Bifibrational Functorial Semantics of Parametric Polymorphism

Functorial semantics of topological theories

Following the categorical approach to universal algebra through algebraic theories, proposed by F.~W.~Lawvere in his PhD thesis, this paper aims at introducing a similar setting for general topology. The cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. We introduce t...

Cubical Categories for Higher-Dimensional Parametricity

Reynolds’ theory of relational parametricity formalizes parametric polymorphism for System F, thus capturing the idea that polymorphically typed System F programs always map related inputs to related results. This paper shows that Reynolds’ theory can be seen as the instantiation at dimension 1 of a theory of relational parametricity for System F that holds at all higher dimensions, including i...

Functorial Semantics of Algebraic Theories and Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories

Semantics of Parametric Polymorphism in Imperative Programming Languages

Programming languages such as CLU, Ada and Modula-3 have included facilities for parametric polymorphism and, more recently, C++ and Java have also added similar facilities. In this paper, we examine the issues of defining denotational semantics for imperative programming languages with polymorphism. We use the framework of reflexive graphs of categories previously developed for a general axiom...

From parametric polymorphism to models of polymorphic FPC

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, a simply typed lambda cal...