notion of coinduction. We believe hidden algebra is the natural next step in the evolution of algebraic semantics and its first order proof technology. Hidden algebra originated in [7], and was developed further in [8, 10, 3, 12, 5] among other places; the most comprehensive survey currently available is [12]
Conditional Circular Coinductive Rewriting with Case Analysis
, 2002
"... We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples. ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
We argue for an algorithmic approach to behavioral proofs, review the hidden algebra approach, develop circular coinductive rewriting for conditional goals, extend it with case analysis, and give some examples.
Hidden Algebra for Software Engineering
 Proceedings Combinatorics, Computation and Logic
, 1999
"... : This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, ma ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
: This paper is an introduction to recent research on hidden algebra and its application to software engineering; it is intended to be informal and friendly, but still precise. We first review classical algebraic specification for traditional "Platonic" abstract data types like integers, vectors, matrices, and lists. Software engineering also needs changeable "abstract machines," recently called "objects," that can communicate concurrently with other objects through visible "attributes" and statechanging "methods." Hidden algebra is a new development in algebraic semantics designed to handle such systems. Equational theories are used in both cases, but the notion of satisfaction for hidden algebra is behavioral, in the sense that equations need only appear to be true under all possible experiments; this extra flexibility is needed to accommodate the clever implementations that software engineers often use to conserve space and/or time. The most important results in hidden algebra are ...
Hidden Congruent Deduction
 Automated Deduction in Classical and NonClassical Logics
, 1998
"... This paper presents some techniques of this kind in the area called hidden algebra, ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
This paper presents some techniques of this kind in the area called hidden algebra,
Behavioral Verification of Distributed Concurrent Systems with BOBJ
 Proceedings, Conference on Quality Software
, 2003
"... Following condensed introductions to classical and behavioral algebraic specification, this paper discusses the verification of behavioral properties using BOBJ, especially its implementation of conditional circular coinductive rewriting with case analysis. This formal method is then applied to prov ..."
Abstract

Cited by 7 (2 self)
 Add to MetaCart
Following condensed introductions to classical and behavioral algebraic specification, this paper discusses the verification of behavioral properties using BOBJ, especially its implementation of conditional circular coinductive rewriting with case analysis. This formal method is then applied to proving correctness of the alternating bit protocol, in one of its less trivial versions. We have tried to minimize mathematics in the exposition, in part by giving concrete illustrations using the BOBJ system.
Observational Proofs by Rewriting
 J. Automated Reasoning
, 1995
"... Observational concepts are fundamental in formal methods since for proving the correctness of a program with respect to a specification it is essential to be able to abstract away from internal implementation details. Data objects can be viewed as equal if they cannot be distinguished by experiments ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Observational concepts are fundamental in formal methods since for proving the correctness of a program with respect to a specification it is essential to be able to abstract away from internal implementation details. Data objects can be viewed as equal if they cannot be distinguished by experiments with
Towards automated proofs of observational properties
 Discrete Mathematics in Theoretical Computer Science
, 2004
"... Observational theories are a generalization of firstorder theories where two objects are observationally equal if they cannot be distinguished by experiments with observable results. Such experiments, called contexts, are usually infinite. Therefore, we consider a special finite set of contexts, ca ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Observational theories are a generalization of firstorder theories where two objects are observationally equal if they cannot be distinguished by experiments with observable results. Such experiments, called contexts, are usually infinite. Therefore, we consider a special finite set of contexts, called covercontexts, “covering” all the observable contexts. Then, we show that to prove that two objects are observationally equal, it is sufficient to prove that they are equal (in the classical sense) under these covercontexts. We give methods based on rewriting techniques, for constructing such covercontexts for interesting classes of observational specifications.
Behavioral Abstraction is Information Hiding
"... We show that for any behavioral Sigmaspecification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigmatheorems of ~ B. The idea is t ..."
Abstract
 Add to MetaCart
We show that for any behavioral Sigmaspecification B there is an ordinary algebraic specification ~ B over a larger signature, such that a model behaviorally satisfies B if and only if it satisfies ~ B, where is the information hiding operator exporting only the Sigmatheorems of ~ B. The idea is to add machinery for contexts and experiments (sorts, operations and equations), use it, and then hide it. We develop a procedure, called unhiding, that takes a finite B and produces a finite ~ B. The practical aspect of this procedure is that one can use any standard equational or inductive theorem prover to derive behavioral theorems, even if neither equational reasoning nor induction is sound for behavioral satisfaction.