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On Probabilistic Applicative Bisimulation and Call-by-Value λ-Calculi (Long Version) [article]

Raphaelle Crubille, Ugo Dal Lago
2014 arXiv   pre-print
In this paper, the technique is applied to a typed, call-by-value, lambda-calculus.  ...  Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting.  ...  A recent paper by Alberti, Sangiorgi and the second author [10] generalizes Abramsky's applicative bisimulation [1] to Λ ⊕ , a call-by-name, untyped λ-calculus endowed with binary, fair, probabilistic  ... 
arXiv:1401.3766v2 fatcat:ed4dtqvtlrba5eamljjdu4wqti

On Probabilistic Applicative Bisimulation and Call-by-Value λ-Calculi [chapter]

Raphaëlle Crubillé, Ugo Dal Lago
2014 Lecture Notes in Computer Science  
In this paper, the technique is applied to a typed, call-by-value, lambdacalculus.  ...  Probabilistic applicative bisimulation is a recently introduced coinductive methodology for program equivalence in a probabilistic, higher-order, setting.  ...  In this paper, we proceed with the study of probabilistic applicative bisimulation, analysing its behaviour when instantiated on call-by-value λ-calculi.  ... 
doi:10.1007/978-3-642-54833-8_12 fatcat:pm6qbwcv3fclbf535vg6tn7m5m

Higher-Order Languages: Bisimulation and Coinductive Equivalences (Extended Abstract) [chapter]

Davide Sangiorgi
2014 Lecture Notes in Computer Science  
This version of bisimulation, called applicative bisimulations, and variants of it, have received considerable attention [Gor93, GR96, Pit97, San98, Las98] .  ...  Secondly, congruence proofs of applicative bisimulations are notoriously hard. Such proofs usually rely on Howe's method [How96] .  ...  passivation, or in a call-by-value λ-calculus, bisimilarity may be recovered [BSV14] . c IFIP International Federation for Information Processing 2014 M.M.  ... 
doi:10.1007/978-3-662-44124-4_1 fatcat:jmcahmpdejauveabvhsxrftwgy

Applicative Bisimulation and Quantum λ-Calculi [chapter]

Ugo Dal Lago, Alessandro Rioli
2015 Lecture Notes in Computer Science  
In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linear λcalculus extended with features such as probabilistic binary choice,  ...  Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages.  ...  In this paper, we define and study applicative bisimulation when instantiated on linear λ-calculi, starting with a purely deterministic language, and progressively extending it with probabilistic choice  ... 
doi:10.1007/978-3-319-24644-4_4 fatcat:cgxlelylhzc3do6m4af5cbyhai

Environmental Bisimulations for Probabilistic Higher-order Languages

Davide Sangiorgi, Valeria Vignudelli
2019 ACM Transactions on Programming Languages and Systems  
As representative calculi, call-by-name and call-by-value λcalculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered.  ...  In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence.  ...  The work has been partially supported by the MIUR-PRIN project 'CINA', and the ANR project 12IS02001 'PACE'.  ... 
doi:10.1145/3350618 fatcat:jrjqpy6xcfehtcs5pmvag3n23u

Environmental bisimulations for probabilistic higher-order languages

Davide Sangiorgi, Valeria Vignudelli
2016 SIGPLAN notices  
As representative calculi, call-by-name and call-by-value λcalculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered.  ...  In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence.  ...  The work has been partially supported by the MIUR-PRIN project 'CINA', and the ANR project 12IS02001 'PACE'.  ... 
doi:10.1145/2914770.2837651 fatcat:edzysoznqvhmnkmw6n3egnlbiq

Environmental bisimulations for probabilistic higher-order languages

Davide Sangiorgi, Valeria Vignudelli
2016 Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL 2016  
As representative calculi, call-by-name and call-by-value λcalculus, and a (call-by-value) λ-calculus extended with references (i.e., a store) are considered.  ...  In contrast with applicative bisimulations, environmental bisimulations are known to be more robust and do not require sophisticated techniques such as Howe's in the proofs of congruence.  ...  The work has been partially supported by the MIUR-PRIN project 'CINA', and the ANR project 12IS02001 'PACE'.  ... 
doi:10.1145/2837614.2837651 dblp:conf/popl/SangiorgiV16 fatcat:sy7akxi3gbdjrfcgkjwaq46gkq

Applicative Bisimulation and Quantum λ-Calculi (Long Version) [article]

Ugo Dal Lago, Alessandro Rioli
2015 arXiv   pre-print
In this paper we show that applicative bisimulation also works when the underlying language of programs takes the form of a linear λ-calculus extended with features such as probabilistic binary choice,  ...  Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages.  ...  Conclusions We show that Abramsky's applicative bisimulation can be adapted to linear λ-calculi endowed with probabilistic choice and quantum data.  ... 
arXiv:1506.06661v1 fatcat:kgmpija4ozgsfh63entfvnqshy

Effectful Normal Form Bisimulation [chapter]

Ugo Dal Lago, Francesco Gavazzo
2019 Lecture Notes in Computer Science  
The technique has been shown to be useful not only when proving metatheorems about λ-calculi and their semantics, but also when looking at concrete examples of terms.  ...  In this paper, we show that there is a way to generalise normal form bisimulation to calculi with algebraic effects,à la Plotkin and Power.  ...  Weak Head Normal Form (Bi)simulation So far we have focused on call-by-value calculi, since in presence of effects the call-by-value evaluation strategy seems the more natural one.  ... 
doi:10.1007/978-3-030-17184-1_10 fatcat:whayrorjs5eqhdryy65k2fhn2e

Effectful applicative bisimilarity: Monads, relators, and Howe's method

Ugo Dal Lago, Francesco Gavazzo, Paul Blain Levy
2017 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)  
We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value λ-calculi with algebraic effects.  ...  We then show how the theory of relators provides precisely what is needed to generalise applicative bisimilarity to such a calculus, and to single out those monads and relators for which applicative bisimilarity  ...  The first and second authors are partially supported by the ANR projects 12IS02001 PACE, 14CE250005 ELICA, and 16CE250011 REPAS, and by the INRIA-JSPS joint project CRECOGI.  ... 
doi:10.1109/lics.2017.8005117 dblp:conf/lics/LagoGL17 fatcat:vptwgwjebvc53byww7awi32jzy

On coinductive equivalences for higher-order probabilistic functional programs

Ugo Dal Lago, Davide Sangiorgi, Michele Alberti
2014 Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '14  
Definitionally, probabilistic applicative bisimulation is obtained by setting up a labelled Markov chain on top of λ-terms, then adapting to it the coinductive scheme introduced by Larsen and Skou in a  ...  The objective of the paper is to understand context equivalence and bisimulation in this paradigmatic probabilistic higher-order language, called Λ ⊕ .  ...  call-by-name and call-by-value applications.  ... 
doi:10.1145/2535838.2535872 dblp:conf/popl/LagoSA14 fatcat:vzrazblhzffpvgsus3eltayyd4

On Coinductive Equivalences for Higher-Order Probabilistic Functional Programs (Long Version) [article]

Ugo Dal Lago, Davide Sangiorgi, Michele Alberti
2013 arXiv   pre-print
We study bisimulation and context equivalence in a probabilistic λ-calculus. The contributions of this paper are threefold.  ...  The resulting equality is that induced by Levy-Longo trees, generally accepted as the finest extensional equivalence on pure λ-terms under a lazy regime.  ...  call-by-name and call-by-value applications.  ... 
arXiv:1311.1722v1 fatcat:irp5m4jzpfatnffshvmjjazcem

On the discriminating power of passivation and higher-order interaction

Marco Bernardo, Davide Sangiorgi, Valeria Vignudelli
2014 Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS) - CSL-LICS '14  
For instance, in the LTS case, the additional discriminating power offered by passivation in concurrency is captured, in sequential languages, by the difference between the call-by-name and call-by-value  ...  This paper studies the discriminating power offered by higherorder concurrent languages, and contrasts this power with those offered by higher-order sequential languages (à la λ-calculus) and by first-order  ...  Acknowledgments The authors acknowledge support from the MIUR-PRIN project 'CINA', and the ANR project 12IS02001 'PACE'.  ... 
doi:10.1145/2603088.2603113 dblp:conf/csl/BernardoSV14 fatcat:uk2kfupinfcl3btzyeygyz5fk4

Uniform Labeled Transition Systems for Nondeterministic, Probabilistic, and Stochastic Process Calculi

Marco Bernardo, Rocco De Nicola, Michele Loreti
2011 Electronic Proceedings in Theoretical Computer Science  
mapping each possible target state to a value of some domain that expresses the degree of one-step reachability of that target state.  ...  In this extended abstract, we show how the resulting model, called ULTraS from Uniform Labeled Transition System, can be naturally used to give semantics to a fully nondeterministic, a fully probabilistic  ...  Acknowledgment: We would like to thank Diego Latella and Mieke Massink for their useful comments on a draft of this paper.  ... 
doi:10.4204/eptcs.60.5 fatcat:ovbxdrqguvewtgz3th6rxknuky

The Discriminating Power of the Let-In Operator in the Lazy Call-by-Name Probabilistic lambda-Calculus

Simona Kasterovic, Michele Pagani, Michael Wagner
2019 International Conference on Rewriting Techniques and Applications  
We consider the notion of probabilistic applicative bisimilarity (PAB), recently introduced as a behavioural equivalence over a probabilistic extension of the untyped λ-calculus.  ...  Alberti, Dal Lago and Sangiorgi have shown that PAB is not fully abstract with respect to the context equivalence induced by the lazy call-by-name evaluation strategy.  ...  A probabilistic applicative simulation is a probabilistic simulation on Λ ⊕,let and a probabilistic applicative bisimulation is a probabilistic bisimulation on Λ ⊕,let .  ... 
doi:10.4230/lipics.fscd.2019.26 dblp:conf/rta/KasterovicP19 fatcat:gzzuue5k4neeppbfl3tood7vs4
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