474 research outputs found
Full abstraction for probabilistic PCF
We present a probabilistic version of PCF, a well-known simply typed
universal functional language. The type hierarchy is based on a single ground
type of natural numbers. Even if the language is globally call-by-name, we
allow a call-by-value evaluation for ground type arguments in order to provide
the language with a suitable algorithmic expressiveness. We describe a
denotational semantics based on probabilistic coherence spaces, a model of
classical Linear Logic developed in previous works. We prove an adequacy and an
equational full abstraction theorem showing that equality in the model
coincides with a natural notion of observational equivalence
Probabilistic call by push value
We introduce a probabilistic extension of Levy's Call-By-Push-Value. This
extension consists simply in adding a " flipping coin " boolean closed atomic
expression. This language can be understood as a major generalization of
Scott's PCF encompassing both call-by-name and call-by-value and featuring
recursive (possibly lazy) data types. We interpret the language in the
previously introduced denotational model of probabilistic coherence spaces, a
categorical model of full classical Linear Logic, interpreting data types as
coalgebras for the resource comonad. We prove adequacy and full abstraction,
generalizing earlier results to a much more realistic and powerful programming
language
On Probabilistic Applicative Bisimulation and Call-by-Value -Calculi (Long Version)
Probabilistic applicative bisimulation is a recently introduced coinductive
methodology for program equivalence in a probabilistic, higher-order, setting.
In this paper, the technique is applied to a typed, call-by-value,
lambda-calculus. Surprisingly, the obtained relation coincides with context
equivalence, contrary to what happens when call-by-name evaluation is
considered. Even more surprisingly, full-abstraction only holds in a symmetric
setting.Comment: 30 page
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