Abstract
Plotkin and Abadi have proposed a syntactic system for parametricity on a second order predicate logic. This paper shows three theorems about that system. The first is consistency of the system, which is proved by the method of relativization. The second is that polyadic parametricities of recursive types axe equivalent to each other. The third is that the theory of parametricity for recursive types is self-realizable. As a corollary of the third theorem, the theory of parametricity for recursive types satisfies the term extraction property.
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References
M. Abadi, L. Cardelli and P.-L. Curien. Formal parametric polymorphism. Theoretical Computer Science, 121, 9–58, 1993.
H. Barendregt. Lambda Calculi with Types. In Handbook of Logic in Computer Science, Vol. 2, 117–309, Oxford Univ. Press, 1992.
R. Bellucci, Martin Abadi, P.-L. Curien. A Model for Formal Parametric Polymorphism: A PER Interpretation for system R. In Typed Lambda Calculi and Applications, Lecture Notes in Computer Science, 902, Springer-Verlag, pp.32–46, 1995.
J.-Y. Girard, et al., Proofs and Types Cambridge Univ. Press, 1989.
R. Hasegawa. Parametricity of extensionally collapsed term models of polymorphism and their categorical properties. In Proceeding of Theoretical Aspects of Computer Science, Lecture Notes In Computer Science 526, pp. 495–512, Springer-Verlag 1991.
R. Hasegawa. Categorical data types in parametric polymorphism. In Mathematical Structures in Computer Science, 4, 71–109, 1994.
G. Plotkin and M. Abadi. A Logic for parametric polymorphism. In Typed Lambda Calculi and Applications, Lecture Notes in Computer Science, 664, Springer-Verlag, pp.361–375, 1993.
J. C. Reynolds. Types, abstraction and parametric polymorphism. In R. E. A. Mason, editor, Information Processing 83, pp. 513–523, Elsevier, 1983.
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© 1997 Springer-Verlag Berlin Heidelberg
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Takeuti, Izumi (1997). An axiomatic system of parametricity. In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_46
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DOI: https://doi.org/10.1007/3-540-62688-3_46
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