Ninth Annual IEEE Symposium on

Logic in Computer Science (LICS 1994)

Paper: Reflexive graphs and parametric polymorphism (at LICS 1994)

Authors: Edmund Robinson Giuseppe Rosolini


The pioneering work on relational parametricity for the second order lambda calculus was done by Reynolds (1983) under the assumption of the existence of set-based models, and subsequently reformulated by him, in conjunction with his student Ma, using the technology of PL-categories. The aim of this paper is to use the different technology of internal category theory to re-examine Ma and Reynolds' definitions. Apart from clarifying some of their constructions, this view enables us to prove that if we start with a non-parametric model which is left exact and which satisfies a completeness condition corresponding to Ma and Reynolds “suitability for polymorphism”, then we can recover a parametric model with the same category of closed types. This implies, for example, that any suitably complete model (such as the PER model) has a parametric counterpart


    author = 	 {Edmund Robinson and Giuseppe Rosolini},
    title = 	 {Reflexive graphs and parametric polymorphism},
    booktitle =  {Proceedings of the Ninth Annual IEEE Symp. on Logic in Computer Science, {LICS} 1994},
    year =	 1994,
    editor =	 {Samson Abramsky},
    month =	 {July}, 
    pages =      {364--371},
    location =   {Paris, France}, 
    publisher =	 {IEEE Computer Society Press}