Results 1  10
of
16
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...
An ImplementationOriented Semantics for Module Composition
, 1997
"... This paper describes an approach to module composition by executing "module expressions" to build systems out of component modules; the paper also gives a novel semantics intended to aid implementers. The semantics is based on set theoretic notions of tuple set, partial signature, and institution, t ..."
Abstract

Cited by 32 (14 self)
 Add to MetaCart
This paper describes an approach to module composition by executing "module expressions" to build systems out of component modules; the paper also gives a novel semantics intended to aid implementers. The semantics is based on set theoretic notions of tuple set, partial signature, and institution, thus avoiding more difficult mathematics theory. Language features include information hiding, both vertical and horizontal composition, and views for binding modules to interfaces. Vertical composition refers to the hierarchical structuring of a system into layers, while horizontal composition refers to the structure of a given layer. Modules may involve information hiding, and views may involve behavioral satisfaction of a theory by a module. Several "Laws of Software Composition" are given, which show how the various module composition operations relate. Taken together, this gives foundations for an algebraic approach to software engineering. 1.1 Introduction The approach to module compos...
Structuring and Modularity
 on Algebraic Foundations of Systems Specification, chapter 6
, 1996
"... this paper, we will describe the main techniques for the semantic definition of some of the most used structuring and modular constructs. Our main aim will be to study the generic, "institutionindependent ", version of each construct. However, in order to provide intuition, in most cases, we will fi ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
this paper, we will describe the main techniques for the semantic definition of some of the most used structuring and modular constructs. Our main aim will be to study the generic, "institutionindependent ", version of each construct. However, in order to provide intuition, in most cases, we will first study these constructions in connection to equational logic.
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 ..."
Abstract

Cited by 5 (5 self)
 Add to MetaCart
: 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...
Using Algebraic Specification Languages for ModelOriented Specifications
, 1996
"... It is common belief that there is a substantial difference between modeloriented (eg. Z and VDM) and algebraic specification languages (eg. LSL and ACTONE) wrt. their applicability to the specification of software systems. While modeloriented specification languages are assumed to be suited b ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
It is common belief that there is a substantial difference between modeloriented (eg. Z and VDM) and algebraic specification languages (eg. LSL and ACTONE) wrt. their applicability to the specification of software systems. While modeloriented specification languages are assumed to be suited better for the description of state based systems (abstract machines), algebraic specification languages are assumed to be better for abstract datatype specifications. In this paper we shall demonstrate how an algebraic specification language (the Larch Shared Language) can be used to write specifications of abstract machines in the style of Z and how support tools for algebraic specification languages, eg. type checker and theorem provers, can be used to reason about abstract machines. Keywords abstract data type, algebraic specification, modeloriented specification, Z, Larch Shared Language, abstract machine, institution iii 1. Introduction In the literature (eg. [16, 15]), t...
QuasiBoolean Encodings and Conditionals in Algebraic Specification
"... We develop a general study of the algebraic specification practice, originating from the OBJ tradition, which encodes atomic sentences in logical specification languages as Boolean terms. This practice originally motivated by operational aspects, but also leading to significant increase in expressiv ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
We develop a general study of the algebraic specification practice, originating from the OBJ tradition, which encodes atomic sentences in logical specification languages as Boolean terms. This practice originally motivated by operational aspects, but also leading to significant increase in expressivity power, has recently become important within the context of some formal verification methodologies mainly because it allows the use of simple equational reasoning for frameworks based on logics that do not have an equational nature. Our development includes a generic rigorous definition of the logics underlying the above mentioned practice, based on the novel concept of ‘quasiBoolean encoding’, a general result on existence of initial semantics for these logics, and presents a general method for employing Birkhoff calculus of conditional equations as a sound calculus for these logics. The high level of generality of our study means that the concepts are introduced and the results are obtained at the level of abstract institutions (in the sense of Goguen and Burstall [12]) and are therefore applicable to a multitude of logical systems and environments.
Types, Subtypes, and ASL+
 In Recent Trends in Data Type Specification, Lecture Notes in Computer Science 906
, 1995
"... . ASL+ is a formalism for specification and programming inthelarge, based on an arbitrary institution. It has rules for proving the satisfaction and refinement of specifications, which can be seen as a type theory with subtyping, including contravariant refinement for \Piabstracted specification ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
. ASL+ is a formalism for specification and programming inthelarge, based on an arbitrary institution. It has rules for proving the satisfaction and refinement of specifications, which can be seen as a type theory with subtyping, including contravariant refinement for \Piabstracted specifications and a notion of stratified equality for higherorder objects. We describe the syntax of the language and a partial equivalence relation semantics. This style of semantics is familiar from subtyping calculi, but a novelty here is the use of a hierarchy of typed domains instead of a single untyped domain. We introduce the formal system for proving satisfaction and refinement and describe how it is linked to proof systems of the underlying programming and specification languages. 1 Introduction There is a simple correspondence between the worlds of type theory and algebraic specification: elementhood, M : A () satisfaction, M 2 Mod(A) subtyping, A A 0 () refinement, A 0 /A The element...
Kan Extensions of Institutions
"... GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
GB92] to formally capture the notion of logical system. Interpreting institutions as functors, and morphisms and representations of institutions as natural transformations, we give elegant proofs for the completeness of the categories of institutions with morphisms and representations, respectively, show that the duality between morphisms and representations of institutions comes from an adjointness between categories of functors, and prove the cocompleteness of the categories of institutions over small signatures with morphisms and representations, respectively. Category: F.3, F.4
Grothendieck Inclusion Systems
 APPLIED CATEGORICAL STRUCTURES
"... Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logicindependent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothe ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
Inclusion systems have been introduced in algebraic specification theory as a categorical structure supporting the development of a general abstract logicindependent approach to the algebra of specification (or programming) modules. Here we extend the concept of indexed categories and their Grothendieck flattenings to inclusion systems. An important practical significance of the resulting Grothendieck inclusion systems is that they allow the development of module algebras for multilogic heterogeneous specification frameworks. At another level, we show that several inclusion systems in use in some syntactic (signatures, deductive theories) or semantic contexts (models) appear as Grothendieck inclusion systems too. We also study several general properties of Grothendieck inclusion systems.
Selected Papers
, 2007
"... The CALCO Young Researchers Workshop, CALCOjnr, was a satellite event for 2nd Conference on Algebra and Coalgebra in Computer Science, August 2024, 2007, Bergen, Norway (CALCO’07). CALCOjnr was dedicated to presentations by PhD students and by those who completed their doctoral studies within the ..."
Abstract
 Add to MetaCart
The CALCO Young Researchers Workshop, CALCOjnr, was a satellite event for 2nd Conference on Algebra and Coalgebra in Computer Science, August 2024, 2007, Bergen, Norway (CALCO’07). CALCOjnr was dedicated to presentations by PhD students and by those who completed their doctoral studies within the past few years. This report contains selected, refereed papers from the workshop.