Results 11 
18 of
18
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,
A Hidden Herbrand Theorem
"... . The benefits of the object, logic (or relational), functional, and constraint paradigms can be combined, by providing existential queries over objects and their attributes, subject to constraints. This paper provides a precise mathematical foundation for this novel programming paradigm, and sh ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
. The benefits of the object, logic (or relational), functional, and constraint paradigms can be combined, by providing existential queries over objects and their attributes, subject to constraints. This paper provides a precise mathematical foundation for this novel programming paradigm, and shows that it is computationally feasible by reducing it to familiar problems over term algebras (i.e., Herbrand universes) . We use the formalism of hidden logic, and our main result is a version of Herbrand's Theorem for that setting. By extending a result of Diaconescu, we lift our results from equational logic to Horn clause logic with equality. ? The research reported in this paper has been supported in part by the Science and Engineering Research Council, the EC under ESPRIT2 BRA Working Groups 6071, ISCORE and 6112, COMPASS, Fujitsu Laboratories Limited, and a contract under the management of the Information Technology Promotion Agency (IPA), Japan, as part of the Industrial Sc...
A Birkhofflike Axiomatizability Result for Hidden Algebra and Coalgebra
, 2000
"... A characterization result for behaviorally definable classes of hidden algebras shows that a class of hidden algebras is behaviorally definable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically ge ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
A characterization result for behaviorally definable classes of hidden algebras shows that a class of hidden algebras is behaviorally definable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a final object and an inclusion system; this is general enough to include all coalgebra categories of interest. As a technical issue, the notions of equation and satisfaction are axiomatized in order to include the different approaches in the literature.
Tossing Algebraic Flowers down the Great Divide
 In People and Ideas in Theoretical Computer Science
, 1999
"... Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly l ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Data Types and Algebraic Semantics The history of programming languages, and to a large extent of software engineering as a whole, can be seen as a succession of ever more powerful abstraction mechanisms. The first stored program computers were programmed in binary, which soon gave way to assembly languages that allowed symbolic codes for operations and addresses. fortran began the spread of "high level" programming languages, though at the time it was strongly opposed by many assembly programmers; important features that developed later include blocks, recursive procedures, flexible types, classes, inheritance, modules, and genericity. Without going into the philosophical problems raised by abstraction (which in view of the discussion of realism in Section 4 may be considerable), it seems clear that the mathematics used to describe programming concepts should in general get more abstract as the programming concepts get more abstract. Nevertheless, there has been great resistance to u...
Hidden Algebraic Engineering
 Conference on Semigroups and Algebraic Engineering
, 1997
"... : This paper outlines a research programme in algebraic engineering. It starts with a review of classical algebraic specification for abstract data types, such as integers, vectors, booleans, and lists. Software engineering also needs abstract machines, recently called "objects," that can communicat ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
: This paper outlines a research programme in algebraic engineering. It starts with a review of classical algebraic specification for abstract data types, such as integers, vectors, booleans, and lists. Software engineering also needs abstract machines, recently called "objects," that can communicate concurrently with other objects, and that have local states with visible "attributes" that are changed by inputs. Hidden algebra is a new development in algebraic semantics for such systems; its most important results are powerful hidden coinduction principles for proving behavioral properties, especially behavioral refinement. 1 Introduction In view of the title of this conference, I should confess to being an algebraic engineer in (perhaps) the following four different senses: 1. I use algebra to build real software systems. 2. I build huge algebras to help build software systems. 3. I build software tools to help deal with these huge algebras. 4. I build new kinds of algebra, to get be...
A Birkholike axiomatizability result for hidden algebra and coalgebra
 In Proceedings of CMCS'98, volume 11 of ENTCS
, 1998
"... Acharacterization result for behaviorally de nable classes of hidden algebras shows that a class of hidden algebras is behaviorally de nable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically gener ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Acharacterization result for behaviorally de nable classes of hidden algebras shows that a class of hidden algebras is behaviorally de nable by equations if and only if it is closed under coproducts, quotients, morphisms and representative inclusions. The second part of the paper categorically generalizes this result to a framework of any category with coproducts, a nal object and an inclusion system; this is general enough to include all coalgebra categories of interest. As a technical issue, the notions of equation and satisfaction are axiomatized in order to include the di erent approaches in the literature. 1
What is Concurrent Connection?
"... Introduction Given two morphisms ' i : P ! P i (i = 1; 2), we can form the concurrent connection (P 1 kP 2 )==P . P @ @ @I ' 1 ' 2 \Gamma \Gamma \Gamma` P 1 P 2 \Gamma \Gamma \Gamma` / 1 / 2 @ @ @I (P 1 kP 2 )==P At present, I don't think we have an adequate understanding of what the concur ..."
Abstract
 Add to MetaCart
Introduction Given two morphisms ' i : P ! P i (i = 1; 2), we can form the concurrent connection (P 1 kP 2 )==P . P @ @ @I ' 1 ' 2 \Gamma \Gamma \Gamma` P 1 P 2 \Gamma \Gamma \Gamma` / 1 / 2 @ @ @I (P 1 kP 2 )==P At present, I don't think we have an adequate understanding of what the concurrent connection is: for example, the original definition [2] requires that each ' i be a hidden sorted theory morphism, which is too strong as the encapsulation condition on theory morphisms means that every operation in P i is in the range of OE i . On the other
Three decades of institution theory
"... 30 years have passed since the introduction by Joseph Goguen and Rod Burstall of the concept of ‘institution’ (in [14] under the name ‘language’). Since then institution theory has gradually developed from a simple and strikingly elegant general category theoretic formulation of the informal notion ..."
Abstract
 Add to MetaCart
30 years have passed since the introduction by Joseph Goguen and Rod Burstall of the concept of ‘institution’ (in [14] under the name ‘language’). Since then institution theory has gradually developed from a simple and strikingly elegant general category theoretic formulation of the informal notion of logical system into an important trend of what is now called ‘universal logic’, with substantial