Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Information and Computation - Semantics of Data Types
Extensional models for polymorphism
Theoretical Computer Science - International Joint Conference on Theory and Practice of Software Development, P
Proofs and types
Non-trivial power types can't be subtypes of polymorphic types
Proceedings of the Fourth Annual Symposium on Logic in computer science
Journal of Information Processing and Cybernetics
FPCA '89 Proceedings of the fourth international conference on Functional programming languages and computer architecture
Logical foundations of functional programming
On functors expressible in the polymorphic lambda calculus
Logical foundations of functional programming
Logical foundations of functional programming
Outline of a proof theory of parametricity
Proceedings of the 5th ACM conference on Functional programming languages and computer architecture
Formal parametric polymorphism
Theoretical Computer Science - A collection of contributions in honour of Corrado Bo¨hm on the occasion of his 70th birthday
An axiomatic system of parametricity
Fundamenta Informaticae - Special issue: typed lambda-calculi and applications, selected papers
Principal type-schemes for functional programs
POPL '82 Proceedings of the 9th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Fundamental Concepts in Programming Languages
Higher-Order and Symbolic Computation
Types, Abstractions, and Parametric Polymorphism, Part 2
Proceedings of the 7th International Conference on Mathematical Foundations of Programming Semantics
A Logic for Parametric Polymorphism
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Towards a theory of type structure
Programming Symposium, Proceedings Colloque sur la Programmation
Polymorphism is Set Theoretic, Constructively
Category Theory and Computer Science
Reasoning about functional programs and complexity classes associated with type disciplines
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
A lightweight implementation of generics and dynamics
Proceedings of the 2002 ACM SIGPLAN workshop on Haskell
The Girard--Reynolds isomorphism
Information and Computation - TACS 2001
The Girard—Reynolds isomorphism (second edition)
Theoretical Computer Science
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The second-order polymorphic lambda calculus, F2, was independently discovered by Girard and Reynolds. Girard additionally proved a representation theorem: every function on natural numbers that can be proved total in second-order intuitionistic propositional logic, P2, can be represented in F2. Reynolds additionally proved an abstraction theorem: for a suitable notion of logical relation, every term in F2 takes related arguments into related results. We observe that the essence of Girard's result is a projection from P2 into F2, and that the essence of Reynolds's result is an embeddingof F2 into P2, and that the Reynolds embeddingfollo wed by the Girard projection is the identity. The Girard projection discards all first-order quantifiers, so it seems unreasonable to expect that the Girard projection followed by the Reynolds embed-dingshould also be the identity. However, we show that in the presence of Reynolds's parametricity property that this is indeed the case, for propositions correspondingto inductive definitions of naturals, products, sums, and fixpoint types.