Introduction to higher order categorical logic
Introduction to higher order categorical logic
Theoretical Computer Science
Call-by-name call-by-value, call-by-need and the linear lambda calculus
Theoretical Computer Science - Special issue on mathematical foundations of programming semantics
A Logic for Parametric Polymorphism
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
MFCS '93 Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science
Free theorems in the presence of seq
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Translating dependency into parametricity
Proceedings of the ninth ACM SIGPLAN international conference on Functional programming
Categorical models for Abadi and Plotkin's logic for parametricity
Mathematical Structures in Computer Science
Domain-theoretical models of parametric polymorphism
Theoretical Computer Science
Parametric Domain-theoretic Models of Polymorphic Intuitionistic / Linear Lambda Calculus
Electronic Notes in Theoretical Computer Science (ENTCS)
Realizability, Volume 152: An Introduction to its Categorical Side
Realizability, Volume 152: An Introduction to its Categorical Side
Multiversal Polymorphic Algebraic Theories: Syntax, Semantics, Translations, and Equational Logic
LICS '13 Proceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science
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This paper shows how PILLY (Polymorphic Intuitionistic/Linear Lambda calculus with a fixed point combinator Y) with parametric polymorphism can be used as a metalanguage for domain theory, as originally suggested by Plotkin more than a decade ago. Using Plotkin's encodings of recursive types in PILLY, we show how parametric models of PILLY give rise to models of FPC, which is a simply typed lambda calculus with recursive types and an operational call-by-value semantics, reflecting a classical result from domain theory. Essentially, this interpretation is an interpretation of intuitionistic logic into linear logic first discovered by Girard, which in this paper is extended to deal with recursive types. Of particular interest is a model based on ‘admissible’ pers over a reflexive domain, the theory of which can be seen as a domain theory for (impredicative) polymorphism. We show how this model gives rise to a parametric and computationally adequate model of PolyFPC, an extension of FPC with impredicative polymorphism. This is to the author's knowledge the first denotational model of a non-linear language with parametric polymorphism and recursive types.