Infiniteness of proof(α) is polynomial-space complete

Theoretical Computer Science

Volumn 206, Issue 1-2, 1998, Pages 331-339

  Hirokawa, Sachio ^a  

^a KYUSHU UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0345767008     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(97)00168-0     Document Type: Article

References (12)

1. C.-B. Ben-Yelles, Type-assignment in the lambda-calculus, Ph.D. Thesis, University College, Swansea, 1979.
2. J.R. Hindley, Basic Simple Type-Theory, Cambridge Univ. Press, London, 1997.
3. J.R. Hindley, J.P. Seldin, Introduction to Combinators and Lambda-Calculus, Cambridge Univ. Press, London, 1986.
4. S. Hirokawa, The number of proofs of an implicational formula (Abstract), J. Symbolic Logic 58 (1993) 1117.
5. W.A. Howard, The formulae-as-types notion of construction, in: Hindley, Seldin (Eds.), To H.B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, 1980, 479-490.
6. Y. Komori, BCK-algebras and lambda calculus, Proc. 10th Symp. on Semigroups, Josai University, Sakado, 1986, pp. 5-11.
7. Y. Komori, S. Hirokawa, The number of proofs for a BCK-formula, J. Symbolic Logic 58 (1993) 626-628.
8. D. Prawitz, Natural Deduction, Almqvist and Wiksell, Stockholm, 1965.
9. R. Statman, Intuitionistic prepositional logic is polynomial-space complete, Theoret. Comput. Sci. 9 (1979) 97-105.
10. M. Takahashi, Y. Akama, S. Hirokawa, Normal proofs and their grammar, Inform. and Comput. 125 (1996) 144-153.
11. M. Zaionc, Lambda-definability on free algebras, Ann. Pure Appl. Logic 51 (1991) 279-300.
12. M. Zaionc, On the number of normal forms in typed lambda calculus, preprint, 1992.