Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-26T09:23:16.437Z Has data issue: false hasContentIssue false
  • English
  • Français

Categorical concepts for parameterized partial specifications†

Published online by Cambridge University Press:  04 March 2009

Ingo Claßen ,
Martin GroßE-Rhode  and
Uwe Wolter
Ingo Claßen
Affiliation:
Technische Universität Berlin, FB Informatik, Sekr. FR 6-1, Franklinstr. 28/29 10587 Berlin, Germany
Martin GroßE-Rhode
Affiliation:
Technische Universität Berlin, FB Informatik, Sekr. FR 6-1, Franklinstr. 28/29 10587 Berlin, Germany
Uwe Wolter
Affiliation:
Technische Universität Berlin, FB Informatik, Sekr. FR 6-1, Franklinstr. 28/29 10587 Berlin, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Categorical constructions inherent to a theory of algebras with strict partial operations are presented and exploited to provide a categorical deduction calculus for conditional existence equations and an alternative definition of such algebras based on the notion of syntactic categories. A compact presentation of the structural theory of parameterized (partial) specifications is given using the categorical approach. This theory is shown to be suitable for providing initial semantics as well as the compositionality results necessary for the definition of specification languages like ACT ONE and ACT TWO

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 5 , Issue 2 , June 1995 , pp. 153 - 188
Copyright
Copyright © Cambridge University Press 1995

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Burstall, R. M. and Goguen, J. A. (1977) Putting theories together to make specifications. In: Proc. Int. Conf. Artificial Intelligence.Google Scholar
Burmeister, P. (1986) A Model Theoretic Oriented Approach to Partial Algebras. Mathematical Research - Mathematische Forschung 32, Akademie-Verlag, Berlin.Google Scholar
Barr, M. and Wells, C. (1990) Category Theory for Computing Science. Prentice Hall International.Google Scholar
Claßen, I., Große-Rhode, M. and Wolter, U. (1992) Categorical concepts for parameterized partial specifications. Technical Report 92–46, Technische Universität Berlin.Google Scholar
Claßen, I. (1992) Towards Partial Algebra Semantics for Data Types in LOTOS. Technical Report Lo/WPl/T1.4/TUB/N0008/Vl, LOTOSPHERE.Google Scholar
Claßen, I. (1993) Compositionality of Application Oriented Structuring Mechanisms for Algebraic Specification Languages with Initial Semantics. PhD thesis, Technische Universität Berlin.Google Scholar
Ehrig, H., Baldamus, M. and Orejas, F. (1991) New concepts for amalgamation and extension in the framework of specification logics. Technical Report 91/05, Technische Universität Berlin.Google Scholar
Ehrig, H., Fey, W. and Hansen, H. (1983) ACT ONE: An algebraic specification language with two levels of semantics. Technical Report 83/03, Technische Universität Berlin.Google Scholar
Ehrig, H., Parisi-Presicce, F., Boehm, P., Rieckhoff, C., Dimitrovici, C. and Große-Rhode, M. (1988) Algebraic data type and process specifications based on projection spaces. In: Sannella, D. and Tarlecki, A. (eds.) Recent Trends in Data Type Specifications. Springer-Verlag Lecture Notes in Computer Science 332 23–43.CrossRefGoogle Scholar
Fey, W. (1988) Pragmatics, concepts, syntax, semantics, and correctness notions of ACT TWO: An algebraic module specification and interconnection language. Technical Report 88/26, Technische Universität Berlin.Google Scholar
Goguen, J.-A. and Burstall, R. M. (1984a) Introducing institutions. In: Proc. Logics of Programming Workshop. Springer-Verlag Lecture Notes in Computer Science 164 221–256.CrossRefGoogle Scholar
Goguen, J.-A. and Burstall, R. M. (1984b) Some fundamental algebraic tools for the semantics of computation - Part 1: Comma categories, colimits, signatures and theories. Theoretical Computer Science 31 175–209.CrossRefGoogle Scholar
Große-Rhode, M. and Dimitrovici, C. (1992) Algebraic specification of action trees and recursive processes. In: Nivat, M. and Podelski, A. (eds.) Tree Automata and Languages, Elsevier 235–290.Google Scholar
Goguen, J.-A. and Meseguer, J. (1989) Order-sorted algebra I. Technical Report SRI-CSL-89–10, SRI.Google Scholar
Goguen, J. A., Thatcher, J. W. and Wagner, E. G. (1978) An initial algebra approach to the specification, correctness and implementation of abstract data types. In: Yeh, R. (ed.) Current Trends in Programming Methodology IV: Data Structuring, Prentice Hall 80–144.Google Scholar
Goguen, J. A., Thatcher, J. W., Wagner, E. G. and Wright, J. B. (1977) Initial algebra semantics and continuous algebras. JACM 24 (1) 68–95.CrossRefGoogle Scholar
Hoehnke, H.-J. (1977) On partial algebras. In: Colloquia Mathematica Societatis Janos Bolyai 29Universal Algebra, Esztergom (Hungary) 373–412.Google Scholar
Hyland, J. M. E. and Pitts, A. M. (1989) The theory of constructions: Categorical semantics and topos-theoretic models. In: Categories in Computer Science and Logic, AMS-IMS-SIAM Joint Summer Research Conference, University of Colorado, Boulder 137–200.CrossRefGoogle Scholar
Jay, C. B. (1990) Extending properties to categories of partial maps. Technical Report LFCS 90–107, University of Edinburgh, Laboratory for Foundations of Computer Science.Google Scholar
Johnstone, P. T. (1977) Topos Theory, Academic Press.Google Scholar
Kaphengst, H. and Reichel, H. (1972) Operative Theorien und Kategorien von operativen Systemen. In: Studien zur Algebra und ihren Anwendungen 16, Akademie-Verlag 41–56.Google Scholar
Kock, A. and Reyes, G. E. (1977) Doctrines in categorical logic. In: Barwise, J. (ed.) Handbook of Mathematical Logic, Elsevier Science Publishers B. V., North-Holland283–313.CrossRefGoogle Scholar
Lawvere, F. W. (1963) Functorial semantics of algebraic theories. In: Proc. National Academy of Science, U.S.A. 50, Columbia University869–872.Google Scholar
Lambek, J. and Scott, P. J. (1986) Introduction to higher order categorical logic, Cambridge studies in advanced mathematics, Cambridge University Press.Google Scholar
Meseguer, J. (1989) General logics. In: Ebbinghaus, H.-D.et al. (eds.) Logic colloquium‘87, Elsevier Science Publishers B. V., North-Holland275–329.Google Scholar
Moggi, E.Partial morphisms in categories of effective objects. Information and Computation 76 250–277.CrossRefGoogle Scholar
Poigné, A. (1985) Algebra categorically. In: Pitt, D., Abramsky, S., Poigné, A. and Rydeheard, D. (eds.) Category Theory and Computer Programming. Springer-Verlag Lecture Notes in Computer Science 240 77–102.Google Scholar
Reichel, H. (1987) Initial Computability, Algebraic Specifications, and Partial Algebras, Oxford University Press.CrossRefGoogle Scholar
Robinson, E. and Rosolini, G. (1988) Categories of partial maps. Information and Computation 79 95–130.CrossRefGoogle Scholar
Seely, R. A. G. (1984) Locally cartesian closed categories and type theory. Mathematical Proceedings Cambridge Philosophical Society 95.CrossRefGoogle Scholar
Seely, R. A. G. (1987) Categorical semantics for higher order polymorphic lambda calculus. Journal of Symbolic Logic 52 (4).CrossRefGoogle Scholar
Tarlecki, A.On the existence of free models in abstract algebraic institutions. Theoretical Computer Science 37 269–304.CrossRefGoogle Scholar
Wolter, U.An Algebraic Approach to Deduction in Equational Partial Horn Theories. J. Inf. Process. EIK 27 (2) 85–128.Google Scholar