 
Summary: A Game Semantics for Generic Polymorphism
Samson Abramsky
Oxford University Computing Laboratory
Radha Jagadeesan
DePaul University
Dedicated to Helmut Schwichtenberg on the occasion of his sixtieth birthday. His commitment
to the highest scientic standards, coupled with a wise and kind humanity, is a continuing
source of inspiration.
Abstract
Genericity is the idea that the same program can work at many dierent data types.
Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe
the structure of their instances by the following equational principle: if two generic programs,
viewed as terms of type 8X:A[X ], are equal at any given instance A[T ], then they are equal
at all instances. They proved that this rule is admissible in a certain extension of System
F, but nding a semantically motivated model satisfying this principle remained an open
problem.
In the present paper, we construct a categorical model of polymorphism, based on game
semantics, which contains a large collection of generic types. This model builds on two novel
constructions:
A direct interpretation of variable types as games, with a natural notion of substitution
