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Abstract: In this paper we introduce a logic for parametric polymorphism. Just as LCF is a logic for the simply-typed -calculus with recursion and arithmetic, our logic is a logic for System F. The logic permits the formal presentation and use of relational parametricity. Parametricity yields---for example---encodings of initial algebras, final co-algebras and abstract datatypes, with corresponding proof principles of induction, co-induction and simulation. (Update)
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BibTeX entry: (Update)
Gordon Plotkin and Mart'in Abadi. A logic for parametric polymorphism. In M. Bezem and J.F. Groote, editors, Typed Lambda Calculi and Applications, volume 664 of Lecture Notes in Computer Science, pages 361--375. Springer-Verlag, March 1993. http://citeseer.ist.psu.edu/plotkin93logic.html More
@inproceedings{ plotkin93logic,
author = "Gordon Plotkin and Mart\'{\i}n Abadi",
title = "A logic for parametric polymorphism",
booktitle = "International Conference on Typed Lambda Calculi and Applications",
number = "664",
publisher = "Springer-Verlag",
address = "Utrecht, The Netherlands",
editor = "M. Bezem and J. F. Groote",
pages = "361--375",
year = "1993",
url = "citeseer.ist.psu.edu/plotkin93logic.html" }
Citations (may not include all citations):311 Abstract types have existential type (context) - Mitchell, Plotkin - 1985
147 abstraction and parametric polymorphism (context) - Reynolds - 1983
91 A final co-algebra theorem (context) - Aczel, Mendler - 1989
63 Theoretical Computer Science (context) - Bainbridge, Freyd et al. - 1990
53 Automatic synthesis of typed-programs on term algebras (context) - Bohm, Berarducci - 1985
49 A co-induction principle for recursively defined domains - Pitts
39 Polymorphism is set-theoretic (context) - Pitts - 1987
38 A type inference approach to reduction properties and semant.. (context) - Mitchell - 1990
35 minimum typing and type-checking in F (context) - Curien, Ghelli et al. - 1992
28 the equivalence of data representations (context) - Mitchell - 1991
21 A note on categorical datatypes (context) - Wraith - 1989
21 Categorical data types in parametric polymorphism (context) - Hasegawa - 1990
20 On functors expressible in the polymorphic typed lambda calc.. (context) - Reynolds, Plotkin - 1990
18 Outline of a proof theory of parametricity - Mairson - 1991
14 and Andre Scedrov (context) - Cardelli, Martini et al. - 1991
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Documents on the same site (http://homepages.inf.ed.ac.uk/gdp/publications/): More
Full Abstraction, Totality and PCF - Plotkin (1997) (Correct)
Subtyping and Parametricity - Plotkin, Abadi, Cardelli (1993) (Correct)
Complete Axioms for Categorical Fixed-point Operators - Simpson, Plotkin (2000) (Correct)
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