Abstract
Algebraic specification frameworks exploit a variety of sort disciplines. The treatment of sorts has a considerable influence on the ease with which such features as partiality and polymorphism can be specified. This survey gives an accessible overview of various frameworks, focusing on their sort disciplines and assessing their strengths and weaknesses for practical applications. Familiarity with the basic notions of algebraic specification is assumed.
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P. Aczel. Term declaration logic and generalized composita. In LICS'91, Proc. 6th Ann. Symp. on Logic in Computer Science, pages 22–30. IEEE, 1991.
H. Andréka, P. Burmeister, and I. Németi. Quasi-varieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras. Preprint 557, FB Mathematik und Informatik, TH Darmstadt, 1980.
E. Astesiano and M. Cerioli. Non-strict don't care algebras and specifications. In Proc. TAPSOFT'91, Brighton, number 493 in Lecture Notes in Computer Science, pages 121–142. Springer-Verlag, 1991.
E. Astesiano and M. Cerioli. Relationships between logical frameworks. This volume, 1992.
G. Bernot, M. Bidoit, and C. Choppy. Abstract data types with exception handling: an initial approach based on a distinction between exceptions and errors. Theoretical Comput. Sci., 46:13–46, 1986.
G. Bernot and P. Le Gall. Label algebras. This volume, 1992.
M. Bidoit. Algebraic specification of exception handling and error recovery by means of declarations and equations. In ICALP'84, Proc. Int. Coll. on Automata, Languages, and Programming, Antwerp, number 172 in Lecture Notes in Computer Science, pages 95–108. Springer-Verlag, 1984.
M. Broy and M. Wirsing. Partial abstract types. Acta Inf., 18:47–64, 1982.
P. Burmeister. A Model-Theoretic Oriented Approach to Partial Algebras. Akademie-Verlag, Berlin, 1986.
H. Comon. Completion of rewrite systems with membership constraints. Technical report, SUNY at Stony Brook, 1991.
R. L. Constable et al. Implementing Mathematics with the Nuprl Proof Development System. Prentice-Hall, 1986.
H. Ehrig and B. Mahr. Fundamentals of Algebraic Specification 1: Equations and Initial Semantics. Number 6 in EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1985.
H. Ehrig, P. Pepper, and F. Orejas. On recent trends in algebraic specification. In ICALP'89, Proc. Int. Coll. on Automata, Languages, and Programming, Torino, number 372 in Lecture Notes in Computer Science, pages 263–288. Springer-Verlag, 1989.
M. Gogolla. Partially ordered sorts in algebraic specifications. In Proc. 1984 Colloq. on Trees in Algebra and Programming, Bordeaux, pages 139–153. Cambridge University Press, 1984.
M. Gogolla. A final algebra semantics for errors and exceptions. In Recent Trends in Data Type Specification, number 116 in Series IFB, pages 89–103. Springer-Verlag, 1985.
M. Gogolla. On parametric algebraic specifications with clean error handling. In TAP-SOFT'87, Proc. Int. Joint Conf. on Theory and Practice of Software Development, Pisa, Volume 1, number 249 in Lecture Notes in Computer Science, pages 81–95. Springer-Verlag, 1987.
M. Gogolla, K. Drosten, U. Lipeck, and H.-D. Ehrich. Algebraic and operational semantics of specifications allowing exceptions and errors. Theoretical Comput. Sci., 34:289–313, 1984.
J. A. Goguen. Abstract errors for abstract data types. In Proc. IFIP Working Conference on the Formal Description of Programming Concepts, St. Andrews, New Brunswick, 1977. North-Holland, 1978.
J. A. Goguen. Order sorted algebra. Semantics and Theory of Computation Report 14, UCLA Computer Science Dept., 1978.
J. A. Goguen. Types as theories. In Proc. Symposium on General Topology and Applications. Oxford University Press, 1990.
J. A. Goguen and R. M. Burstall. Introducing institutions. In Proc. Logics of Programming Workshop, number 164 in Lecture Notes in Computer Science, pages 221–256. Springer-Verlag, 1984.
J. A. Goguen and R. M. Burstall. A study in the foundations of programming methodology: specifications, institutions, charters and parchments. In Proc. Workshop on Category Theory and Computer Programming, Guildford, number 240 in Lecture Notes in Computer Science, pages 313–333. Springer-Verlag, 1986.
J. A. Goguen and J. Meseguer. Order-sorted algebra I: Equational deduction for multiple inheritance, overloading, exceptions and partial operations. Technical Report SRI-CSL-89-10, Computer Science Lab., SRI International, July 1989.
J. A. Goguen, J. W. Thatcher, and E. G. Wagner. An initial algebra approach to the specification, correctness, and implementation of abstract data types. In R. T. Yeh, editor, Current Trends in Programming Methodology, volume IV. Prentice-Hall, 1978.
J. A. Goguen and T. Winkler. Introducing OBJ3. Technical Report SRI-CSL-88-9, Computer Science Lab., SRI International, 1988.
C. Kirchner and H. Kirchner. Order-sorted computations in G-algebra. Draft, INRIA-Lorraine & CRIN, Nancy, December 1991.
H.-J. Kreowski. Partial algebras flow from algebraic specifications. In ICALP'87, Proc. Int. Coll. on Automata, Languages, and Programming, Karlsruhe, number 267 in Lecture Notes in Computer Science, pages 521–530. Springer-Verlag, 1987.
V. Manca, A. Salibra, and G. Scollo. Equational type logic. Theoretical Comput. Sci., 77:131–159, 1990.
V. Manca, A. Salibra, and G. Scollo. On the expressiveness of equational type logic. In The Unified Computation Laboratory. Oxford University Press, 1992. To appear.
N. MartÃ-Oliet and J. Mesguer. Inclusions and subtypes. Technical Report SRI-CSL-90-16, Computer Science Lab., SRI International, 1990.
A. Mégrelis. Algèbre Galactique. PhD thesis, Univ. de Nancy, 1990.
A. Mégrelis. Partial algebra + order-sorted algebra = galactic algebra. Tech. Report CRIN 90-R-108, Centre de Recherche en Informatique de Nancy, 1990.
B. Möller. On the algebraic specification of infinite objects — ordered and continuous models of algebraic types. Acta Inf., 22:537–578, 1985.
P. D. Mosses. Unified algebras and action semantics. In STACS'89, Proc. Symp. on Theoretical Aspects of Computer Science, Paderborn, number 349 in Lecture Notes in Computer Science, pages 17–35. Springer-Verlag, 1989.
P. D. Mosses. Unified algebras and institutions. In LICS'89, Proc. 4th Ann. Symp. on Logic in Computer Science, pages 304–312. IEEE, 1989.
P. D. Mosses. Unified algebras and modules. In POPL'89, Proc. 16th Ann. ACM Symp. on Principles of Programming Languages, pages 329–343. ACM, 1989.
P. D. Mosses. Action Semantics. Tracts in Theoretical Computer Science. Cambridge University Press, 1992.
O. Owe and O.-J. Dahl. Generator induction in order-sorted algebras. Formal Aspects of Computing, 3:2–20, 1991.
A. Poigné. Another look at parameterization using algebraic specifications with subsorts. In MFCS'84, Proc. Symp. on Math. Foundations of Computer Science, number 176 in Lecture Notes in Computer Science. Springer-Verlag, 1984.
A. Poigné. Partial algebras, subsorting and dependent types. In D. Sannella and A. Tarlecki, editors, Recent Trends in Data Type Specification, number 332 in Lecture Notes in Computer Science, pages 208–234. Springer-Verlag, 1988.
A. Poigné. Typed Horn logic. In MFCS'90, Proc. Symp. on Math. Foundations of Computer Science, number 452 in Lecture Notes in Computer Science, pages 470–477. Springer-Verlag, 1990.
A. Poigné. Once more on order-sorted algebra. In MFCS'91, Proc. Symp. on Math. Foundations of Computer Science, number 520 in Lecture Notes in Computer Science, pages 397–405. Springer-Verlag, 1991.
Z. Qian. Relation-sorted algebraic specifications with built-in coercers: parameterization and parameter passing. In Proc. Workshop on Categorical Methods in Computer Science with Aspects from Topology, number 393 in Lecture Notes in Computer Science, pages 244–260. Springer-Verlag, 1989.
H. Reichel. Initial Computability, Algebraic Specifications, and Partial Algebras. Number 2 in The International Series of Monographs on Computer Science. Oxford University Press, 1987.
D. Sannella and A. Tarlecki. Specifications in an arbitrary institution. Information and Computation, 76:165–210, 1988.
G. Scollo. On the use of equational type logic for software engineering and protocol design. In Numidio, editor, Proc. 1st Maghrebin Conf. on Artificial Intelligence and Software Engineering, Constantine, Algeria, 1989, pages 460–485,1991. Also available as Memoranda Informatica 89-52, Univ. Twente.
G. Smolka. Order-sorted Horn logic: Semantics and deduction. SEKI Report SR-86-17, FB Informatik, Universität Kaiserslautern, 1986.
G. Smolka. Logic Programming over Polymorphically Order-Sorted Types. PhD thesis, Universität Kaiserslautern, 1989.
G. Smolka, W. Nutt, J. A. Goguen, and J. Meseguer. Order-sorted equational computation. In Proc. Colloq. on Resolution of Equations in Algebraic Structures, Austin. Academic Press, 1989.
W. W. Wadge. Classified algebras. Theory of Computation Report 46, University of Warwick, 1982.
U. Waldmann. Semantics of order-sorted specifications. To appear in Theoretical Comput. Sci., 1992.
M. Wirsing. Algebraic specification. In J. van Leeuwen, A. Meyer, M. Nivat, M. Paterson, and D. Perrin, editors, Handbook of Theoretical Computer Science, volume B, chapter 13. Elsevier Science Publishers, Amsterdam; and MIT Press, 1990.
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Mosses, P.D. (1993). The use of sorts in algebraic specifications. In: Bidoit, M., Choppy, C. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1991 1991. Lecture Notes in Computer Science, vol 655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56379-2_35
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