[LI] ================================================ AMAST Links 02 04

Two papers concerning game semantics for languages with recursive types
                  by Samson Abramsky and Guy McCusker

   Two papers, `Games for Recursive Types' and `Games and Full 
   Abstraction for the Lazy Lambda-Calculus' are now available.

**Games for Recursive Types**

  We present results concerning the solution of recursive domain
equations in the category G of games, previously used to construct a
fully abstract model of PCF. Namely, we show how to construct solutions
to equations of the form D = F(D,D) for a large class of functors
F: G^{op} x G --> G  and verify that these solutions satisfy Freyd's
minimal invariant property. 
  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.
  To appear in proceedings of the Second Workshop of the Theory and
Formal Methods Section, Department of Computing, Imperial College.
  Available via WWW from URL: http://theory.doc.ic.ac.uk/~gam

**Games and Full Abstraction for the Lazy Lambda Calculus**

  We define a category of games G, and its extensional quotient E.
A model of the lazy lambda-calculus, a type-free functional language
based on evaluation to weak head normal form, is given in G, yielding
an extensional model in E. This model is shown to be fully abstract
with respect to applicative simulation. This is, so far as we know, the
first purely semantic construction of a fully abstract model for a
reflexively-typed sequential language.
  To appear in proceedings of 10th annual IEEE symposium on Logic in
Computer Science, 1995.
  Available via WWW from URL: http://theory.doc.ic.ac.uk/~gam