Relating CASL with other specification languages: the institution level

In this work, we investigate various specification languages and their relation to CASL, the recently developed Common Algebraic Specification Language. In particular, we consider the languages Larch, OBJ3 and functional CafeOBJ, ACT ONE, ASF, and HEP-theories, as well as various sublanguages of CASL. All these languages are translated to an appropriate sublanguage of CASL.The translation mainly concerns the level of specification in-the-small: the logics underlying the languages are formalized as institutions, and representations among the institutions are developed. However, it is also considered how these translations interact with specification in-the-large.Thus, we obtain, on the one hand, translations of any of the above-mentioned specification languages to an appropriate sublanguage of CASL. This allows us to take libraries and case studies that have been developed for other languages and re-use them in CASL.On the other hand, we set up institution representations going from the CASL institution (and some of its subinstitutions) to simpler subinstitutions. Given a theorem proving tool for such a simpler subinstitution, with the help of a representation, it can also be used for a more complex institution. Thus, first-order theorem provers and conditional term rewriting tools become usable for CASL.

[1]  Till Mossakowski.  Specifications in an Arbitrary Institution with Symbols , 1999, WADT.

[2]  Till Mossakowski,et al.  Combining and representing logical systems using model-theoretic parchments , 1997, WADT.

[3]  Peter D. Mosses.  CASL for ASF+SDF Users , 1997 .

[4]  H. Baumeister,et al.  State-Based Extension of CASL ? / ? ? , 2000 .

[5]  Doug DeGroot,et al.  Logic programming - functions, relations and equations , 1986 .

[6]  Till Mossakowski,et al.  Equivalences among Various Logical Frameworks of Partial Algebras , 1995, CSL.

[7]  James J. Horning,et al.  Report on the Larch Shared Language , 1986, Sci. Comput. Program..

[8]  P. Burmeister.  A Model Theoretic Oriented Approach to Partial Algebras , 1986 .

[9]  Gianna Reggio,et al.  CASL-CHART: A Combination of Statecharts and of the Algebraic Specification Language CASL , 2000, AMAST.

[10]  Hartmut Ehrig,et al.  Fundamentals of Algebraic Specification 1 , 1985, EATCS Monographs on Theoretical Computer Science.

[11]  Till Mossakowski.  Colimits of order-sorted specifications , 1997, WADT.

[12]  Donald Sannella,et al.  Extended ML: Past, Present, and Future , 1990, ADT.

[13]  Peter Padawitz,et al.  Computing in Horn Clause Theories , 1988, EATCS Monographs on Theoretical Computer Science.

[14]  Alexandre V. Zamulin,et al.  State-Based Extensions of CASL , 2000, IFM.

[15]  Peter Burmeister,et al.  Partial algebras—survey of a unifying approach towards a two-valued model theory for partial algebras , 1982 .

[16]  J. Meseguer,et al.  Order-Sorted Algebra Solves the Constructor-Selector, Multiple Representation, and Coercion Problems , 1993, Inf. Comput..

[17]  Anne Elisabeth Haxthausen,et al.  Permissive Subsorted Partial Logic in CASL , 1997, AMAST.

[18]  T. Broadbent,et al.  Module Algebra , 1970, Nature.

[19]  Till Mossakowski.  Representations, hierarchies and graphs of institutions , 1996 .

[20]  Andrzej Tarlecki,et al.  On the Existence of Free Models in Abstract Algebraic Institutuons , 1985, Theor. Comput. Sci..

[21]  José Meseguer,et al.  May I Borrow Your Logic? (Transporting Logical Structures Along Maps) , 1997, Theor. Comput. Sci..

[22]  Donald Sannella,et al.  Specifications in an Arbitrary Institution , 1988, Inf. Comput..

[23]  MICHAEL BARR.  MODELS OF HORN THEORIES , 2004 .

[24]  Horst Herrlich,et al.  Abstract and concrete categories , 1990 .

[25]  Friederike Nickl,et al.  Pushouts of Order-Sorted Algebraic Specifications , 1996, AMAST.

[26]  Till Mossakowski.  A Hierarchy of Institutions Seperated by Properties of Parameterized Abstract Data Types , 1994, COMPASS/ADT.

[27]  Hans-Jörg Kreowski,et al.  Recent Trends in Data Type Specification , 1985, Informatik-Fachberichte.

[28]  José Meseguer,et al.  Remarks on remarks on many-sorted equational logic , 1987, SIGP.

[29]  José Meseguer,et al.  Remarks on remarks on many-sorted algebras with possibly emtpay carrier sets , 1986, Bull. EATCS.

[30]  Peter D. Mosses,et al.  CoFI: The Common Framework Initiative for Algebraic Specification and Development , 2001, Current Trends in Theoretical Computer Science.

[31]  Till Mossakowski,et al.  From Total Equational to Partial First-Order Logic , 1999, Algebraic Foundations of Systems Specification.

[32]  Hans-Jörg Kreowski,et al.  Equivalence and difference between institutions: simulating Horn Clause Logic with based algebras , 1995, Mathematical Structures in Computer Science.

[33]  Peter D. Mosses.  CASL for CafeOBJ Users , 2000 .

[34]  Till Mossakowski,et al.  HASCASL: Towards Integrated Specification and Development of Functional Programs , 2002, AMAST.

[35]  J. Meseguer.  Rewriting as a unified model of concurrency , 1990, OOPSLA/ECOOP '90.

[36]  Jean-Pierre Jouannaud,et al.  Operational Semantics for Order-Sorted Algebra , 1985, ICALP.

[37]  Martin Wirsing,et al.  Algebraic Specification , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[38]  Peter D. Mosses,et al.  CASL: the Common Algebraic Specification Language , 2002, Theor. Comput. Sci..

[39]  Tomasz Borzyszkowski.  Logical systems for structured specifications , 2002, Theor. Comput. Sci..

[40]  José Meseguer,et al.  Membership algebra as a logical framework for equational specification , 1997, WADT.

[41]  Roberto Bruni,et al.  Recent Trends in Algebraic Development Techniques , 2002, Lecture Notes in Computer Science.

[42]  Hubert Baumeister.  Relations between abstract datatypes modeled as abstract datatypes , 1998 .

[43]  Stephen J. Garland,et al.  Larch: Languages and Tools for Formal Specification , 1993, Texts and Monographs in Computer Science.

[44]  J. Lloyd.  Foundations of Logic Programming , 1984, Symbolic Computation.

[45]  Petros S. Stefaneas,et al.  Logical support for modularisation , 1993 .

[46]  Vincenzo Manca,et al.  Equational Type Logic , 1990, Theor. Comput. Sci..

[47]  Till Mossakowski,et al.  Static semantic analysis and theorem proving for CASL , 1997, WADT.

[48]  J. W. Lloyd,et al.  Foundations of logic programming; (2nd extended ed.) , 1987 .

[49]  K. J. Barwise,et al.  Axioms for abstract model theory , 1974 .

[50]  K. Mani Chandy,et al.  Current trends in programming methodology , 1977 .

[51]  Andrzej Tarlecki,et al.  Towards Heterogeneous Specifications , 1998, FroCoS.

[52]  José Meseguer,et al.  EQLOG: Equality, Types, and Generic Modules For Logic Programming , 1986, Logic Programming: Functions, Relations, and Equations.

[53]  Joseph A. Goguen,et al.  Institutions: abstract model theory for specification and programming , 1992, JACM.

[54]  Till Mossakowski,et al.  Using Limits of Parchment to Systematically Construct Institutions of partial Algebras , 1995, COMPASS/ADT.

[55]  Hartmut Ehrig,et al.  Algebraic Specifications with Generating Constraints , 1983, ICALP.

[56]  Davide Ancona,et al.  Extending Casl by Late Binding , 1999, WADT.

[57]  Mercè Llabrés,et al.  Pushout complements for partly total algebras , 2002, Mathematical Structures in Computer Science.

[58]  Horst Reichel,et al.  Initial Computability, Algebraic Specifications, and Partial Algebras , 1987 .

[59]  Peter D. Mosses,et al.  Unified algebras and institutions , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[60]  José Meseguer,et al.  Order-Sorted Algebra I: Equational Deduction for Multiple Inheritance, Overloading, Exceptions and Partial Operations , 1992, Theor. Comput. Sci..

[61]  Till Mossakowski.  CASL: From Semantics to Tools , 2000, TACAS.

[62]  Egidio Astesiano,et al.  Algebraic Foundations of Systems Specification , 1999, IFIP State-of-the-Art Reports.

[63]  Egidio Astesiano,et al.  Free Objects and Equational Deduction for Partial Conditional Specifications , 1995, Theor. Comput. Sci..

[64]  Andrzej Tarlecki.  Moving Between Logical Systems , 1995, COMPASS/ADT.

[65]  José Meseguer,et al.  Conditioned Rewriting Logic as a United Model of Concurrency , 1992, Theor. Comput. Sci..

[66]  Krzysztof R. Apt,et al.  Logic Programming , 1990, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[67]  Razvan Diaconescu,et al.  Extra Theory Morphisms for Institutions: Logical Semantics for Multi-Paradigm Languages , 1997, Appl. Categorical Struct..

[68]  Anne Elisabeth Haxthausen,et al.  Subsorted Partial Higher-Order Locig as an Extension of CASL , 1999, WADT.

[69]  Hartmut Ehrig,et al.  Algebraic Specification Techniques and Tools for Software Development: The Act Approach , 1993, AMAST Series in Computing.