Results 1  10
of
36
Specifications in an arbitrary institution
 Inform. and Comput
, 1988
"... A formalism for constructing and using axiomatic specifications in an arbitrary logical system is presented. This builds on the framework provided by Goguen and Burstallâ€™s work on the notion of an institution as a formalisation of the concept of a logical system for writing specifications. We show h ..."
Abstract

Cited by 92 (23 self)
 Add to MetaCart
A formalism for constructing and using axiomatic specifications in an arbitrary logical system is presented. This builds on the framework provided by Goguen and Burstallâ€™s work on the notion of an institution as a formalisation of the concept of a logical system for writing specifications. We show how to introduce free variables into the sentences of an arbitrary institution and how to add quantitiers which bind them. We use this foundation to define a set of primitive operations for building specifications in an arbitrary institution based loosely on those in the ASL kernel specification language. We examine the set of operations which results when the definitions are instantiated in institutions of total and partial tirstorder logic and compare these with the operations found in existing specification languages. We present proof rules which allow proofs to be conducted in specifications built using the operations we define. Finally, we introduce a simple mechanism for defining and applying parameterised specifications and briefly discuss the program development process. 1 1988 Academic Press. Inc. 1.
Logical Support for Modularisation
 LOGICAL ENVIRONMENTS
, 1993
"... Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of ..."
Abstract

Cited by 85 (28 self)
 Add to MetaCart
Modularisation is important for managing the complex structures that arise in large theorem proving problems, and in large software and/or hardware development projects. This paper studies some properties of logical systems that support the definition, combination, parameterisation and reuse of modules. Our results show some new connections among: (1) the preservation of various kinds of conservative extension under pushouts; (2) various distributive laws for information hiding over sums; and (3) (Craig style) interpolation properties. In addition, we study differences between syntactic and semantic formulations of conservative extension properties, and of distributive laws. A model theoretic property that we call exactness plays an important role in some results. This paper explores the interplay between syntax and semantics, and thus lies in the tradition of abstract model theory. We represent logical systems as institutions. An important technical foundation is a new ...
On Observational Equivalence and Algebraic Specification
, 1987
"... The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation are studied. We begin with a defmition of observational equivalence which is adequate to handle reachable algebras only, and show how to extend it to cope wit ..."
Abstract

Cited by 66 (17 self)
 Add to MetaCart
The properties of a simple and natural notion of observational equivalence of algebras and the corresponding specificationbuilding operation are studied. We begin with a defmition of observational equivalence which is adequate to handle reachable algebras only, and show how to extend it to cope with unreachable algebras and also how it may be generalised to make sense under an arbitrary institution. Behavioural equivalence is treated as an important special case of observational equivalence, and its central role in program development is shown by means of an example.
Metalogical Frameworks
, 1992
"... In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the me ..."
Abstract

Cited by 57 (15 self)
 Add to MetaCart
In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? This paper considers that question and more. We show that by taking the view that the metalogic is primary, these other parts are related in standard ways. The metalogic should be suitably rich so that the object logic can be presented as an abstract data type, and it must be suitably computational (or constructive) so that an instance of that type is an implementation. The data type abstractly encodes all that is relevant for metareasoning, i.e., not only the term constructing functions but also the...
Essential Concepts of Algebraic Specification and Program Development
, 1996
"... The main ideas underlying work on the modeltheoretic foundations of algebraic specification and formal program development are presented in an informal way. An attempt is made to offer an overall view, rather than new results, and to focus on the basic motivation behind the technicalities presente ..."
Abstract

Cited by 55 (15 self)
 Add to MetaCart
The main ideas underlying work on the modeltheoretic foundations of algebraic specification and formal program development are presented in an informal way. An attempt is made to offer an overall view, rather than new results, and to focus on the basic motivation behind the technicalities presented elsewhere.
Relating CASL with Other Specification Languages: the Institution Level
, 2000
"... In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or ..."
Abstract

Cited by 34 (16 self)
 Add to MetaCart
In this work, we investigate various specification languages and their relation to Casl, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3, CafeOBJ, ACT ONE, ASF, and HEPtheories, as well as various sublanguages of Casl that more or less directly correspond to these. All these languages are translated to an appropriate sublanguage of Casl. The translation mainly concerns the level of specification inthesmall: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification inthelarge. Thus, we obtain one hand translations of any of the abovementioned specification languages to an appropriate sublanguage of Casl. This allows us to take libraries and case studies that have been developed for other languages and reuse them in Casl. On the other hand, we set up institution repre...
Categorybased Semantics for Equational and Constraint Logic Programming
, 1994
"... This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equation ..."
Abstract

Cited by 24 (10 self)
 Add to MetaCart
This thesis proposes a general framework for equational logic programming, called categorybased equational logic by placing the general principles underlying the design of the programming language Eqlog and formulated by Goguen and Meseguer into an abstract form. This framework generalises equational deduction to an arbitrary category satisfying certain natural conditions; completeness is proved under a hypothesis of quantifier projectivity, using a semantic treatment that regards quantifiers as models rather than variables, and regards valuations as model morphisms rather than functions. This is used as a basis for a model theoretic categorybased approach to a paramodulationbased operational semantics for equational logic programming languages. Categorybased equational logic in conjunction with the theory of institutions is used to give mathematical foundations for modularisation in equational logic programming. We study the soundness and completeness problem for module imports i...
Institutions: An Abstract Framework for Formal Specifications
"... In this chapter we present some basic concepts and results of the theory of institutions, introduced by Goguen and Burstall to formally capture the informal notion of a logical system viewed from a modeltheoretic perspective. We also sketch some possibilities of linking this to more prooforiented ..."
Abstract

Cited by 24 (1 self)
 Add to MetaCart
In this chapter we present some basic concepts and results of the theory of institutions, introduced by Goguen and Burstall to formally capture the informal notion of a logical system viewed from a modeltheoretic perspective. We also sketch some possibilities of linking this to more prooforiented concepts. We argue that the theory of institutions provides an appropriate framework for much of the work on formal software specification and development, as presented in this volume. Many standard logical systems used in particular versions of the algebraic specification paradigm may be viewed as institutions; some examples are given explicitly here, some others are hinted at. Developing (as much as possible) the ideas common to different versions of the algebraic specification paradigm in the framework of an arbitrary institution, and in particular providing a theory of formal specification and software development parameterized by an arbitrary institution rather than having a particular logical system built in, should be beneficial both by helping to avoid repetitious work and by bringing the concepts and results to an
Extended ML: an institutionindependent framework for formal program development
 PROC. WORKSHOP ON CATEGORY THEORY AND COMPUTER PROGRAMMING
, 1986
"... The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system use ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
The Extended ML specification language provides a framework for the formal stepwise development of modular programs in the Standard ML programming language from specifications. The object of this paper is to equip Extended ML with a semantics which is completely independent of the logical system used to write specifications, building on Goguen and Burstall's work on the notion of an institution as a formalisation of the concept of a logical system. One advantage of this is that it permits freedom in the choice of the logic used in writing specifications; an intriguing sideeffect is that it enables Extended ML to be used to develop programs in languages other than Standard ML since we view programs as simply Extended ML specifications which happen to include only "executable" axioms. The semantics of Extended ML is defined in terms of the primitive specificationbuilding operations of the ASL kernel specification language which itself has an institutionindependent semantics. It is no...