Summary: A Game Semantics for Generic Polymorphism
Oxford University Computing Laboratory
Dedicated to Helmut Schwichtenberg on the occasion of his sixtieth birthday. His commitment
to the highest scientific standards, coupled with a wise and kind humanity, is a continuing
source of inspiration.
Genericity is the idea that the same program can work at many different 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 X. 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 finding a semantically motivated model satisfying this principle remained an open
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
· A direct interpretation of variable types as games, with a natural notion of substitution