Enlargements of functional algebras for the lambda calculus

Theoretical Computer Science

Volumn 198, Issue 1-2, 1998, Pages 177-200

  Goldblatt, Robert ^a  

^a VICTORIA UNIVERSITY OF WELLINGTON   (New Zealand)

Author keywords

Environment models; Lambda abstraction algebras; Lambda calculus; Nonstandard mathematics

Indexed keywords

EID: 0343909131     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3975(97)00126-6     Document Type: Article

References (26)

1. H.P. Barendregt, The type free lambda calculus, in: J. Barwise (Ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, 1977, pp. 1091-1132.
2. H.P. Barendregt, The Lambda Calculus, Its Syntax and Semantics, 2nd ed., North-Holland, Amsterdam, 1985.
3. A. Church, A set of postulates for the foundations of logic, Ann. Math. 33 (1932) 346-366: II paper: 34 (1933) 839-864.
4. A. Church, A set of postulates for the foundations of logic, Ann. Math. 33 (1932) 346-366: II paper: 34 (1933) 839-864.
5. M. Davis, Applied Nonstandard Analysis, Wiley, New York, 1977.
6. R. Goldblatt, The functional lambda abstraction algebras form a variety, in: D.S. Bridges et al. (Eds.), Combinatories, Complexity and Logic: Proc. DMTCS'96 (First Conference of the Centre for Discrete Mathematics and Theoretical Computer Science, Auckland, New Zealand, December 1996), Springer, Singapore, 1997, pp. 226-243.
7. R. Hindley, G. Longo, Lambda-calculus models and extensionality, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 26 (1980) 289-310.
8. A.E. Hurd, P.A. Loeb, An Introduction to Nonstandard Real Analysis, Academic Press, New York, 1985.
9. L. Henkin, J.D. Monk, A. Tarski, Cylindric Algebras I, North-Holland, Amsterdam, 1971.
10. L. Henkin, J.D. Monk, A. Tarski, H. Andréka, I. Németi, Cylindric Set Algebras, Lecture Notes in Mathematics, vol. 883, Springer, Berlin, 1981.
11. L. Henkin, J.D. Monk, A. Tarski, Cylindric Algebras II, North-Holland, Amsterdam, 1985.
12. A.R. Meyer, What is a model of the lambda calculus? Inform, and Control 52 (1982) 87-122.
13. J.D. Monk, Nonfinitisability of classes of representable cylindric algebras, J. Symbol. Logic 34 (1969) 331-343.
14. E. Palmgren, A constructive approach to nonstandard analysis, Ann. Pure Appl. Logic 73 (1995) 297-325.
15. E. Palmgren, V. Stoltenberg-Hansen, Logically presented domains, in: D. Kozen (Ed.), Proc. 10th Annual IEEE Symp. on Logic in Computer Science, IEEE Computer Society Press, 1995, pp. 455-463.
16. G.D. Plotkin, A set-theoretical definition of application, Memorandum MIP-R-95, School of Artificial Intelligence, University of Edinburgh, March 1972. Published as Part I of [16].
17. G.D. Plotkin, Set-theoretical and other elementary models of the λ-calculus, Theoret. Comput. Sci. 121 (1993) 351-409.
18. D. Pigozzi, A. Salibra, An introduction to lambda abstraction algebras, in: IX Simposio Latinoamericano de Logica Matematica, Notas de Logica Matematica, vol. 38, Universidad Nacional del Sur, Bahia Blanca, Argentina, 1993, pp. 93-112.
19. D. Pigozzi, A. Salibra, Lambda abstraction algebras: representation theorems, Theoret. Comput. Sci. 140 (1995) 5-52.
20. M.M. Richter, M.E. Szabo, Towards a nonstandard analysis of programs, in: A.E. Hurd (Ed.), Nonstandard Analysis-Recent Developments, Lecture Notes in Mathematics, vol. 983, Springer, Berlin, 1983, pp. 186-203.
21. A. Robinson, Non-standard Analysis, Amsterdam, North-Holland, 1966.
22. A, Salibra, R. Goldblatt, A finite equational axiomatisation of the functional algebras for the lambda calculus. Research Report 96-174, Mathematics Department, Victoria University of Wellington, January 1996.
23. D. Scott, Continuous lattices, in: F.W. Lawvere (Ed.), Toposes, Algebraic Geometry, and Logic, Lecture Notes in Mathematics, vol. 274, Springer, Berlin, 1972.
24. D. Scott, Data types as lattices, SIAM J. Comput. 5 (1976) 522-587.
25. D. Scott, Lambda calculus: some models, some philosophy, in: J. Barwise, H.J. Keisler, K. Kunen (Ed.), The Kleene Symposium, North-Holland, Amsterdam, 1980, pp. 381-421.
26. D. Scott, Relating theories of the λ calculus, in: J.P. Seldin, J.R. Hindley (Eds.), To H.B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press, New York, 1980, pp. 403-450.