Working with mathematical structures in type theory

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

Volumn 4941 LNCS, Issue , 2008, Pages 157-172

  Sacerdoti Coen, Claudio ^a   Tassi, Enrico ^a  

^a UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGEBRA; COMPUTATIONAL METHODS; HEURISTIC METHODS; PROBLEM SOLVING; THEOREM PROVING;

COMPUTATIONAL VERSION; LEIBNIZ EQUALITY; MATHEMATICAL STRUCTURES; TYPE THEORY;

NUMERICAL METHODS;

EID: 44649155851     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-68103-8_11     Document Type: Conference Paper

References (17)

1. Bailey, A.: Coercion synthesis in computer implementations of type-theoretic frameworks. In: Giménez, E. (ed.) TYPES 1996. LNCS, vol. 1512, pp. 9-27. Springer, Heidelberg (1998)
2. Bailey, A.: The Machine-Checked Literate Formalisation Of Algebr. In: Type Theory. PhD thesis, University of Manchester (1998)
3. Barthe, G.: Implicit coercions in type systems. In: Berardi, S., Coppo, M. (eds.) TYPES 1995. LNCS, vol. 1158, pp. 1-15. Springer, Heidelberg (1996)
4. Betarte, G., Tasistro, A.: Formalization of systems of algebras using dependent record types and subtyping: An example. In: Proceedings of the 7th. Nordic workshop on Programming Theory, Gothenburg (1995)
5. Betarte, G., Tasistro, A.: Extension of Martin-Löf's type theory with record types and subtyping. In: Twenty-five Years of Constructive Type Theory, Oxford Science Publications (1998)
6. Chen, G.: Subtyping, Type Conversion and Transitivity Elimination. PhD thesis, University Paris 7 (1998)
7. Chen, G.: Coercive subtyping for the calculus of constructions. In: The 30th Annual ACM SIGPLAN - SIGACT Symposium on Principle of Programming Language (POPL) (2003)
8. Coquand, T., Pollack, R., Takeyama, M.: A logical framework with dependently typed records. Fundamenta Informaticae 65(1-2), 113-134 (2005)
9. Cruz-Filipe, L., Geuvers, H., Wiedijk, F.: C-corn, the constructive coq repository at nijmegen. In: Asperti, A., Bancerek, G., Trybulec, A. (eds.) MKM 2004. LNCS, vol. 3119, pp. 88-103. Springer, Heidelberg (2004)
10. Dybjer, P.: A general formulation of simultaneous inductive-recursive definitions in type theory. Journal of Symbolic Logic 65(2) (2000)
11. Gonthier, G.: A computer-checked proof of the four-colour theorem. Available at: http://research.microsoft.com/∼gonthier/4colproof.pdf
12. Hedberg, M.: Unpublished proof formalized in lego by T. Kleymann and in coq by B. Barras, http://coq.inria.fr/library/Coq.Logic.Eqdep_dec.html
13. Luo, Z.: An Extended Calculus of Constructions. PhD thesis, University of Edinburgh (1990)
14. Luo, Z.: Coercive subtyping. J. Logic and Computation 9(1), 105-130 (1999)
15. Muñoz, C.: A Calculus of Substitutions for Incomplete-Proof Representation in Type Theory, November 1997. PhD thesis, INRIA (1997)
16. Pollack, R.: Dependently typed records in type theory. Formal Aspects of Computing 13, 386-402 (2002)
17. Saibi, A.: Typing algorithm in type theory with inheritance. In: The 24th Annual ACM SIGPLAN - SIGACT Symposium on Principle of Programming Language (POPL) (1997)