The mechanisation of barendregt-style equational proofs (the residual perspective)

Electronic Notes in Theoretical Computer Science

Volumn 58, Issue 1, 2001, Pages 18-36

  Vestergaard, René ^a   Brotherston, James ^b  

^a CNRS   (France)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; NUMERICAL METHODS; PROBLEM SOLVING; THEOREM PROVING;

ABSTRACT SYNTAX; BARENDREGT VARIABLE CONVENTION; HIGHER-ORDER LANGUAGE (HOL); NORMALIZATION;

COMPUTER PROGRAMMING LANGUAGES;

EID: 0038348848     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1571-0661(04)00277-4     Document Type: Conference Paper

References (28)

1. Barendregt H. "The Lambda Calculus - Its Syntax and Semantics (Revised Edition)," 1984;North-Holland
2. Brotherston J., "Formalizing Proofs in Isabelle/HOL of Equational Properties for the Lambda-Calculus using One-Sorted Variable Names", Honours dissertation, University of Edinburgh (2001). Available from the author's homepage.
3. Burstall R. Proving properties of programs by structural induction. The Computer Journal. 12:1967
4. Church A., Rosser J.B. Some properties of conversion. Transaction of the American Mathematical Society. 39:1936
5. Curry H.B., Feys R. "Combinatory Logic," 1958;North-Holland, Amsterdam
6. David R. Une preuve simple de rèsultats classiques en λ calcul. Comptes Rendus de l'Acadèmie des Sciences. 320:1995;1401-1406. série I.
7. de Bruijn N. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser Theorem. Indag. Math. 34:1972;381-392
8. Despeyroux J. and A. Hirschowitz, Higher-order abstract syntax with induction in Coq, in: F. Pfenning, editor, Proceedings of LPAR-5, LNAI 822 (1994).
9. Despeyroux J., F. Pfenning and C. Schürmann, Primitive recursion for higher-order abstract syntax, in: P. De Groote and J. R. Hindley, editors, Proceedings of TLCA-3, LNCS 1210 (1997).
10. Fiore M., G. Plotkin and D. Turi, Abstract syntax and variable binding, in: Longo [19], pp. 193-202.
11. Gabbay, M. J. and A. M. Pitts, A new approach to abstract syntax involving binders, in: Longo [19], pp. 214-224.
12. Gordon, A. D. and T. Melham, Five axioms of alpha-conversion, in: J. Von Wright, J. Grundy and J. Harrison, editors, Proceedings of TPHOL-9, LNCS 1125 (1996).
13. Hindley, J. R., "The Church-Rosser Property and a Result in Combinatory Logic," Ph.D. thesis, University of Newcastle upon Tyne (1964).
14. Hofmann M., Semantical analysis of higher-order abstract syntax, in: Longo [19], pp. 204-213.
15. Huet G. Residual theory in λ-calculus: A formal development. Journal of Functional Programming. 4:1994;371-394
16. Joachimski F. and R. Matthes, Standardization and confluence for a lambda calculus with generalized applications, in: L. Bachmair, editor, Proceedings of RTA-11, LNCS 1833 (2000).
17. Joachimski F. and R. Matthes, Short proofs of normalization for the simply-typed lambda-calculus, permutative conversions and Gödel's T, Archive for Mathematical Logic (200X), to appear.
18. Klop J.W. "Combinatory Reduction Systems," 1980;Mathematical Centre Tracts 127, Mathematisch Centrum, Amsterdam
19. G. Longo, editor, "Proceedings of LICS-14," IEEE CS Press, 1999.
20. McKinna J., Pollack R. Some lambda calculus and type theory formalized. Journal of Automated Reasoning. 23:1999
21. Nipkow T., More Church-Rosser proofs (in Isabelle/HOL), in: Proceedings of CADE-13, LNCS 1104 (1996).
22. Schroer, D. E., "The Church-Rosser theorem," Ph.D. thesis, Cornell (1965).
23. Shankar N. A mechanical proof of the Church-Rosser Theorem. Journal of the ACM. 35:1988;475-522
24. Stoughton A. Substitution revisited. Theoretical Computer Science. 59:1988;317-325
25. Takahashi M. Parallel reductions in λ-calculus. Information and Computation. 118:1995;120-127
26. Vestergaard R., "First-Order Equational Reasoning about Higher-Order Languages," Ph.D. thesis, Heriot-Watt University (2001), forthcoming.
27. Vestergaard R. and J. Brotherston, A formalised first-order confluence proof for the λ-calculus using one-sorted variable names (Barendregt was right after all... almost), in: A. Middeldorp editor, Proceedings of RTA-12, LNCS 2051 (2001).
28. Wells J. and R. Vestergaard, Equational reasoning for linking with first-class primitive modules, in: G. Smolka, editor, Proceedings of ESOP-9, LNCS 1782 (2000).