Proofs and types
The definition of Standard ML
Theoretical Computer Science - Special issue: Fourth workshop on mathematical foundations of programming semantics, Boulder, CO, May 1988
Proceedings of the fifth international conference on Mathematical foundations of programming semantics
Outline of a proof theory of parametricity
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POPL '92 Proceedings of the 19th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Types, Abstractions, and Parametric Polymorphism, Part 2
Proceedings of the 7th International Conference on Mathematical Foundations of Programming Semantics
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
An Extension of System F with Subtyping
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Principals in programming languages: a syntactic proof technique
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ACM Transactions on Programming Languages and Systems (TOPLAS)
POPL '03 Proceedings of the 30th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
System F with type equality coercions
TLDI '07 Proceedings of the 2007 ACM SIGPLAN international workshop on Types in languages design and implementation
Unembedding domain-specific languages
Proceedings of the 2nd ACM SIGPLAN symposium on Haskell
A game semantics for generic polymorphism
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Realizability and parametricity in pure type systems
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Adding equations to system f types
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
A Computational Interpretation of Parametricity
LICS '12 Proceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science
Parametric And Type-Dependent Polymorphism
Fundamenta Informaticae
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A polymorphic function is parametric if its behavior does notdepend on the type at which it is instantiated. Starting with Reynolds'work, the study of parametricity is typically semantic. In this paper,we develop a syntactic approach to parametricity, and a formal systemthat embodies this approach: system R. Girard's system F deals with terms and types;R is an extension of F that deals also with relationsbetween types.In R**, it is possible to derive theorems about functionsfrom their types, or “theorems for free”, as Wadler callsthem. An easy “theorem for free” asserts that the type ∀XX→Bool contains only constantfunctions; this is not provable in F. There are many harder and moresubstantial examples. Various metatheorems can also be obtained, such asa syntactic version of Reynolds' abstraction theorem.