Formalizing Synthetic Domain Theory: The Basic Definitions

Journal of Automated Reasoning

Volumn 23, Issue 3, 1999, Pages 411-444

  Reus, Bernhard ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Domain theory; Formal verification; LCF; Programming logics; Synthetic domain theory; Type theory

Indexed keywords

COMPUTATIONAL LINGUISTICS; FORMAL LOGIC; PROGRAMMING THEORY; THEOREM PROVING;

ABSTRACT AXIOMATIZATION; DENOTATIONAL SEMANTICS; PROGRAM VERIFICATION; SYNTHETIC DOMAIN THEORY; TYPE THEORY;

LOGIC PROGRAMMING;

EID: 0033321455     PISSN: 01687433     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006258506401     Document Type: Article

References (35)

1. Agerholm, S. (1994): A HOL Basis for Reasoning about Functional Programs, Ph.D. Thesis, BRICS, University of Aarhus. Also available as BRICS report RS-94-44.
2. Bailey, A. (1998): The Machine-Checked Literate Formalisation of Algebra in Type Theory, Ph.D. Thesis, University of Manchester.
3. Burstall, R. and McKinna, J. (1992): Deliverables: A categorical approach to program development in type theory, Technical Report ECS-LFCS-92-242, Edinburgh University.
4. Fiore, M. and Plotkin, G. (1994): An axiomatisation of computationally adequate domain theoretic models of FPC, in Proc. 9th Logic in Computer Science, Washington, pp. 92-102.
5. Fiore, M. and Rosolini, G. (1998): Domains in script H sign. To appear in TCS.
6. Freyd, P. (1991): Algebraically complete categories, in A. Carboni, M. Pedicchio, and G. Rosolini (eds.), Proceedings of the 1990 Como Category Theory Conference, Lecture Notes in Math. 1488. Berlin, pp. 95-104.
7. Freyd, P., Mulry, P., Rosolini, G. and Scott, D. (1992): Extensional PERs, Informat. and Comput. 98, 211-227.
8. Gunter, C. and Scott, D. (1990): Semantic domains, in J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Chapt. 12, Elsevier Science Publisher, pp. 635-674.
9. Hyland, J. (1991): First steps in synthetic domain theory, in A. Carboni, M. Pedicchio, and G. Rosolini (eds.), Proceedings of the 1990 Como Category Theory Conference, Lecture Notes in Math. 1488. Berlin, pp. 131-156.
10. Hyland, J. M. E. and Moggi, E. (1995): The S-replete construction, in CTCS 1995, LNCS 953.
11. Kock, A. (1981): Synthetic Differential Geometry, Cambridge University Press.
12. Lambek, J. and Scott, P. (1980): Introduction to Higher Order Categorical Logic, Cambridge Studies in Adv. Math. 7, Cambridge University Press.
13. Longley, J. (1994): Realizability Toposes and Language Semantics, Ph.D. Thesis, University of Edinburgh.
14. Longley, J. and Simpson, A. (1997): A uniform approach to domain theory in realizability models, MSCS 7(5), 453-468. Special edition of MSCS for the Workshop on Logic, Domains and Programming Languages, Darmstadt, Germany.
15. Luo, Z. (1990): An Extended Calculus of Constructions, Ph.D. Thesis, University of Edinburgh. Available as report ECS-LFCS-90-118.
16. Luo, Z. (1994): Computation and Reasoning - A Type Theory for Computer Science, Monographs on Comput. Sci. 11, Oxford University Press.
17. Luo, Z. (1999): Coercive subtyping, J. Logic Comput. 9(1).
18. Luo, Z. and Pollack, R. (1992): LEGO Proof Development System: User's Manual, Technical Report ECS-LFCS-92-211, Edinburgh University.
19. Paulson, L. (1987): Logic and Computation, Cambridge Tracts in Theoret. Comput. Sci. 2, Cambridge University Press.
20. Phoa, W. (1990): Domain Theory in Realizability Toposes, Ph.D. Thesis, University of Cambridge. Also available as report ECS-LFCS-91-171, University of Edinburgh.
21. Pollack, R. (1994): The Theory of LEGO - A Proof Checker for the Extended Calculus of Constructions, Ph.D. Thesis, University of Edinburgh.
22. Regensburger, F. (1994): HOLCF: Eine konservative Erweiterung von HOL um LCF, Ph.D. Thesis, Technische Universität München.
23. Reus, B. (1995): Program Verification in Synthetic Domain Theory, Ph.D. Thesis, Ludwig-Maximilians-Universität München, Shaker Verlag, Aachen, 1996.
24. Reus, B. (1996): Synthetic domain theory in type theory: another logic of computable functions, in J. von Wright, J. Grundy, and J. Harrison (eds.), Theorem Proving in Higher Order Logics: 9th International Conference, TPHOLs'96, Lecture Notes in Comput. Sci. 1125, pp. 363-381.
25. Reus, B. (1999): Extensional ∑-spaces in type theory, Appl. Cat. Structures 7, 159-183.
26. Reus, B. and Streicher, T. (1993a): Naive synthetic domain theory - A logical approach, Draft.
27. Reus, B. and Streicher, T. (1993b): Verifying properties of module construction in type theory, in A. Borzyszkowski and S. Sokolowski (eds.), MFCS'93, Lecture Notes in Comput. Sci. 711, pp. 660-670.
28. Reus, B. and Streicher, T. (1999): General synthetic domain theory - A logical approach, Math. Struct. in Comput. Sci. 9, 177-223.
29. Rogers, H. (1967): Theory of Recursive Functions and Effective Computability, McGraw-Hill.
30. Rosolini, G. (1986): Continuity and effectiveness in topoi, Ph.D. Thesis, University of Oxford.
31. Rosolini, G. (1995): Notes on synthetic domain theory, draft.
32. Simpson, A. (1995): Private communication.
33. Simpson, A. (1996): Domain theory in intuitionistic set theory, draft.
34. Taylor, P. (1991): The fixed point property in synthetic domain theory, in 6th Symp. on Logic in Computer Science, Washington, pp. 152-160.
35. Taylor, P. (1993): Synthetic domain theory notes, draft.