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A Logic for Parametric Polymorphism
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APLAS '08 Proceedings of the 6th Asian Symposium on Programming Languages and Systems
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From parametric polymorphism to models of polymorphic fpc
Mathematical Structures in Computer Science
A realizability model for impredicative Hoare type theory
ESOP'08/ETAPS'08 Proceedings of the Theory and practice of software, 17th European conference on Programming languages and systems
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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
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ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
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We present a domain-theoretical model of parametric polymorphism based on admissible per's over a domain-theoretical model of the untyped lambda calculus. The model is shown to be a model of Abadi & Plotkin's logic for parametricity, by the construction of an LAPL-structure as defined by the authors in [L. Birkedal, R.E. Mogelberg, R.L. Petersen, Parametric domain-theoretical models of polymorphic intuitionistic/linear lambda calculus, in: M. Escardo, A. Jung, M. Mislove (Eds.), Proceedings of Mathematical Foundations of Programming Semantics 2005, vol. 155, 2005, pp. 191-217; L. Birkedal, R.E. Mogelberg, R.L. Petersen, Category theoretical models of linear Abadi & Plotkin logic, 2006 (submitted for publication)]. This construction gives formal proof of solutions to a large class of recursive domain equations, which we explicate. As an example of a computation in the model, we explicitly describe the natural numbers object obtained using parametricity. The theory of admissible per's can be considered a domain theory for (impredicative) polymorphism. By studying various categories of admissible and chain complete per's and their relations, we discover a picture very similar to that of domain theory.