298 research outputs found
Full Abstraction for PCF
An intensional model for the programming language PCF is described, in which
the types of PCF are interpreted by games, and the terms by certain
"history-free" strategies. This model is shown to capture definability in PCF.
More precisely, every compact strategy in the model is definable in a certain
simple extension of PCF. We then introduce an intrinsic preorder on strategies,
and show that it satisfies some striking properties, such that the intrinsic
preorder on function types coincides with the pointwise preorder. We then
obtain an order-extensional fully abstract model of PCF by quotienting the
intensional model by the intrinsic preorder. This is the first
syntax-independent description of the fully abstract model for PCF. (Hyland and
Ong have obtained very similar results by a somewhat different route,
independently and at the same time).
We then consider the effective version of our model, and prove a Universality
Theorem: every element of the effective extensional model is definable in PCF.
Equivalently, every recursive strategy is definable up to observational
equivalence.Comment: 50 page
Focusing in Asynchronous Games
Game semantics provides an interactive point of view on proofs, which enables
one to describe precisely their dynamical behavior during cut elimination, by
considering formulas as games on which proofs induce strategies. We are
specifically interested here in relating two such semantics of linear logic, of
very different flavor, which both take in account concurrent features of the
proofs: asynchronous games and concurrent games. Interestingly, we show that
associating a concurrent strategy to an asynchronous strategy can be seen as a
semantical counterpart of the focusing property of linear logic
Extensional Collapse Situations I: non-termination and unrecoverable errors
We consider a simple model of higher order, functional computation over the
booleans. Then, we enrich the model in order to encompass non-termination and
unrecoverable errors, taken separately or jointly. We show that the models so
defined form a lattice when ordered by the extensional collapse situation
relation, introduced in order to compare models with respect to the amount of
"intensional information" that they provide on computation. The proofs are
carried out by exhibiting suitable applied {\lambda}-calculi, and by exploiting
the fundamental lemma of logical relations
- …