Probabilistic coherence spaces as a model of higher-order probabilistic computation

Danos, Vincent; Ehrhard, Thomas

doi:10.1016/j.ic.2011.02.001

Cited by 93 publications

(184 citation statements)

References 16 publications

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“…This could be used to model a variant of CP with complexity measures. Probabilistic Coherence Spaces, introduced by Danos and Ehrhard [11], are another refinement that model probabilistic computation.…”

Section: Discussionmentioning

confidence: 99%

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

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Abstract. Classical Linear Logic (CLL) has long inspired readings of its proofs as communicating processes. Wadler's CP calculus is one of these readings. Wadler gave CP an operational semantics by selecting a subset of the cut-elimination rules of CLL to use as reduction rules. This semantics has an appealing close connection to the logic, but does not resolve the status of the other cut-elimination rules, and does not admit an obvious notion of observational equivalence. We propose a new operational semantics for CP based on the idea of observing communication. We use this semantics to define an intuitively reasonable notion of observational equivalence. To reason about observational equivalence, we use the standard relational denotational semantics of CLL. We show that this denotational semantics is adequate for our operational semantics. This allows us to deduce that, for instance, all the cut-elimination rules of CLL are observational equivalences.

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Section: Discussionmentioning

confidence: 99%

Observed Communication Semantics for Classical Processes

Atkey

2017

Programming Languages and Systems

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“…This system is a minor variant with respect to the probabilistic extension of PCF presented in [4] (see Remark 6). The grammar of terms is obtained by adding to standard PCF a random number generator rand.The typing rules (Figure 1(b)) are the usual ones, with rand of type Int ⇒ Int.…”

Section: Probabilistic Pcfmentioning

confidence: 99%

“…Also, both ⊕κ and rand are definable as ⊕ n i=1 κiMi, and the latter 4 The numeral 0 chosen for testing the equality is not significant. Indeed, from a context Q semi-separating two terms M , N on a numeral n, i.e.…”

Section: Proposition 4 ([4 Lemma 32])mentioning

confidence: 99%

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Ehrhard

Tasson

Pagani

2014

Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in PCoh characterizes the operational indistinguishability of programs in PCF with a random primitive. This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series.Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.

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“…The category of probabilistic coherence spaces is also considered by Danos and Ehrhard in [11]. In that paper, the authors show that this category is not only * -autonomous, but supports the structure of a full model of classical linear logic.…”

Section: Related Workmentioning

confidence: 81%

“…Girard introduces the category of probabilistic coherence spaces with the intent of using semantic and proof-theoretic ideas in the consideration of structures arising in quantum mechanics. Probabilistic coherence spaces were also studied extensively by Danos and Erhard in [11]. They wish to consider this notion as providing semantics of a probabilistic version of PCF, as well as a framework for considering probabilistic games in the sense of [12].…”

Section: Introductionmentioning

confidence: 99%

Deep Inference and Probabilistic Coherence Spaces

Blute

Panangaden

Slavnov

2010

Appl Categor Struct

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This paper proposes a definition of categorical model of the deep inference system BV, defined by Guglielmi. Deep inference introduces the idea of performing a deduction in the interior of a formula, at any depth. Traditional sequent calculus rules only see the roots of formulae. However in these new systems, one can rewrite at any position in the formula tree. Deep inference in particular allows the syntactic description of logics for which there is no sequent calculus. One such system is BV, which extends linear logic to include a noncommutative self-dual connective. This is the logic our paper proposes to model. Our definition is based on the notion of a linear functor, due to Cockett and Seely. A BV-category is a linearly distributive category, possibly with negation, with an additional tensor product which, when viewed as a bivariant functor, is linear with a degeneracy condition. We show that this simple definition implies all of the key isomorphisms of the theory.We consider Girard's category of probabilistic coherence spaces and show that it contains a self-dual monoidal structure in addition to the * -autonomous structure exhibited by Girard. This structure makes the category a BV-category. We believe this structure is also of independent interest, as well-behaved noncommutative operators generally are.

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Probabilistic coherence spaces as a model of higher-order probabilistic computation

Cited by 93 publications

References 16 publications

Observed Communication Semantics for Classical Processes

Observed Communication Semantics for Classical Processes

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Deep Inference and Probabilistic Coherence Spaces

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