Y. Afek, H. Attiya, D. Dolev, E. Gafni, M. Merritt et al., Atomic snapshots of shared memory, J. ACM, vol.40, issue.4, 1993.

J. H. Anderson, Composite registers, Conference on Principles of Distributed Computing, p.14, 1993.

M. Ben-or, Another advantage of free choice (extended abstract): Completely asynchronous agreement protocols, Proceedings of the Second Annual ACM Symposium on Principles of Distributed Computing, PODC '83, pp.27-30, 1983.

S. Ofer-biran, S. Moran, and . Zaks, A combinatorial characterization of the distributed tasks which are solvable in the presence of one faulty processor, Proceedings of the seventh annual ACM Symposium on Principles of distributed computing, p.14, 1988.

R. Bonichon, G. Canet, L. Correnson, É. Goubault, E. Haucourt et al., Rigorous evidence of freedom from concurrency faults in industrial control software, p.15, 2011.
URL : https://hal.archives-ouvertes.fr/cea-01809015

E. Borowsky and E. Gafni, Generalized FLP impossibility result for t-resilient asynchronous computations, Proc. of the 25th STOC, p.14, 1993.

S. Chaudhuri, More choices allow more faults: Set consensus problems in totally asynchronous systems, Inf. Comput, vol.105, issue.1, p.12, 1993.

L. Fajstrup, É. Goubault, and M. Raussen, Detecting deadlocks in concurrent systems, CONCUR, number 1466 in LNCS, p.15, 1998.

L. Fajstrup, É. Goubault, E. Haucourt, S. Mimram, and M. Raussen, Directed Algebraic Topology and Concurrency, vol.15, p.17, 2016.

L. Fajstrup, M. Raußen, and E. Goubault, Algebraic topology and concurrency, Theoretical Computer Science, vol.357, issue.1, p.15, 2006.

L. Fajstrup, E. Goubault, E. Haucourt, S. Mimram, and M. Raußen, Trace spaces: An efficient new technique for state-space reduction, ESOP, vol.15, p.17, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00684615

J. Michael, N. A. Fischer, M. Lynch, and . Paterson, Impossibility of distributed consensus with one faulty process, Journal of the ACM (JACM), vol.32, issue.2, p.14, 1985.

. Peter-c-fishburn, Intransitive indifference with unequal indifference intervals, Journal of Mathematical Psychology, vol.7, issue.1, p.27, 1970.

G. Gierz, A Compendium of continuous lattices, p.17, 1980.

É. Goubault, The Geometry of Concurrency, p.15, 1995.

É. Goubault, Some geometric perspectives in concurrency theory. Homology, Homotopy and Appl, vol.15, p.18, 2003.

É. Goubault and E. Haucourt, A practical application of geometric semantics to static analysis of concurrent programs, CONCUR 2005, p.15, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00150857

É. Goubault and T. P. Jensen, Homology of higher-dimensional automata, Proc. of CONCUR, p.15, 1992.

É. Goubault, T. Heindel, and S. Mimram, A geometric view of partial order reduction, MFPS, Electr. Notes Theor. Comput. Sci, vol.298, p.15, 2013.
URL : https://hal.archives-ouvertes.fr/cea-01836517

É. Goubault, S. Mimram, and C. Tasson, From geometric semantics to asynchronous computability, Distributed Computing-29th International Symposium, vol.9363, p.15, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01207146

É. Goubault, S. Mimram, and C. Tasson, Iterated chromatic subdivisions are collapsible, DISTRIBUTED COMPUTING Éric Goubault, Samuel Mimram, and Christine Tasson. Geometric and combinatorial views on asynchronous computability. Distributed Computing, vol.23, p.15, 2015.
URL : https://hal.archives-ouvertes.fr/cea-01822918

M. Grandis, Directed Algebraic Topology : Models of Non-Reversible Worlds, New Mathematical Monographs, vol.13, 2009.

J. Gunawardena, Homotopy and concurrency, Bulletin of the EATCS, vol.54, p.15, 1994.

M. Herlihy and N. Shavit, The asynchronous computability theorem for t-resilient tasks, Proceedings of the twenty-fifth annual ACM symposium on Theory of computing, vol.14, p.16, 1993.
DOI : 10.1145/167088.167125

URL : http://www.cs.brown.edu/research/pubs/pdfs/1993/Herlihy-1993-ACT.pdf

M. Herlihy and N. Shavit, The topological structure of asynchronous computability, Journal of the ACM (JACM), vol.46, issue.6, p.23, 1999.
DOI : 10.1145/331524.331529

URL : http://www.math.tau.ac.il/~shanir/publications/HS-topology.ps

M. Herlihy, D. Kozlov, and S. Rajsbaum, Distributed Computing Through Combinatorial Topology, vol.15, p.24, 2014.

D. Kozlov, Chromatic subdivision of a simplicial complex, Homology, Homotopy and Applications, vol.14, issue.2, p.26, 2012.
DOI : 10.4310/hha.2012.v14.n2.a12

URL : http://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2012/0014/0002/HHA-2012-0014-0002-a012.pdf

D. Kozlov, Topology of the view complex, vol.12, p.27, 2013.
DOI : 10.4310/hha.2015.v17.n1.a15

URL : http://www.intlpress.com/site/pub/files/_fulltext/journals/hha/2015/0017/0001/HHA-2015-0017-0001-a015.pdf

M. C. Loui and H. H. Abu-amara, Memory requirements for agreement among unreliable asynchronous processes, Advances in Computing Research, vol.4, p.14, 1987.

A. Nancy and . Lynch, Distributed algorithms, vol.14, p.16, 1996.

H. Mendes, C. Tasson, and M. Herlihy, Distributed computability in Byzantine asynchronous systems, Symposium on Theory of Computing, STOC 2014, vol.12, p.15, 2014.
DOI : 10.1145/2591796.2591853

URL : http://arxiv.org/pdf/1302.6224.pdf

L. Nachbin, Topology and order. Van Nostrand mathematical studies, p.17, 1965.

V. Pratt, Modeling concurrency with geometry, POPL, p.15, 1991.
DOI : 10.1145/99583.99625

URL : http://boole.stanford.edu/pub/cg.pdf

M. E. Saks and F. Zaharoglou, Wait-free k-set agreement is impossible: the topology of public knowledge, STOC, p.14, 1993.
DOI : 10.1137/s0097539796307698

R. Van-glabbeek, Bisimulation semantics for higher dimensional automata, p.15, 1991.

R. Street, The formal theory of monads, J. Pure Appl. Algebra, vol.2, issue.2, p.37, 1972.
DOI : 10.1016/0022-4049(72)90019-9

URL : https://doi.org/10.1016/0022-4049(72)90019-9

R. Street, Limits indexed by category-valued 2-functors, Journal of Pure and Applied Algebra, vol.8, issue.2, p.39, 1976.
DOI : 10.1016/0022-4049(76)90013-x

URL : https://doi.org/10.1016/0022-4049(76)90013-x

M. Tanaka, Abstract syntax and variable binding for linear binders, Mathematical Foundations of Computer Science, vol.34, p.55, 2000.
DOI : 10.1007/3-540-44612-5_62

C. Tasson and L. Vaux, Transport of finiteness structures and applications, Mathematical Structures in Computer Science, vol.28, issue.7, p.35, 2018.
URL : https://hal.archives-ouvertes.fr/hal-00475004

T. Tsukada, K. Asada, and L. Ong, Generalised species of rigid resource terms
DOI : 10.1109/lics.2017.8005093

B. Vallette, 7 Bibliography An explicit formula for the free exponential modality of linear logic, Mathematical Structures in Computer Science, vol.208, issue.2, p.68, 2007.

R. Amadio and P. Curien, Domains and lambda-calculi, Cambridge Tracts in Theoretical Computer Science, vol.46, p.83, 1998.
DOI : 10.1017/cbo9780511983504

URL : https://hal.archives-ouvertes.fr/inria-00070008

T. Andô, On fundamental properties of a banach space with a cone, Pacific Journal of Mathematics, vol.12, issue.4, p.97, 1962.

R. J. Aumann, Borel structures for function spaces, Illinois J. Math, vol.5, issue.4, p.63, 1961.

G. Berry, Stable models of typed lambda-calculi, Automata, Languages and Programming, vol.62, p.98, 1978.
DOI : 10.1007/3-540-08860-1_7

G. Bierman, What is a categorical model of intuitionistic linear logic?, Proceedings of the second Typed Lambda-Calculi and Applications conference, vol.902, p.66, 1995.
DOI : 10.1007/bfb0014046

URL : http://www.cl.cam.ac.uk/users/gmb/Publications/../Papers/tlca95.ps

J. Borgström, U. D. Lago, A. D. Gordon, and M. Szymczak, A lambda-calculus foundation for universal probabilistic programming, Proceedings of the 21st ACM SIGPLAN International Conference on Functional Programming, vol.95, p.104, 2016.

G. E. Box and M. E. Muller, A note on the generation of random normal deviates, Ann. Math. Statist, vol.29, issue.2, p.1958

A. Bucciarelli, A. Carraro, T. Ehrhard, and G. Manzonetto, Full Abstraction for Resource Calculus with Tests, LIPIcs. Schloss DagstuhlLeibniz-Zentrum fuer Informatik, vol.12, p.84, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00707814

S. Castellan, P. Clairambault, H. Paquet, and G. Winskel, The concurrent game semantics of probabilistic PCF, LICS, p.63, 2018.
DOI : 10.1145/3209108.3209187

URL : https://hal.archives-ouvertes.fr/hal-01886965

R. Crubillé, Probabilistic stable functions on discrete cones are power series, LICS, p.106, 2018.

R. Crubillé, T. Ehrhard, M. Pagani, and C. Tasson, The Free Exponential Modality of Probabilistic Coherence Spaces, Proceedings of the 20th International Conference on Foundations of Software Science and Computation Structures, vol.64, p.68, 2017.

V. Danos and T. Ehrhard, Probabilistic coherence spaces as a model of higher-order probabilistic computation, Information and Computation, vol.152, issue.1, p.95, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00640435

T. Ehrhard, Call-by-push-value from a linear logic point of view, ESOP, vol.9632, p.90, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01375814

T. Ehrhard, An introduction to differential linear logic: proof-nets, models and antiderivatives, Mathematical Structures in Computer Science, vol.28, issue.7, p.72, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01326738

T. Ehrhard and C. Tasson, Accepted for publication, under minor revisions, Logical Methods in Computer Science, vol.61, p.92, 2018.

T. Ehrhard, M. Pagani, and C. Tasson, The computational meaning of probabilistic coherence spaces, LICS, vol.63, p.76, 2011.

T. Ehrhard, M. Pagani, and C. Tasson, Probabilistic coherence spaces are fully abstract for probabilistic PCF, The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL '14, vol.61, p.63, 2014.
DOI : 10.1145/2535838.2535865

URL : http://www.pps.univ-paris-diderot.fr/%7Etasson/doc/recherche/fapcoh.pdf

T. Ehrhard, M. Pagani, and C. Tasson, Full abstraction for probabilistic PCF, Journal of the ACM, vol.65, issue.4, p.78, 2018.
DOI : 10.1145/3164540

URL : https://hal.archives-ouvertes.fr/hal-01223791

T. Ehrhard, M. Pagani, and C. Tasson, Measurable cones and stable, measurable functions: a model for probabilistic higher-order programming, POPL, vol.59, p.64, 2018.
DOI : 10.1145/3158147

URL : https://hal.archives-ouvertes.fr/hal-01622046

M. Escardó, Pcf extended with real numbers, Theoretical Computer Science, vol.162, issue.1, p.94, 1996.

J. Girard, Linear logic, Theoretical Computer Science, vol.50, p.92, 1987.
URL : https://hal.archives-ouvertes.fr/inria-00075966

J. Girard, Normal functors, power series and the ?-calculus, Annals of Pure and Applied Logic, vol.37, p.61, 1988.

J. Girard, Between logic and quantic: a tract, Linear Logic in Computer Science, vol.316, p.61, 2004.

M. Giry, A categorical approach to probability theory, vol.63, p.106, 1982.

D. Noah, J. B. Goodman, and . Tenenbaum, Probabilistic models of cognition, p.63, 2014.

N. D. Goodman, K. Vikash, D. M. Mansinghka, K. Roy, J. B. Bonawitz et al., Church: a language for generative models, UAI 2008, Proceedings of the 24th Conference in Uncertainty in Artificial Intelligence, p.63, 2008.

C. Heunen, O. Kammar, S. Staton, and H. Yang, A convenient category for higher-order probability theory, LICS, vol.63, p.104, 2017.

M. Hyland, A syntactic characterization of the equality in some models for the lambda calculus, J. London Math. Soc, vol.12, p.76, 1976.

C. Jones and G. Plotkin, A probabilistic powerdomains of evaluation, Proceedings of the 4th Annual IEEE Symposium on Logic in Computer Science, p.62, 1989.

A. Jung and R. Tix, The troublesome probabilistic powerdomain, Electr. Notes Theor. Comput. Sci, vol.13, p.63, 1998.

K. Keimel and G. D. Plotkin, Mixed powerdomains for probability and nondeterminism, Logical Methods in Computer Science, vol.13, issue.1

D. Kozen, Semantics of probabilistic programs, 20th Annual Symposium on Foundations of Computer Science, vol.62, p.63, 1979.

J. Laird, G. Manzonetto, G. Mccusker, and M. Pagani, Weighted relational models of typed lambda-calculi, 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013, p.100, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01144064

B. Mcmillan, Absolutely Monotone Functions, Annals of Mathematics, vol.60, issue.3, p.98, 1954.

P. Melliès, Categorical semantics of linear logic. Panoramas et Synthèses, vol.27, p.72, 2009.

E. Moggi, Computational lambda-calculus and monads, LICS, p.62, 1989.

P. Panangaden, PROBMIV'98, First International Workshop on Probabilistic Methods in Verification, Electronic Notes in Theoretical Computer Science, vol.22, p.106, 1999.

S. Park, F. Pfenning, and S. Thrun, A probabilistic language based on sampling functions, ACM Trans. Program. Lang. Syst, vol.31, issue.1, p.95, 2008.

A. M. Pitts, Computational adequacy via 'mixed' inductive definitions, Mathematical Foundations of Programming Semantics, vol.77, p.91, 1994.

G. Plotkin, A powerdomain construction, SIAM Journal of Computing, vol.5, issue.3, p.62, 1976.

G. Plotkin, LCF considered as a programming language, Theoretical Computer Science, vol.5, p.100, 1977.

M. Rennela, Convexity and order in probabilistic call-by-name FPC. CoRR, 2016.

J. C. Reynolds, On the relation between direct and continuation semantics, Lecture Notes in Comput. Sci, vol.14, p.76, 1974.

A. Scibior, O. Kammar, M. Vákár, S. Staton, H. Yang et al., Denotational validation of higher-order bayesian inference, PACMPL, vol.2, 2018.

P. Selinger, Towards a semantics for higher-order quantum computation, Proceedings of the 2nd International Workshop on Quantum Programming Languages, vol.33, p.97, 2004.

S. Staton, H. Yang, F. D. Wood, C. Heunen, and O. Kammar, Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints, LICS, vol.63, p.95, 2016.

A. Tarski, A lattice theoretical fixpoint theorem and its applications, Pacific J. Math, vol.5, p.77, 1955.

J. Vuillemin, Exact real computer arithmetic with continued fractions, Proceedings of the 1988 ACM Conference on LISP and Functional Programming, LFP '88, pp.14-27, 1988.
URL : https://hal.archives-ouvertes.fr/inria-00075792

F. D. Wood, J. Van-de-meent, and V. Mansinghka, A new approach to probabilistic programming inference, AISTATS, volume 33 of JMLR Workshop and Conference Proceedings, p.63, 2014.

, List of Figures 1

.. .. Protocol,

, The collapse of the chromatic subdivision complex for three processes, p.13

, Protocol complex with traces and interval orders of 2 processes, 2 rounds, p.25

. , Interval order complex with traces of 3 processes, 1 round

. Constructions and . .. Pcoh,

. , Definition of the reflexive object in Pcoh

. +. Syntax,

. .. Syntax-of-ppcf,

. .. Pcoh, , vol.87

. .. Syntax-of-prpcf,

.. .. Structure,

C. Relationship-between-pcoh and .. .. ,