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Probabilistic coherence spaces are fully abstract for probabilistic PCF

Thomas Ehrhard, Christine Tasson, Michele Pagani
2014 SIGPLAN notices  
This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series.  ...  Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series.  ...  The main contribution of the present work is to show that probabilistic coherence spaces provide a fully abstract model of PPCF, a probabilistic extension of the functional programing language PCF [28  ... 
doi:10.1145/2578855.2535865 fatcat:c75r4pccv5axznqebfhp4beyhu

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Thomas Ehrhard, Christine Tasson, Michele Pagani
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series.  ...  Probabilistic coherence spaces (PCoh) yield a semantics of higherorder probabilistic computation, interpreting types as convex sets and programs as power series.  ...  The main contribution of the present work is to show that probabilistic coherence spaces provide a fully abstract model of PPCF, a probabilistic extension of the functional programing language PCF [28  ... 
doi:10.1145/2535838.2535865 dblp:conf/popl/EhrhardTP14 fatcat:vu7xvpgr4jfblhz4ftjrvnyghu

Fully Abstract Models of the Probabilistic lambda-calculus

Pierre Clairambault, Hugo Paquet, Michael Wagner
2018 Annual Conference for Computer Science Logic  
We obtain that the relational model is also fully abstract.  ...  Probabilistic Böhm trees and probabilistic strategies are shown to be related by a precise correspondence theorem, in the spirit of existing work for the pure λ-calculus.  ...  In [11] , the authors define an operational semantics for Λ + and study a model in the category of probabilistic coherence spaces, an existing model [9] of Probabilistic PCF.  ... 
doi:10.4230/lipics.csl.2018.16 dblp:conf/csl/ClairambaultP18 fatcat:23jtwzvvgvd35baxkm2vcklazm

Probabilistic Stable Functions on Discrete Cones are Power Series (long version) [article]

Raphaëlle Crubillé
2018 arXiv   pre-print
We look at Cstabm as a model for discrete probabilities, by showing the existence of a cartesian closed, full and faithful functor which embeds probabilistic coherence spaces (a fully abstract denotational  ...  , based on game semantics; and in [3] Ehrhard, Pagani and Tasson showed that the category Pcoh of probabilistic coherence spaces gives a fully abstract model for PCF ⊕ , a discrete probabilistic variant  ...  cannot be a model for PCF sample : indeed it doesn't even seem possible to write a probabilistic coherence space for the real type.  ... 
arXiv:1805.00512v1 fatcat:gtm57h2omfdj3psb3ltgldszje

The concurrent game semantics of Probabilistic PCF

Simon Castellan, Pierre Clairambault, Hugo Paquet, Glynn Winskel
2018 Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '18  
It follows that our model is intensionally fully abstract.  ...  relational model recently proved fully abstract by Ehrhard et al.  ...  The weighted relational model In [14] , Ehrhard et al proved that probabilistic coherence spaces (PCoh) are fully abstract for PPCF: two PPCF terms are contextually equivalent iff they have the same denotation  ... 
doi:10.1145/3209108.3209187 dblp:conf/lics/CastellanCPW18 fatcat:uwzdgjexrvdgflxv7dw6fq7c2u

From Qualitative to Quantitative Semantics [chapter]

James Laird
2017 Lecture Notes in Computer Science  
fully abstract.  ...  This is induced by a monoidal functor from the category of coherence spaces to the category of modules over a complete semiring R.  ...  So, for example, our model is fully abstract for Probabilistic Algol.  ... 
doi:10.1007/978-3-662-54458-7_3 fatcat:xswaap3whzcz3omv4pb64bb7sm

Strong Adequacy and Untyped Full-Abstraction for Probabilistic Coherence Spaces [chapter]

Thomas Leventis, Michele Pagani
2019 Green Chemistry and Sustainable Technology  
We consider the probabilistic untyped lambda-calculus and prove a stronger form of the adequacy property for probabilistic coherence spaces (PCoh), showing how the denotation of a term statistically distributes  ...  As a consequence, we get full abstraction for PCoh.  ...  is proved to be fully abstract for the call-by-name probabilistic PCF [7] . This result has been also extended to richer languages, e.g. call-by-push-value probabilistic PCF [8] .  ... 
doi:10.1007/978-3-030-17127-8_21 dblp:conf/fossacs/LeventisP19 fatcat:pegtpjfx2rfmxcoxneqbg7kvti

Full abstraction for non-deterministic and probabilistic extensions of PCF I: The angelic cases

Jean Goubault-Larrecq
2015 Journal of Logical and Algebraic Methods in Programming  
We examine several extensions and variants of Plotkin's language PCF, including non-deterministic and probabilistic choice constructs.  ...  Beyond this, we establish full abstraction (the observational preorder coincides with the denotational preorder) in a number of cases.  ...  While this paper was being reviewed, Ehrhard, Tasson and Pagani independently produced a denotational model of probabilistic PCF that is fully abstract [7] , based on probabilistic coherence spaces.  ... 
doi:10.1016/j.jlamp.2014.09.003 fatcat:obalij2shbf4vj62gklmsaudui

Weighted Relational Models of Typed Lambda-Calculi

Jim Laird, Giulio Manzonetto, Guy McCusker, Michele Pagani
2013 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science  
what probability" (for probabilistic PCF).  ...  Specific instances of R allow us to compare programs not only with respect to "what they can do", but also "in how many steps" or "in how many different ways" (for non-deterministic PCF) or even "with  ...  of probabilistic coherence spaces and entire functions. Corollary VI.8. For every program M of PCF or , M • P n = Red ∞ M,n which is the probability that M reduces to n.  ... 
doi:10.1109/lics.2013.36 dblp:conf/lics/LairdMMP13 fatcat:5rlghyqarndr3a5lqesk2ygsru

Full abstraction for probabilistic PCF [article]

Thomas Ehrhard
2015 arXiv   pre-print
We describe a denotational semantics based on probabilistic coherence spaces, a model of classical Linear Logic developed in previous works.  ...  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.  ...  of PCF, interpreted in the probabilistic coherence space model.  ... 
arXiv:1511.01272v1 fatcat:ftuzqurizffsxb3fpbtsp56ppm

Full Abstraction for Probabilistic PCF

Thomas Ehrhard, Michele Pagani, Christine Tasson
2018 Journal of the ACM  
We describe a denotational semantics based on probabilistic coherence spaces, a model of classical Linear Logic developed in previous works.  ...  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.  ...  of PCF, interpreted in the probabilistic coherence space model.  ... 
doi:10.1145/3164540 fatcat:5sdzrax6fzbedeaw26nrjejtje

The Free Exponential Modality of Probabilistic Coherence Spaces [chapter]

Raphaëlle Crubillé, Thomas Ehrhard, Michele Pagani, Christine Tasson
2017 Lecture Notes in Computer Science  
Probabilistic coherence spaces yield a model of linear logic and lambda-calculus with a linear algebra flavor.  ...  Formulas/types are associated with convex sets of R + -valued vectors, linear logic proofs with linear functions and λ-terms with entire functions, both mapping the convex set of their domain into the  ...  Acknowledgments We thank Sam Staton, Hugh Steele, Lionel Vaux and the anonymous reviewers for useful comments and discussions.  ... 
doi:10.1007/978-3-662-54458-7_2 fatcat:uwfd7xwkivfc3f2ufsyhuo64sm

Convexity and Order in Probabilistic Call-by-Name FPC [article]

Mathys Rennela
2020 arXiv   pre-print
Consequently, Kegelspitzen form a denotational model of pPCF, an abstract functional programming language for probabilistic computing.  ...  We conclude the present work with a discussion of the interpretation of (probabilistic) recursive types, which are types for entities which might contain other entities of the same type, such as lists  ...  It is also worth mentioning that previous work proved that probabilistic coherence spaces constitute a fully abstract model of pPCF (see e.g. [6, 7, 9, 10] ).  ... 
arXiv:1607.04332v5 fatcat:642kk5elmfc4neklpdzluuyqqe

The Power of Synchronisation: Formal Analysis of Power Consumption in Networks of Pulse-Coupled Oscillators [article]

Paul Gainer, Sven Linker, Clare Dixon, Ullrich Hustadt, Michael Fisher
2017 arXiv   pre-print
This provides a principled basis for the formal analysis of a much broader range of large-scale network protocols.  ...  use the widely adopted approach of bio-inspired, pulse-coupled oscillators to achieve network-wide synchronisation and provide an extended formal model of just such a protocol, enhanced with structures for  ...  The authors would like to thank the Networks Sciences and Technology Initiative (NeST) of the University of Liverpool for the use of their computing facilities and David Shield for the corresponding technical  ... 
arXiv:1709.04385v3 fatcat:l5igk3fp4ff45p6dxsq2e6ulgy

Convexity and Order in Probabilistic Call-by-Name FPC

Mathys Rennela
2016 Logical Methods in Computer Science  
Consequently, Kegelspitzen form a denotational model of pPCF, an abstract functional programming language for probabilistic computing.  ...  We conclude the present work with a discussion of the interpretation of (probabilistic) recursive types, which are types for entities which might contain other entities of the same type, such as lists  ...  It is also worth mentioning that previous work proved that probabilistic coherence spaces constitute a fully abstract model of pPCF (see e.g. [6, 7, 9, 10] ).  ... 
doi:10.23638/lmcs-16(4:10)2020 fatcat:lky72qwitvaxpiwmqjky44oju4
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