A note on inconsistencies caused by fixpoints in a Cartesian closed category
Theoretical Computer Science
Axiomatic domain theory in categories of partial maps
Axiomatic domain theory in categories of partial maps
Types and programming languages
Types and programming languages
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
Parametric polymorphism and operational equivalence
Mathematical Structures in Computer Science
Categorical models for Abadi and Plotkin's logic for parametricity
Mathematical Structures in Computer Science
From parametric polymorphism to models of polymorphic fpc
Mathematical Structures in Computer Science
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We present a formalization of a version of Abadi and Plotkin's logic for parametricity for a polymorphic dual intuitionistic / linear type theory with fixed points, and show, following Plotkin's suggestions, that it can be used to define a wide collection of types, including solutions to recursive domain equations. We further define a notion of parametric LAPL-structure and prove that it provides a sound and complete class of models for the logic, and conclude that such models have solutions for a wide class of recursive domain equations. Finally, we present a concrete parametric LAPL-structure based on suitable categories of partial equivalence relations over a universal model of the untyped lambda calculus.