A Theory of Parametric Polymorphism and an Application
Doctoral thesis, 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

Author

Jean-Philippe Bernardy

Chalmers, Computer Science and Engineering (Chalmers), Software Technology (Chalmers)

Testing Polymorphic Properties

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),; Vol. 6012(2010)p. 125-144

Paper in proceeding

Parametricity and dependent types

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

Paper in proceeding

Realizability and Parametricity in Pure Type Systems

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics),; Vol. 6604(2011)p. 108-122

Paper in proceeding

Areas of Advance

Information and Communication Technology

Roots

Basic sciences

Subject Categories

Computer Science

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

More information

Created

10/8/2017