Discovering new languages from the study of games semantics

Alexis Goyet (1)

1 PPS - Preuves, Programmes et Systèmes

This is a master thesis for the MPRI (http://mpri.master.univ-paris7.fr). We give a generalisation of game semantics, in the spirit of Harmer, Hyland and Melies's work "Categorical Combinatorics for Innocent Strategies", but with more general definitions. In particular, this description encompasses "cellular" strategies as well as innocent ones. New general notions of "embeddings" and "history operators" are defined on games. A generic language for all history operators is given, along with a reduction. History operators define sets of strategies; in particular, both innocent and cellular strategies can be defined in this way. Thus the generic syntax gives them both a language, and their terms can interact through the reduction given. The generic syntax exhibits a new symmetry between functions and arguments, who can both name the terms exchanged. This property comes from the symmetry between the two players on the arenas of the games defined. In the same way, we gain a more precise access control on what part of the execution history can be read or refered to by the strategies. In comparison, neither the usual language for innocent strategies (PCF), nor our initial specific syntax for cellular strategies make these apparent.

Mots clés: game semantics; languages; history operators; embeddings; cellular strategies; innocent strategies; lambda calculus

Domaines: Informatique et langage [cs.CL]

Alexis Goyet. Discovering new languages from the study of games semantics. 2009. ⟨hal-00413040⟩