A Theory of Parametric Polymorphism and an Application
Doktorsavhandling, 2011

This thesis revisits the well-known notion of parametric polymorphism in the light of modern developments in type-theory. Additionally, applications of parametric polymorphism are also presented. The first part of the thesis presents a theoretical investigation of the semantics of parametric polymorphism of and within type-theories with dependent types. It is shown how the meaning of polymorphic, possibly dependent, types can be reflected within type-theory itself, via a simple syntactic transformation. This self-referential property opens the door to internalise the transformation in type-theory, and we study one possible way to do so. We also examine how the translation relates to various specific features of type-theory, such as proof irrelevance and realizability. The second part is concerned an application of parametric polymorphism relevant to software engineers. We present a schema to reduce polymorphic properties to equivalent monomorphic properties, for the purpose of testing. Our proof uses parametricity and properties of initial algebras.

lecture room EF, ED&IT building, Rännvägen 6B
Opponent: Prof. Stephanie Weirich

Författare

Jean-Philippe Bernardy

Chalmers, Data- och informationsteknik, Programvaruteknik

Testing Polymorphic Properties

Lecture Notes in Computer Science,; Vol. 6012(2010)p. 125-144

Paper i proceeding

Parametricity and dependent types

International Conference on Functional Programming, September 27-29, 2010, Baltimore, Maryland,; (2010)

Paper i proceeding

Realizability and Parametricity in Pure Type Systems

Lecture Notes in Computer Science,; Vol. 6604(2011)p. 108-122

Paper i proceeding

Styrkeområden

Informations- och kommunikationsteknik

Fundament

Grundläggande vetenskaper

Ämneskategorier

Datavetenskap (datalogi)

ISBN

978-91-7385-514-3

Technical report D - Department of Computer Science and Engineering, Chalmers University of Technology and Göteborg University: 77D

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie: 3195

lecture room EF, ED&IT building, Rännvägen 6B

Opponent: Prof. Stephanie Weirich