 
Summary: A Game Semantics for Generic Polymorphism
Samson Abramsky 1? and Radha Jagadeesan 2??
1 Oxford University Computing Laboratory
samson@comlab.ox.ac.uk
2 DePaul University
rjagadeesan@cs.depaul.edu
Abstract. Genericity is the idea that the same program can work at
many dierent data types. Longo, Milsted and Soloviev proposed to cap
ture 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 ad
missible 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 of games. This allows moves in games A[T ] to
be decomposed into the generic part from A, and the part pertaining
