Abstract
The system of formal parametric polymorphism has the same theory as second order Peano arithmetic with regard to the provable equality of numerical functions.
This work is supported by EPSRC GR1J97366.
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M. Abadi, L. Cardelli, and P.-L. Curien, Formal parametric polymorphism, Theoret. Comput. Sci. 121 (1993) 9–58.
E. S. Bainbridge, P. J. Freyd, A. Scedrov, and P. J. Scott, Functorial polymorphism, Theoret. Comput. Sci. 70 (1990) 35–64; Corrigendum, 71 (1990) 431.
H. P. Barendregt, The lambda calculus, Its syntax and semantics, revised edition, (North-Holland, 1984).
C. Böhm and A. Berarducci, Automatic synthesis of typed Λ-programs on term algebras, Theoret. Comput. Sci. 39 (1985) 135–154.
P. Freyd, Structural polymorphism, Theoret. Comput. Sci. 115 (1993) 107–129.
J.-Y. Girard, Interprétation Fonctionnelle et Élimination des Coupures de l'Arithmétique d'Ordre Supérieur, Thèse d'Etat, Université Paris VII (1972).
J.-Y. Girard, Proof Theory and Logical Complexity, Volume I, Studies in Proof Theory, (Bibliopolis, 1987).
J.-Y. Girard, P. Taylor and Y. Lafont, Proofs and Types, (Cambridge University Press, 1989).
K. Gödel, Über eine bisher noch nicht benützte Erweiterung des finiten Standpunktes, Dialectica 12 (1958) 280–287; English translation in J. Philosophical Logic 9 (1980) 133–142; reprinted in Kurt Gödel, Collected Works, Volume II, Publications 1938–1974, S. Feferman et al., eds., (Oxford University Press, 1990) pp. 240–251.
R. Hasegawa, Categorical data types in parametric polymorphism, Math. Struct. Comput. Sci. 4 (1994) 71–109.
R. Hasegawa, Relational limits in general polymorphism, Publ. Research Institute for Mathematical Sciences 30 (1994) 535–576.
J. R. Hindley and J. P. Seldin, Introduction to Combinators and λ-Calculus, (London Math. Soc., 1986).
S. C. Kleene, Introduction to Metamathematics, (North-Holland, 1964).
D. Leivant, Reasoning about functional programs and complexity classes associated with type disciplines, in: IEEE 24th Annual Symp. on Foundations of Computer Science, (IEEE, 1983) pp. 460–469.
R. Loader, Models of linear logic and inductive datatypes, Mathematical Institute, Oxford University, preprint (1994).
G. Plotkin and M. Abadi, A logic for parametric polymorphism, in: Typed Lambda Calculi and Applications, M. Bezem, J. F. Groote, eds., 1993, Utrecht, The Netherlands, Lecture Notes in Computer Science 664, (Springer, 1993) 361–375.
J. C. Reynolds, Towards a theory of type structure, in: B. Robinet ed., Programming Symposium, Paris, Lecture Notes in Computer Science 19 (Springer, 1974) pp. 408–425.
J. C. Reynolds, Types, abstraction, and parametric polymorphism, in: Information Processing 83, R. E. A. Mason, ed., (North-Holland, 1983) pp. 513–523.
R. A. G. Seely, Categorical semantics for higher order polymorphic lambda calculus, J. Symbolic Logic 52 (1987) 969–989.
R. M. Smullyan, Theory of Formal Systems, Annals of Mathematics Studies 47, (Princeton University Press, 1961).
C. Spector, Provably recursive functionals of analysis: A consistency proof of analysis by an extension of principles formulated in current intuitionistic mathematics, in: Recursive Function Theory, J. C. E. Dekker, ed., Proceedings of Symposia in Pure Mathematics, Volume V, (AMS, 1962) pp. 1–27.
R. Statman, Number theoretic functions computable by polymorphic programs (extended abstract), in: IEEE 22nd Annual Symp. on Foundations of Computer Science, Los Angels, 1981 (IEEE, 1981) pp. 279–282.
A. S. Troelstra, Mathematical Investigations of Intuitionistic Arithmetic and Analysis, Lecture Notes in Mathematics 344, (Springer, 1973).
A. S. Troelstra, Introductory note to 1958 and 1972, in: Kurt Gödel, Collected Works, Volume II, Publications 1938–1974, S. Feferman et al., eds., (Oxford University Press, 1990) pp. 217–241.
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Hasegawa, R. (1996). A logical aspect of parametric polymorphism. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_44
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DOI: https://doi.org/10.1007/3-540-61377-3_44
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