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Categorical Methods for Concurrency, Interaction, and Mobility (CONCUR 2002 Satellite workshop)

作者： Schweimeier, Ralf Department of Computing City University London United Kingdom

category theory has proved a useful tool in the study of type systems for sequential programming languages. Various approaches have been proposed to use categorical models to examine the type structures appropriate to concurrent systems. In this paper, we outline some of these approaches, such as interaction categories, and argue that they are not appropriate to model the handshake communication mechanism as used e.g. in CCS or the π-calculus. We propose an alternative general categorical framework for examining the type structure of such systems, and exhibit its categorical structure, which is similar to that of existing approaches. We then examine in detail an instance of this framework, based on a simple fragment of CCS. We prove that it is isomorphic to a syntactic category constructed from a process algebra similar to CCS, with a fusion operator, as in the fusion calculus. Thus, we make explicit some of the type structure implicitly present in such a process algebra. ©2002 Published by Elsevier Science B. V.

关键词： computer programming languages

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A model theory for generic schema management 8th

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8th International workshop on Database programming Languages, DBPL 2001

作者： Alagić, Suad Bernstein, Philip A. Microsoft Research One Microsoft Way RedmondWA98052-6399 United States Computer Science Department University of Southern Maine 96 Falmouth Street P.O. Box 9300 PortlandME04104-9300 United States

ISBN: (纸本)9783540440802

The core of a model theory for generic schema management is developed. This theory has two distinctive features: it applies to a variety of categories of schemas, and it applies to transformations of both the schema structure and its integrity constraints. A subtle problem of schema integration is considered in its general form, not bound to any particular category of schemas. The proposed solution, as well as the overall theory, is based entirely on schema morphisms that carry both structural and semantic properties. Duality results that apply to the schema and the data levels are established. These results lead to the main contribution of this paper: a formal schema and data management framework for generic schema management. Implications of this theory are established that apply to integrity problems in schema integration. The theory is illustrated by a particular category of schemas with objectoriented features along with typical database integrity constraints. © Springer-Verlag Berlin Heidelberg 2002.

关键词： Information management

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Concrete process categories

Concrete process categories

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Categorical Methods for Concurrency, Interaction, and Mobility (CONCUR 2002 Satellite workshop)

作者： Worytkiewicz, Krzysztof LTI Swiss Federal Institute of Technology CH1015-Lausanne Switzerland

This paper presents a rather concrete view of a semantic universe for typed concurrent computation. Starting with a notion of sets and functions organized in a category B featuring the type theory at hand, we identify the lax slice F//Span (B) of pseudo-functors from a free category into the bicategory of spans over B and triangles commuting up-to a lax natural transformation with representable components as a category of models of concurrency over which the semantic universe unfolds. By analogy, we call the objects of F//Span (B) categorical transition systems and demonstrate their relevance in giving meaning to a range of everyday phenomena including message passing among imperative programs. We identify the bicategory of spans Span(F//Span (B)) as organizing processes at a basic level and address the question of their equality, articulated as bisimulation w.r.t. actions observable at the interfaces given by the legs of such spans. An appropriate notion of simulation yields a system of open maps by which to quotient Span(F//Span (B)), a construction originally considered by Cockett and Spooner in its generality. The resulting process category Proc(F//Span (B),ω¯) properly contains the well-known interaction category SProc introduced by Abramsky et al. ©2002 Published by Elsevier Science B. V.

关键词： computer programming

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Using category theory to model software component dependencies

Using category theory to model software component dependenci...

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International Conference and workshop on Engineering of computer-Based Systems

作者： Jiang Guo Department of Computer Science California State University Bakersfield Bakersfield CA USA

ISBN: (纸本)0769515495

As the size and complexity of software systems grow, the identification and proper management of interconnection dependencies among various pieces of a system have become responsible for an increasingly important part of the development effort. In today's large systems, the variety of encountered interconnection relationships (such as implements, uses, and extends) is very large, while the complexity of protocols for managing them can be very high. The paper tries to address this problem by using category theory. It also gives a framework of dependency modeling.

关键词： Protocols Software systems computer languages LAN interconnection programming profession Application software Software development management Software tools computer science Packaging

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Computable queries for object oriented databases

Computable queries for object oriented databases

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WoLLIC'2002, 9th workshop on Logic, Language, Information and Computation

作者： Schewe, Klaus-Dieter Turull-Torres, Jose-Maria Massey University Department of Information Systems Private Bag 11222 Palmerston North NZ New Zealand

A relational database can be considered as a finite structure for a finite relational signature in first-order logic, i.e., there are no function symbols. Interpreting the logic over this signature in such structures allows the expressiveness and complexity of queries to be studied in detail. This is the starting point for finite model theory which has proven to be a viable tool to study relational database theory. In particular, it is known that computable queries expressed as isomorphism-preserving partial recursive functions can be formalized by Reflective Relational Machines. These are extended Turing Machines with an additional relational store, a query tape and the facility to evaluate the query on the tape against the database in the store in a single step. In this paper we start to generalize the theory to post-relational databases. We first consider the case of having set-based complex values and references such that the semantics can still be expressed in finite sets. Following the approach that object oriented databases in general including those, where the underlying type systems does no longer allow the semantics defined by sets, can be expressed as theories in higher-order intuitionistic logic, we use such a logic instead of first-order logic. However, as we are not yet exploiting the full power of such logics, we can interpret the logic in the category FINSET of finite sets, i.e., again in a structure defined by a database. Having done this the definition of computable queries and the model of Reflective Relational Machines carry over easily. We can show that the new model of Reflective Object Machines guarantees completeness, i.e., all computable queries can be expressed by the model. ©2002 Published by Elsevier Science B.V.

关键词： Object oriented programming

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New foundations for rewriting logic

New foundations for rewriting logic

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The 3rd International workshop on Rewriting Logic and its Applications

作者： Hilberdink, Hendrik Koryo International Women's College 4-4 Sagamine Komenoki-cho Nisshin-shi Aichi 470-0193 Japan

This paper presents an abstract treatment of the foundations of rewriting logic, generalising in three ways: an arbitrary 2-category plays the role of the specific 2-category Cat;the foundations are rendered fully independent of the underlying equational logic;and the semantics covers non-conventional sentences. Despite the high level of abstraction a number of properties of interest to Computing Science are seen to hold including the existence of initial models, liberality along theory morphisms, exactness, and a completeness theorem for a very abstract notion of deduction. ©2000 Published by Elsevier Science B. V.

关键词： Logic programming

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A fully abstract model for sequential computation

A fully abstract model for sequential computation

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workshop on Domains IV

作者： Marz, Michael Fachbereich Mathematik Technische Universität Darmstadt Schloßgartenstraße 7 D-64289 Darmstadt Germany

A fully abstract model for sequential computation which is purely syntactic is presented. Some domain theoretic concepts and notations are introduced and a cartesian closed category SD of domains to capture the concept of sequentiality is constructed. SD can be used as a framework for a fully abstract model for sequential programming languages like PCF or FPC. The relational account of full abstraction identifies invariants of sequential functions.

关键词： Computation theory

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Data refinement for call-by-value programming languages 13th

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8th Annual Conference of the European-Association-for-computer-Science-Logic (EACSL)/13th International workshop on computer Science Logic (CSL 99)

作者： Kinoshita, Y Power, J Electrotech Lab Tsukuba Ibaraki 305 Japan Univ Edinburgh Lab Fdn Comp Sci Edinburgh EH9 3JZ Midlothian Scotland

ISBN: (纸本)3540665366

We give a category theoretic framework for data-refinement in call-by-value programming languages. One approach to data refinement for the simply typed lambda -calculus is given by generalising the notion of logical relation to one of lax logical relation, so that binary lax logical relations compose. So here, we generalise the notion of lax logical relation, defined in category theoretic terms, from the simply typed lambda -calculus to the computational lambda -calculus as a model of data refinement.

关键词： category theory categorical models and logic denotational semantics lambda and combinatory calculi

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11th workshop on Abstract Data Types, 1995

11th Workshop on Abstract Data Types, 1995

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Joint 11th workshop on Abstract Data Types was held jointly with the 8th workshop on Recent Trends in Data Type Specification, COMPASS 1995

ISBN: (纸本)3540616292

The proceedings contain 31 papers. The special focus in this conference is on Abstract Data Types, 1995. The topics include: Seven years of COMPASS;inductively defined relations;on the role of category theory in the area of algebraic specifications;a challenge for computing science;the larch shared language: some open problems;the lambda calculus as an abstract data type;unifying theories in different institutions;interchange format for inter-operability of tools and translation;experiments with partial evaluation domains for rewrite specifications;class-sort polymorphism in glider;deontic concepts in the algebraic specification of dynamic systems;reification - changing viewpoint but preserving truth;a category-based equational logic semantics to constraint programming 200;concurrent state transformations on abstract data types;categories of circuits;combining algebraic and set-theoretic specifications;minimal term rewriting systems;an interactive theorem and completeness prover for algebraic specifications with conditional equations;the non-ground case completeness;termination of curryfied rewrite systems;correctness and oracle;behavioural equivalence, bisimulation, and minimal realisation;using limits of parchments to systematically construct institutions of partial algebras;behavioural specifications in type theory;syntax, semantics, and theory;context institutions;object-oriented functional programming and type reconstruction;moving between logical systems;modular algebraic specifications and the orientation of equations into rewrite rules;a model for I/O in equational languages with don't care non-determinism and tool design for structuring mechanisms for algebraic specification languages with initial semantics.

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A LOGIC FOR category theory

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THEORETICAL computer SCIENCE 1993年第1-2期111卷 211-252页

作者： GILMORE, PC TSIKNIS, GK Department of Computer Science University of British Columbia Vancouver B.C. V6T 1Z2 Canada

MacLane and Feferman have argued that the traditional set theories of Zermelo-Fraenkel and Godel-Bernays are not suitable foundations for category theory because of the requirement for self-referencing abstractions. The necessity for distinguishing between small and large categories reflects this unsuitability. The purpose of this paper is to demonstrate that a formalization within a natural-deduction-based logic and set theory called NaDSet avoids the difficulties that arise with the use of the traditional set theories. Definitions are provided within NaDSet for most of the fundamental concepts and constructs in category theory. The main result of the paper is a proof that the set of all functors forms a category under appropriate definitions of composition and equivalence. Additional definitions and discussions on products, comma categories, universals, limits and adjoints are presented. They provide evidence to support the claim that any construct. not only in categories, but also in toposes, sheaves, triples and similar theories can be formalized within NaDSet. NaDSet succeeds as a logic and set theory for category theory because the resolution of the paradoxes provided for it is based on an extension of Tarski's reductionist semantics for first-order logic. Self-membership and self-reference is not explicitly excluded. The reductionist semantics is most simply presented as a natural-deduction logic. A sketch of the elementary and logical syntax or proof theory of the logic is provided. A consistency proof for NaDSet is provided elsewhere.

关键词： computer programming languages

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