3 research outputs found
An Explicit Framework for Interaction Nets
Interaction nets are a graphical formalism inspired by Linear Logic
proof-nets often used for studying higher order rewriting e.g. \Beta-reduction.
Traditional presentations of interaction nets are based on graph theory and
rely on elementary properties of graph theory. We give here a more explicit
presentation based on notions borrowed from Girard's Geometry of Interaction:
interaction nets are presented as partial permutations and a composition of
nets, the gluing, is derived from the execution formula. We then define
contexts and reduction as the context closure of rules. We prove strong
confluence of the reduction within our framework and show how interaction nets
can be viewed as the quotient of some generalized proof-nets
Isomorphisms of types in the presence of higher-order references (extended version)
We investigate the problem of type isomorphisms in the presence of
higher-order references. We first introduce a finitary programming language
with sum types and higher-order references, for which we build a fully abstract
games model following the work of Abramsky, Honda and McCusker. Solving an open
problem by Laurent, we show that two finitely branching arenas are isomorphic
if and only if they are geometrically the same, up to renaming of moves
(Laurent's forest isomorphism). We deduce from this an equational theory
characterizing isomorphisms of types in our language. We show however that
Laurent's conjecture does not hold on infinitely branching arenas, yielding new
non-trivial type isomorphisms in a variant of our language with natural
numbers