The logic of the partial A-Calculus with equality

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3210, Issue , 2004, Pages 385-399

  Schröder, Lutz ^a  

^a UNIVERSITY OF BREMEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; COMPUTATIONAL LINGUISTICS; COMPUTATIONAL MECHANICS; DIFFERENTIATION (CALCULUS); FORMAL LOGIC; RECONFIGURABLE HARDWARE; SPECIFICATION LANGUAGES;

ALGEBRAIC SPECIFICATION LANGUAGES; DEPENDENT TYPE THEORY; FUNDAMENTAL THEOREMS; HIGHER ORDER LOGIC; HIGHER-ORDER; LAMBDA CALCULUS; PARTIAL CARTESIAN CLOSED CATEGORIES; SEMANTICAL FOUNDATIONS;

COMPUTER CIRCUITS;

EID: 33244463606     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30124-0_30     Document Type: Article

References (28)

1. J. Adámek, H. Herrlich, and G. E. Strecker, Abstract and concrete categories, Wiley Interscience, 1990.
2. M. Bidoit and P. D. Mosses, CASL user manual, LNCS, vol. 2900, Springer, 2004.
3. M. Broy, C. Facchi, R. Grosu, R. Hettler, H. Hussmann, D. Nazareth, F. Regensburger, and K. Stølen, The requirement and design specification language SPECTRUM, Tech. report, Technical University of Munich, 1993.
4. A. Bucalo, C. Fürmann, and A. Simpson, Equational lifting monads, Category Theory and Computer Science, ENTCS, vol. 29, 1999.
5. P. Burmeister, A model theoretic oriented approach to partial algebras, AkademieVerlag, 1986.
6. P.-L. Curien and A. Obtulowicz, Partiality, cartesian closedness and toposes, Information and Computation 80 (1989), 50-95.
7. P. Preyd, Aspects of topoi, Bull. Austral. Math. Soc. 7 (1972), 1-76.
8. C. George, P. Haff, K. Havelund, A. Haxthausen, R. Milne, C. Nielson, S. Prehn, and K. Wagner, The Raise Specification Language, Prentice Hall, 1992.
9. M. Hofmann, On the interpretation of type theory in locally cartesian closed categories, Computer Science Logic, LNCS, vol. 933, 1995, pp. 427-441.
10. P. Johnstone, Sketches of an elephant: a topos theory compendium, vol. 2, Clarendon, 2002.
11. J. Lambek and P. Scott, Introduction to higher order categorical logic, Cambridge University Press, 1986.
12. W. Mitchell, Boolean topoi and the theory of sets, J. Pure Appl. Algebra 2 (1972), 261-274.
13. E. Moggi, Categories of partial morphisms and the λ-calculus, Category Theory and Computer Programming, LNCS, vol. 240, Springer, 1986, pp. 242-251.
14. ____, The partial lambda calculus, Ph.D. thesis, University of Edinburgh, 1988.
15. P. D. Mosses (ed.), CASL reference manual, LNCS, vol. 2960, Springer, 2004.
16. J. Penon, Quasi-topos, C. R. Acad. Sci., Paris, Sér. A 276 (1973), 237-240.
17. E. Robinson and G. Rosolini, Categories of partial maps, Inform, and Comput. 79 (1988), 95-130.
18. G. Rosolini, Continuity and effectiveness in topoi, Ph.D. thesis, Merton College, Oxford, 1986.
19. L. Schröder, The HASCASL prologue: categorical syntax and semantics of the partial λ-calculus, available as http://www.informatik.uni-bremen. de/~lschrode/ hascasl/plam.ps
20. ____, Classifying categories for partial equational logic, Category Theory and Computer Science, ENTCS, vol. 69, 2002.
21. ____, Henkin models of the partial X-calculus, Computer Science Logic, LNCS, vol. 2803, Springer, 2003, pp. 498-512.
22. L. Schröder and T. Mossakowski, Monad-independent dynamic logic in HASCASL, J. Logic Comput., to appear. Earlier version in Recent Developments in Algebraic Development Techniques (WADT 02), LNCS, vol. 2755, Springer, 2003, 425-441.
23. ____, HASCASL: Towards integrated specification and development of functional programs, Algebraic Methodology And Software Technology, LNCS, vol. 2422, Springer, 2002, pp. 99-116.
24. ____, Monad-independent Hoare logic in HASCASL, Fundamental Aspects of Software Engineering (M. Pezze, ed.), LNCS, vol. 2621, 2003, pp. 261-277.
25. L. Schröder, T. Mossakowski, and C. Maeder, HASCASL - Integrated functional specification and programming. Language summary, available at http://www. informatik.uni-bremen.de/agbkb/forschung/formal_methods/CoFI/HASCASL
26. D. Scott, Continuous lattices, Toposes, Algebraic Geometry and Logic, LNM, vol. 274, Springer, 1972, pp. 97-136.
27. R. A. G. Seely, Locally cartesian closed categories and type theory, Math. Proc. Cambridge Philos. Soc. 95 (1984), 33-48.
28. O. Wyler, Lecture notes on topoi and quasitopoi, World Scientific, 1991.