General synthetic domain theory — a logical approach

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

Volumn 1290, Issue , 1997, Pages 293-313

  Reus, B ^a   Streicher, Th ^b  

^a UNIVERSITY OF MUNICH   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; COMPUTERS;

CONSTRUCTIVE TYPE THEORY; DOMAIN THEORY; INDUCTION PRINCIPLES; LOGICAL APPROACHES; SYNTHETIC DOMAIN THEORY;

ARTIFICIAL INTELLIGENCE;

EID: 70350112612     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0026995     Document Type: Conference Paper

References (21)

1. R.L. Crole and A.M. Pitts. New foundations for fbcpoint computations: Fix-hyperdoctrines and the fix-logic. Information and Computation, 98:171-210, 1992.
2. M. Fiore and G. Rosolini. Two models of synthetic domain theory. 1996. To appear in the Freyd Festschrift.
3. P. Freyd. Remarks on algebraically compact categories. In Applications of Categories in Computer Science, volume 177 in Notes of the London Mathematical Society, 1992.
4. P. Freyd and G. Kelly. Categories of continuous functors. Journal of Pure and Applied Algebra, 2:169-191, 1972.
5. P. Freyd, P. Mulry, G. Rosolini, and D. Scott. Extensional PERs. Information and Computation, 98:211-227, 1992.
6. J.M.E. Hyland. First steps in synthetic domain theory. In A. Carboni, M.C. Pedicchio, and G. Rosolini, eds., Proc. of the 1990 Como Category Theory Conference, volume 1488 of Lecture Notes in Mathematics, pages 131-156, Berlin, 1991. Springer.
7. M. Jibladze. A presentation of the initial lift-algebra. JPAA, 116(2-3):199-220, 1997.
8. J.R. Longley. Realizability Toposes and Language Semantics. PhD thesis, University of Edinburgh, 1994.
9. J.R. Longley and A.K. Simpson. A uniform account of domain theory in realizability models. To appear in the special edition of Math.Str.Comp.Sc. for LDPL 1995.
10. Z. Luo. An Extended Calculus of Constructions. PhD thesis, University of Edinburgh, 1990. Available as report ECS-LFCS-90-118.
11. W.K. Phoa. Domain Theory in Realizability Toposes. PhD thesis, University of Cambridge, 1990. Also available as report ECS-LFCS-91-171, University of Edinburgh.
12. B. Reus. Program Verification in Synthetic Domain Theory. PhD thesis, Ludwig-Maximilians-Universitat Miinchen, 1995. Shaker Verlag, Aachen, 1996.
13. B. Reus. Synthetic domain theory in type theory: Another logic of computable functions. In J. Grundy, J. von Wright and J. Harrison, eds., TPHOLs'96, volume 1125 of LNCS, pages 363-381. Springer, 1996.
14. B. Reus and T. Streicher. Naive Synthetic Domain Theory - a logical approach. Draft, September 1993.
15. G. Rosolini. Continuity and effectiveness in topoi. PhD thesis, University of Oxford, 1986.
16. G. Rosolini. Notes on synthetic domain theory. Draft, August 1995.
17. A.K. Simpson. Domain theory in intuitionistic set theory. Draft, 1996.
18. M.B. Smyth and G.D. Plotkin. The category-theoretic solution to recursive domain equations. SIAM Journal of Computing, 11:761-783, 1982.
19. T. Streicher. Semantics of Type Theory, Correctness, Completeness and Independence Results. Birkhauser, 1991.
20. T. Streicher. Inductive Construction of Repletion. To appear in Applied Categorical Structures, 1997.
21. P. Taylor. The fixed point property in synthetic domain theory. In 6th Symp. on Logic in Computer Science, pages 152-160, Washington, 1991. IEEE Computer Soc. Press.