paper on game semantics for untyped lambda-calculus

The following technical report is now available at
http://www.dimi.uniud.it/~pietro/Papers/Soft-copy-ps/games.ps.gz

Game semantics for untyped lambda-calculus

by Pietro Di Gianantonio, Gianluca Franco, and Furio Honsell
Dipartimento di Matematica e Informatica, Universita' di Udine.

ABSTRACT

We study models of the untyped lambda calculus in the setting
of the game semantics introduced by Abramsky and Hyland. In
particular we show that two natural, and apparently general,
model constructions give extensional lambda-models which,
somewhat unexpectedly, all induce the same theory. This is H*,
the maximal theory induced by the classical $D_{\infty}$ model,
introduced by D. Scott in 1968. New techniques for overcoming
this apparent rigidity of game lambda-models are called for.