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Foundations of Behavioural Specification in Rewriting Logic
, 1996
"... We extend behavioural specification based on hidden sorts to rewriting logic by constructing a hybrid between the two underlying logics. This is achieved by defining a concept of behavioural satisfaction for rewriting logic. Our approach is semantic in that it is based on a general construction on m ..."
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Cited by 9 (2 self)
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We extend behavioural specification based on hidden sorts to rewriting logic by constructing a hybrid between the two underlying logics. This is achieved by defining a concept of behavioural satisfaction for rewriting logic. Our approach is semantic in that it is based on a general construction on models, called behaviour image, which uses final models in an essential way. However we provide syntactic characterisations for the for the behavioural satisfaction relation, thus opening the door for shifting recent advanced proof techniques for behavioural satisfaction to rewriting logic. We also show that the rewriting logic behavioural satisfaction obeys the socalled "satisfaction condition" of the theory of institutions, thus providing support for OBJ style modularisation for this new paradigm. 1 Introduction This research aims at integrating two different semantic approaches on objects and concurrency by internalising behavioural specification [12] to [conditional] rewriting logic (abb...
Categorybased Constraint Logic
, 1999
"... This paper presents an (abstract) model theoretic semantics for ECLP, without directly addressing the computational aspect. This is a rather novel approach on the area of constraints where almost all efforts have been devoted to computational and operational issues; it is important the reader unders ..."
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Cited by 7 (3 self)
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This paper presents an (abstract) model theoretic semantics for ECLP, without directly addressing the computational aspect. This is a rather novel approach on the area of constraints where almost all efforts have been devoted to computational and operational issues; it is important the reader understands the modeltheoretic and foundational orientation of this paper. However, we plan to gradually develop the computational side based on these foundations as further research (Section 7.2 sketches some of the directions of such further research). Some computational aspects of this theory can already be found in (Diaconescu, 1996c). This semantics is
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 ..."
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Cited by 6 (0 self)
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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...
Categorybased Modularisation for Equational Logic Programming
 Acta Informatica
, 1996
"... : Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction conditio ..."
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Cited by 5 (5 self)
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: Although modularisation is basic to modern computing, it has been little studied for logicbased programming. We treat modularisation for equational logic programming using the institution of categorybased equational logic in three different ways: (1) to provide a generic satisfaction condition for equational logics; (2) to give a categorybased semantics for queries and their solutions; and (3) as an abstract definition of compilation from one (equational) logic programming language to another. Regarding (2), we study soundness and completeness for equational logic programming queries and their solutions. This can be understood as ordinary soundness and completeness in a suitable "nonlogical" institution. Soundness holds for all module imports, but completeness only holds for conservative module imports. Categorybased equational signatures are seen as modules, and morphisms of such signatures as module imports. Regarding (3), completeness corresponds to compiler correc...
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 ..."
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Cited by 5 (3 self)
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. 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...
Some Notes on Logic Programming with a Relational Machine (Extended Abstract)
 Relational Methods in Computer Science, Technical Report Nr. 199803
, 1998
"... James Lipton Dept. of Mathematics Wesleyan University Emily Chapman Dept. of Mathematics Wesleyan University Abstract We study the use of relation calculi for compilation and execution of Horn Clause programs with an extended notion of input and output. We consider various other extensions to the Pr ..."
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James Lipton Dept. of Mathematics Wesleyan University Emily Chapman Dept. of Mathematics Wesleyan University Abstract We study the use of relation calculi for compilation and execution of Horn Clause programs with an extended notion of input and output. We consider various other extensions to the Prolog core.
Encapsulating data in Logic Programming via Categorical Constraints
 Meinke (Eds.), Principles ofDeclarative Programming, Lecture Notes in Computer Sciences
, 1998
"... We define a framework for writing executable declarative specifications which incorporate categorical constraints on data, Horn Clauses and datatype specification over finiteproduct categories. We construct a generic extension of a base syntactic category of constraints in which arrows correspond t ..."
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We define a framework for writing executable declarative specifications which incorporate categorical constraints on data, Horn Clauses and datatype specification over finiteproduct categories. We construct a generic extension of a base syntactic category of constraints in which arrows correspond to resolution proofs subject to the specified data constraints. 1 Introduction Much of the research in logic programming is aimed at expanding the expressive power and efficiency of declarative languages without compromising the logical transparency commitment: programs should (almost) read like specifications. One approach is to place more expressive power and more of the control components into the logic itself, possibly by expanding the scope of the underlying mathematical formalism. This has been the goal of constraint logic programming (CLP, Set constraints, Prolog III), and extensions to higherorder and linear logic, to name a few such efforts. This paper is a step in this direction. ...
CafeOBJ Jewels
"... This paper gives an overview of the main features and methodologies of CafeOBJ by means of a collection of elegant examples. Therefore, this paper may also serve as a tutorial introduction to CafeOBJ. We hope that besides the strength of CafeOBJ, the reader will also appreciate the beauty of this la ..."
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This paper gives an overview of the main features and methodologies of CafeOBJ by means of a collection of elegant examples. Therefore, this paper may also serve as a tutorial introduction to CafeOBJ. We hope that besides the strength of CafeOBJ, the reader will also appreciate the beauty of this language.
Complete Categorical Deduction for Satisfaction as Injectivity
"... Abstract. Birkhoff (quasi)variety categorical axiomatizability results have fascinated many scientists by their elegance, simplicity and generality. The key factor leading to their generality is that equations, conditional or not, can be regarded as special morphisms or arrows in a special catego ..."
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Abstract. Birkhoff (quasi)variety categorical axiomatizability results have fascinated many scientists by their elegance, simplicity and generality. The key factor leading to their generality is that equations, conditional or not, can be regarded as special morphisms or arrows in a special category, where their satisfaction becomes injectivity, a simple and abstract categorical concept. A natural and challenging next step is to investigate complete deduction within the same general and elegant framework. We present a categorical deduction system for equations as arrows and show that, under appropriate finiteness requirements, it is complete for satisfaction as injectivity. A straightforward instantiation of our results yields complete deduction for several equational logics, in which conditional equations can be derived as well at no additional cost, as opposed to the typical method using the theorems of constants and of deduction. At our knowledge, this is a new result in equational logics. 1