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Games for recursive types Samson Abramsky and Guy McCusker

Summary: Games for recursive types
Samson Abramsky and Guy McCusker
Imperial College
13 October 1994
We present results concerning the solution of recursive domain equations
in the category G of games, which is a modified version of the category
presented in [AJM94]. New constructions corresponding to lifting and
separated sum for games are presented, and are used to generate games
for two simple recursive types: the vertical and lazy natural numbers.
Recently, the ``game semantics'' paradigm has been used to model the multi­
plicative fragment of linear logic [AJ94], and to provide a solution to the full
abstraction problem for PCF [AJM94, HO94], where the intensional structure
of the games model captures both the sequential and functional nature of the
language. In the light of these results, it is natural to ask whether recursive types
can be handled in this setting. Here we show that they can: for a wide class of
functors \Phi, including all of the usual type constructors, the equation D ' \Phi(D)
has a (canonical) solution. In fact we solve this equation up to identity, and the
solution can be constructed in the usual way by iterating the action of the functor
on (the object corresponding to) the empty type.


Source: Abramsky, Samson - Computing Laboratory, University of Oxford
McCusker, Guy - Department of Computer Science, University of Bath


Collections: Computer Technologies and Information Sciences