Abstract. Institutions formalise the intuitive notion of logical system, including syntax, semantics, and the relation of satisfaction between them. Our exposition emphasises 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 generalise 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 ‘semi-natural’ 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 a generalisation of universal algebra; these illustrate various points in the main text. A final appendix makes explicit a greater generality for the institution concept, clarifies certain details and proves some results that lift institution theory to this level.

Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ (Behavioral OBJects) behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.

Abstract. We describe an approach to user interface design based on ideas from social science, narratology (the theory of stories), cognitive science, and a new area called algebraic semiotics. Social analysis helps to identify certain roles for users with their associated requirements, and suggests ways to make proofs more understandable, while algebraic semiotics, which combines semiotics with algebraic specification, provides rigorous theories for interface functionality and for a certain technical notion of quality. We apply these techniques to designing user interfaces for a distributed cooperative theorem proving system, whose main component is a website generation and proof assistance tool called Kumo. This interface integrates formal proving, proof browsing, animation, informal explanation, and online background tutorials, drawing on a richer than usual notion of proof. Experience with using the interface is reported, and some conclusions are drawn.

This paper describes some tools to support formal methods, and conversely some formal methods for developing such tools. We focus on distributed cooperative proving over the web. Our tools include a proof editor/assistant, servers for remote proof execution, a distributed truth protocol, an editor generator; and a new method for interface design called algebraic semiotics, which combines semiotics with algebraic specification. Some examples are given.

The paper discusses an approach to software architecture based on concepts from parameterized programming, particularly its language of "module expressions". A module expression describes the architecture of a system as an interconnection of component modules, and executing the expression actually builds the system. Language features include: modules parameterized by theories, which declare interfaces; a number of module composition operations; views for binding modules to interfaces; and both vertical and horizontal composition. Modules may involve information hiding, theories may declare semantic restrictions with axioms, and views assert behavioral satisfaction of axioms by a module. Some "laws of software composition" are given, showing how various module composition operations are related. We also show how a variety of architectural styles can be supported, and how this approach can be extended to support evolution and traceability. All this is intended to ease the development of large systems, and in particular, to make reuse more effective in practice.

This paper surveys several different variants of order sorted algebra (abbreviatedOSA), comparing some of the main approaches (overloaded OSA, universe OSA, unified algebra, term declaration algebra,etc.), emphasising motivation and intuitions, and pointing out features that distinguish the original ‘overloaded’ OSA approach from some later developments. These features include sort constraints and retracts; the latter is particularly useful for handling multiple data representations (including automatic coercions among them). Many examples are given, for most of which, runs are shown on the OBJ3 system. This paper also significantly generalises overloaded OSA by dropping the regularity and monotonicity assumptions, and by adding signatures of non-monotonicities, which support simple semantics for some aspects of object oriented programming. A number of new results for this generalisation are proved, including initiality, variety, and quasi-variety theorems. Axiomatisability results àlaBirkhoff are also proved for unified algebras.

Social issues in requirements engineering are classified according to what groups are involved. Topics discussed include issues within the client organization, requirement team issues, issues between the client organization and the requirements team, and development team issues.>

The authors survey and evaluate techniques for eliciting requirements of computer-based systems, paying particular attention to dealing with social issues. The methods surveyed include introspection, interviews, questionnaires, and protocol, conversation, interaction, and discourse analyses. The last three techniques grew out of ethnomethodology and sociolinguistics. They can elicit tacit knowledge by observing actual interactions in the workplace, and can also be applied to the system development process itself.>

There is a population explosion among the logical systems used in computing science. Examples include first-order logic, equational logic, Horn-clause logic, higher-order logic, infinitary logic, dynamic logic, intuitionistic logic, order-sorted logic, and temporal logic; moreover, there is a tendency for each theorem prover to have its own idiosyncratic logical system. The concept of institution is introduced to formalize the informal notion of “logical system.” The major requirement is that there is a satisfaction relation between models and sentences that is consistent under change of notation. Institutions enable abstracting away from syntactic and semantic detail when working on language structure “in-the-large”; for example, we can define language features for building large logical system. This applies to both specification languages and programming languages. Institutions also have applications to such areas as database theory and the semantics of artificial and natural languages. A first main result of this paper says that any institution such that signatures (which define notation) can be glued together, also allows gluing together theories (which are just collections of sentences over a fixed signature). A second main result considers when theory structuring is preserved by institution morphisms. A third main result gives conditions under which it is sound to use a theorem prover for one institution on theories from another. A fourth main result shows how to extend institutions so that their theories may include, in addition to the original sentences, various kinds of constraint that are useful for defining abstract data types, including both “data” and “hierarchy” constraints. Further results show how to define institutions that allow sentences and constraints from two or more institutions. All our general results apply to such “duplex” and “multiplex” institutions.

This paper uses concepts from sheaf theory to explain phenomena in concurrent systems, including object, inheritance, deadlock, and non-interference, as used in computer security. The approach is very; general, and applies not only to concurrent object oriented systems, but also to systems of differential equations, electrical circuits, hardware description languages, and much more. Time can be discrete or continuous, linear or branching, and distribution is allowed over space as well as time. Concepts from categpru theory help to achieve this generality: objects are modelled by sheaves; inheritance by sheaf morphisms; systems by diagrams; and interconnection by diagrams of diagrams. In addition, behaviour is given by limit, and the result of interconnection by colimit. The approach is illustrated with many examples, including a semantics for a simple concurrent object-based programming language.

This paper tries to explain why and how category theory is useful in computing science, by giving guidelines for applying seven basic categorical concepts: category, functor, natural transformation, limit, adjoint, colimit and comma category. Some examples, intuition, and references are given for each concept, but completeness is not attempted. Some additional categorical concepts and some suggestions for further research are also mentioned. The paper concludes with some philosophical discussion.

This paper studies unification for order-sorted equational logic. This logic generalizes unsorted equational logic by allowing a partially ordered set of sorts, with the ordering interpreted as set-theoretic containment in the models; it also allows overloading of function symbols, such as + for integer and rational number addition, with the overloaded functions of greater rank interpreted in the models as extensions of those of smaller rank. Our presentation emphasizes semantic aspects, and gives a categorical treatment of unification that has substantial advantages in this context over the usual treatment of unifiers as endomorphisms of a single free algebra. Given system Γ of equations and a set E of axioms that is sort-preserving and does not impose restrictions on the sorts of its variables, the main results characterize when an order-sorted signature has a minimal (or finite, or most general when Γ is solvable) family of order-sorted E-unifiers for Γ. In addition, for unitary signatures, where each solvable system of equations has a most general unifier, we give a quasi-linear algorithm for syntactic unification (i.e., for E= ) a la Martelli-Montanari, that is more efficient than the unsorted one for failures.

This paper applies some recent advances in algebraic specification technology to plane geometry. The two most important specification techniques are parameterized modules and order-sorted algebra; the latter provides a systematic treatment of subtypes. This exercise also indicates how a rigorous semantic foundation in equational logic can be given for many techniques in knowledge representation, including is-a hierarchies (with multiple inheritance), multiple representations, implicit (one-way) coercion of representation and parameterized modular structuring. Degenerate cases (which can be a particular nuisance in computational geometry), exception handling, information hiding, block structure, and pattern-driven rules are also treated, and again have rigorous semantic foundations. The geometric constructions which illustrate all this are specified over any ordered field having square roots of nonnegative elements; thus, we also specify some algebra, including rings, fields, and determinants. All specifications are written in a variant of the OBJ language.

Article Principles of OBJ2 Share on Authors: Kokichi Futatsugi Electrotechnical Laboratory, 1-1-4 Umezono, Sakura, Niibari, Ibaraki 305, Japan Electrotechnical Laboratory, 1-1-4 Umezono, Sakura, Niibari, Ibaraki 305, JapanView Profile , Joseph A. Goguen SRI International, Menlo Park CA and Center for the Study of Language and Information, Stanford University SRI International, Menlo Park CA and Center for the Study of Language and Information, Stanford UniversityView Profile , Jean-Pierre Jouannaud CRIN, Campus Scientifique, BP 239, 54506 Vandoeuvre-les-Nancy, Cedex, France CRIN, Campus Scientifique, BP 239, 54506 Vandoeuvre-les-Nancy, Cedex, FranceView Profile , José Meseguer SRI International, Menlo Park CA and Center for the Study of Language and Information, Stanford Universit SRI International, Menlo Park CA and Center for the Study of Language and Information, Stanford UniversitView Profile Authors Info & Claims POPL '85: Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languagesJanuary 1985 Pages 52–66https://doi.org/10.1145/318593.318610Online:01 January 1985Publication History 308citation447DownloadsMetricsTotal Citations308Total Downloads447Last 12 Months14Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

This paper discusses two main ideas, unwinding and inference control. While both concern computer security, they are not closely related to each other. Unwinding is a verification technique for general security requirements based on noninterference assertions as in [Goguen & Meseguer 82a]. The inference control problem concerns preventing inference of unauthorized information by combining authorized information. The main result in this paper is an unwinding theorem that gives a very simple necessary and sufficient condition for a system to satisfy the MLS security policy system. A subsidiary topic is secure interfaces, which we show how to treat with noninterferce assertions.

Parameterized programming is a powerful technique for the reliable reuse of software. In this technique, modules are parameterized over very general interfaces that describe what properties of an environment are required for the module to work correctly. Reusability is enhanced by the flexibility of the parameterization mechanism proposed here. Reliability is further enhanced by permitting interface requirements to include more than purely syntactic information. This paper introduces three new ideas that seem especially useful in supporting parameterized programming: 1) theories, which declare global properties of program modules and interfaces; 2) views, which connect theories with program modules in an elegant way; and 3) module expressions, a kind of general structured program transformation which produces new modules by modifying and combining existing modules. Although these ideas are illustrated with some simple examples in the OBJ programming language, they should also be taken as proposals for an Ada1library system, for adding modules to Prolog, and as considerations for future language design efforts. OBJ is an ultra-high level programming language, based upon rewrite rules, that incorporates these ideas, and many others from modern programming methodology.

We assune that the reader is familiar with the ubiquity of information in the modern world and is sympathetic with the need for restricting rights to read, add, modify, or delete information in specific contexts. This need is particularly acute for systems having computers as significant components.

Americanae nace como un proyecto conjunto que surge dentro de la Red Europea de Información y Documentación sobre América Latina (REDIAL), y que ha afrontado la Biblioteca de la Agencia Española de Cooperación Internacional para el Desarrollo (AECID). Esta nueva biblioteca virtual hace más accesibles los libros digitales de tema americanista a los investigadores y usuarios interesados de cualquier parte del mundo.

Many apparently divergent approaches to specifying formal semantics of programming languages are applications of initial algebra semantics. In this paper an overview of initial algebra semantics is provided. The major technical feature is an initial continuous algebra which permits unified algebraic treatment of iterative and recursive semantic features in the same framework as more basic operations.

In a wide variety of situations, computer science has found it convenient to define complex object as (fixed-point) solutions of certain equations. This has been done in both algebraic and order-theoretic settings, and has often been contrasted with other approaches. This paper shows how to formulate such solutions in a setting which encompasses both algebraic and order-theoretic aspects, so that the advantages of both worlds are available. Moreover, we try to show how this is consistent with other approaches to defining complex objects, through a number of applications, including: languages defined by context-free grammars; flow charts and their interpretations; and monadic recursive program schemes. The main mathematical results concern free rational theories and quotients of rational theories. However, the main goal has been to open up what we believe to be a beautiful and powerful new approach to the syntax and semantics of complex recursive specifications.

Axioms characterizing combinatorial discrimination information are given and extended to characterize arbitrary measure theoretic discrimination information.