## Paper: Parametric Limits (at LICS 2004)

**Brian Dunphy Uday S. Reddy**

### Abstract

We develop a categorical model of polymorphic lambda calculi using the notion of parametric limits, which extend the notion of limits in categories to reflexive graphs of categories. We show that a number of parametric models of polymorphism can be captured in this way. We also axiomatize the structure of reflexive graphs needed for modelling parametric polymorphism based on ideas of fibrations, and show that it leads to proofs of representation results such as the initial algebra and final coalgebra properties one expects in polymorphic lambda calculi.

### BibTeX

@InProceedings{DunphyReddy-ParametricLimits, author = {Brian Dunphy and Uday S. Reddy}, title = {Parametric Limits}, booktitle = {Proceedings of the Nineteenth Annual IEEE Symposium on Logic in Computer Science (LICS 2004)}, year = {2004}, month = {July}, pages = {242--251}, location = {Turku, Finland}, publisher = {IEEE Computer Society Press} }