Formalising formulas-as-types-as-objects

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

Volumn 1956, Issue , 2000, Pages 174-193

  Haiyan, Qiao ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; DIFFERENTIATION (CALCULUS);

CARTESIAN CLOSED CATEGORY; FORMALISATION; LAMBDA TERMS; MINIMAL LOGIC; NATURAL DEDUCTION PROOFS; NATURAL DEDUCTION SYSTEMS; PROOF ASSISTANT; TYPED LAMBDA CALCULUS;

FORESTRY;

EID: 84876618201     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-44557-9_11     Document Type: Conference Paper

References (20)

1. T. Altenkirch. A formalisation of the strong normalisation proof for system F in LEGO. Lecture Notes in Computer Science, Vol. 664, pp.13-28,Springer-Verlag, 1993.
2. T. Altenkirch and M. Hofmann and T. Streicher. Categorical Reconstruction of a Reduction Free Normalization Proof. Lecture Notes in Computer Science, Vol. 953, pp. 182-199, 1995.
3. B. Barras. Coq en Coq. Technical Report, RR-3026, Inria, Institut National de Recherche en Informatique et en Automatique, 1996.
4. A. Bove. A Machine-assisted Proof that Well Typed Expressions Cannot Go Wrong. Technical Report, DCS, Chalmers University, 1998.
5. J. Cartmell. Generalised Algebraic Theories and Contextual Categories. Annals of Pure and Applied Logic, Vol. 32, pp. 209-243, 1986.
6. C. Coquand. From Semantics to Rules: A Machine Assisted Analysis. Proceedings of the 7th Workshop on Computer Science Logic, pp. 91-105, Springer-Verlag LNCS 832, 1993.
7. T. Coquand and P. Dybjer. Intuitionistic model constructions and normalization proofs. Mathematical Structures in Computer Science, Vol. 7, pp. 75-94, Feb. 1997.
8. D. Cubric and P. Dybjer and P. Scott. Normalization and the Yoneda embedding. Mathematical Structures in Computer Science, Vol. 8, No.2, pp. 153-192, Apr. 1998.
9. P. Dybjer. Inductive Families. Formal Aspects of Computing, Vol. 6, No. 4, pp. 440-465, 1994.
10. P. Dybjer. Internal Type Theory. Lecture Notes in Computer Science, Vol. 1158, pp. 120-134, 1996.
11. M. Hofmann. Syntax and Semantics of Dependent Types. Semantics of Logic of Computation, P. Dybjer and A. Pitts, eds. Cambridge University Press, 1997.
12. G. Huet. Residual Theory in A-Calculus: A Formal Development. Journal of Functional Programming, Vol. 4, No. 3, pp. 371-394, 1994.
13. B. Jacobs. Simply typed and untyped Lambda Calculus revisited. Applications of Categories in Computer Science, Vol. 177, pp.119-142, Cambridge University Press, 1991.
14. L. Magnusson and B. Nordstrom. The ALF Proof Editor and Its Proof Engine. Types for Proofs and Programs, pp. 213-237, Springer-Verlag LNCS 806, Henk Barendregt and Tobias Nipkow, eds, 1994.
15. J. McKinna and R. Pollack. Some Type Theory and Lambda Calculus Formalised. Journal of Automated Reasoning, Special Issue on Formalised Mathematical Theories, ed. F. Pfenning, 1998.
16. B. Nordstrom and K. Petersson and J. M. Smith. Programming in Martin-Lof’s type theory: An Introduction. Oxford: Clarendon, 1990.
17. A. Obtulowicz and A. Wiweger. Categorical, Functorial and Algebraic Aspects of the Type Free Lambda Calculus. Universal Algebra and Applications, pp. 399-422, Banach Center Publications 9. 1982.
18. A. M. Pitts. Categorical Logic. Handbook of Logic in Computer Science, Oxford University Press, 1997.
19. A. Sai’bi. Formalisation of a A-Calculus with Explicit Substitutions in Coq. Proceedings of the International Workshop on Types for Proofs and Programs, pp. 183-202, P. Dybjer and B. Nordstrom and J. Smith, eds, Springer-Verlag LNCS 996, 1994.
20. R. A. G. Seely. Locally cartesian closed categories and type theory. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 95, pp. 33-48, Cambridge Philosophical Society, 1984.