2 research outputs found
Axioms for Definability and Full Completeness
Axioms are presented which encapsulate the properties satisfied by categories
of games which form the basis of results on full abstraction for PCF and other
programming languages, and on full completeness for various logics and type
theories.
Axioms are presented on models of PCF from which full abstraction can be
proved. These axioms have been distilled from recent results on definability
and full abstraction of game semantics for a number of programming languages.
Full completeness for pure simply-typed -calculus is also axiomatized.Comment: 18 page
Types of Fireballs (Extended Version)
The good properties of Plotkin's call-by-value lambda-calculus crucially rely
on the restriction to weak evaluation and closed terms. Open call-by-value is
the more general setting where evaluation is weak but terms may be open. Such
an extension is delicate, and the literature contains a number of proposals.
Recently, Accattoli and Guerrieri provided detailed operational and
implementative studies of these proposals, showing that they are equivalent
from the point of view of termination, and also at the level of time cost
models.
This paper explores the denotational semantics of open call-by-value,
adapting de Carvalho's analysis of call-by-name via multi types (aka
non-idempotent intersection types). Our type system characterises normalisation
and thus provides an adequate relational semantics. Moreover, type derivations
carry quantitative information about the cost of evaluation: their size bounds
the number of evaluation steps and the size of the normal form, and we also
characterise derivations giving exact bounds.
The study crucially relies on a new, refined presentation of the fireball
calculus, the simplest proposal for open call-by-value, that is more apt to
denotational investigations