On proving the correctness of program transformations based on free theorems for higher-order polymorphic calculi

Mathematical Structures in Computer Science

Volumn 15, Issue 2, 2005, Pages 201-229

  Johann, Patricia ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33644612433     PISSN: 09601295     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0960129504004578     Document Type: Article

References (27)

1. Abadi, M. (2000) TT-closed relations and admissibility. Mathematical Structures in Computer Science 10 313-320.
2. Abadi, M., Cardelli, L. and Curien, P.-L. (1993) Formal parametric polymorphism. Theoretical Computer Science 121 9-58.
3. Breazu-Tannen, V. and Coquand, T. (1988) Extensional models for polymorphism. Theoretical Computer Science 59 85-114.
4. Bruce, K. B. and Meyer, A. R. (1984) The semantics of second-order polymorphic lambda calculus. In: Semantics of Data Types. Springer-Verlag Lecture Notes in Computer Science 173 131-144.
5. Fiore, M. and Plotkin, G. (1994) An axiomatization of computationally adequate domain theoretic models of FPC. Proceedings, 9th Annual Symposium on Logic in Computer Science 92-102.
6. Gill, A. (1996) Cheap Deforestation for Non-strict Functional Languages. Ph.D. thesis, Glasgow University.
7. Gill, A., Launchbury, J. and Peyton Jones, S.L. (1993) A short cut to deforestation. Proceedings, Conference on Functional Programming and Computer Architecture 223-232.
8. Hu, Z., Iwasaki, H. and Takeichi, M. (1996) Deriving structural hylomorphisms from recursive definitions. Proceedings, International Conference on Functional Programming 73-82.
9. Johann, P. (2002) A generalization of short-cut fusion and its correctness proof. Higher-Order and Symbolic Computation 15 273-300.
10. (An earlier version of this paper appears as Johann, P. (2001) Short Cut Fusion: Proved and Improved. Proceedings, Workshop on Semantics, Applications, and Implementation of Program Generation. Springer-Verlag Lecture Notes in Computer Science 219647-71.)
11. Johann, P. (2003) Short cut fusion is correct. Journal of Functional Programming 13 (4) 797-814.
12. Johann, P. and Voigtländer, J. (2004) Free Theorems in the Presence of seq. Proceedings, Conference on Principles of Programming Languages 99-110.
13. Mitchell, J. C. (1996) Foundations for Programming Languages, MIT Press.
14. Mitchell, J. C. and Meyer, A. R. (1985) Second-order logical relations. In Logic of Programs. Springer-Verlag Lecture Notes in Computer Science 193 235-236.
15. Onoue, Y., Hu, Z., Iwasaki, H. and Takeichi, M. (1997) A calculational system HYLO. Proceedings, IFIP TC 2 Working Conference on Algorithmic Languages and Calculi 76-106.
16. Pitts, A. (1998a) Parametric polymorphism, recursive types, and operational equivalence. Unpublished Manuscript.
17. Pitts, A. (1998b) Existential types: Logical relations and operational equivalence. Proceedings, International Colloquium on Automata, Languages, and Programming 309-326.
18. Pitts, A. (2000) Parametric polymorphism and operational equivalence. Mathematical Structures in Computer Science 10 1-39.
19. Plotkin, G. D. and Abadi, M. (1993) A logic for parametric polymorphism. Proceedings, Conference on Typed Lambda Calculus and Applications. Springer-Verlag Lecture Notes in Computer Science 664 361-375.
20. Takano, A. and Meijer, E. (1995) Shortcut deforestation in calculational form. Proceedings, Conference on Functional Programming and Computer Architecture 324-333.
21. Reynolds, J. C. (1974) Toward a theory of type structure. Proceedings, Paris Colloquium on Programming. Springer-Verlag Lecture Notes in Computer Science 19 408-425.
22. Reynolds, J. C. (1983) Types, abstraction, and parametric polymorphism. Information Processing 83 513-523.
23. Reynolds, J. C. (1998) Theories of Programming Languages, Cambridge University Press.
24. Reynolds, J. C. and Plotkin, G. D. (1993) On functors expressible in the polymorphic typed lambda calculus. Information and Computation 121 411-440.
25. Svenningsson, J. (2002) Shortcut fusion for accumulating parameters and zip-like functions. Proceedings, International Conference on Functional Programming 124-132.
26. Tarski, A. (1955) A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5 285-309.
27. Wadler, P. (1989) Theorems for free! Proceedings, Conference on Functional Programming and Computer Architecture 347-359.