Categorical Models for Abadi - Plotkin ’ s Logic for Parametricity LARS BIRKEDAL
نویسنده
چکیده
We propose a new category-theoretic formulation of relational parametricity based on a logic for reasoning about parametricity given by Abadi and Plotkin (Plotkin and Abadi, 1993). The logic can be used to reason about parametric models, such that we may prove consequences of parametricity that to our knowledge have not been proved before for existing category-theoretic notions of relational parametricity. We provide examples of parametric models and we describe a way of constructing parametric models from given models of the second-order lambda calculus.
منابع مشابه
Category-theoretic Models of Linear Abadi & Plotkin Logic
This paper presents a sound and complete category-theoretic notion of models for Linear Abadi & Plotkin Logic [Birkedal et al., 2006], a logic suitable for reasoning about parametricity in combination with recursion. A subclass of these called parametric LAPL structures can be seen as an axiomatization of domain theoretic models of parametric polymorphism, and we show how to solve general (nest...
متن کاملOperational Semantics and Models of Linear Abadi-Plotkin Logic
We present a model of Linear Abadi and Plotkin Logic for parametricity [8] based on the operational semantics of LILY, a polymorphic linear lambda calculus endowed with an operational semantics [3]. We use it to formally prove definability of general recursive types in LILY and to derive reasoning principles for the recursive types.
متن کاملLinear Abadi & Plotkin Logic
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 existential types, inductive types, coinductive types and general recursive types. We show that the recursive types satis...
متن کاملLinear Abadi and Plotkin Logic
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 existential types, inductive types, coinductive types and general recursive types. We show that the recursive types satisfy...
متن کاملOn Plotkin-Abadi Logic for Parametric Polymorphism Towards a Categorical Understanding
The idea of parametric polymorphism is that of a single operator that can be used for di erent data types and whose behaviour is somehow uniform for each type. Reynolds [Reynolds, 1983] uses binary relations to de ne a uniformity condition for parametric polymorphism. In [Plotkin & Abadi, 1993] the authors proposed a second order logic for second order lambda-calculus; this logic is able to han...
متن کامل