Coalgebraic Methods in Computer Science: 12th IFIP WG 1.3 by Marcello M. Bonsangue (eds.)

By Marcello M. Bonsangue (eds.)

This ebook constitutes the completely refereed post-proceedings of the twelfth overseas Workshop on Coalgebraic tools in desktop technology, CMCS 2014, colocated with ETAPS 2014, held in Grenoble, France, in April 2014. the ten revised complete papers have been rigorously reviewed and chosen from 20 submissions. additionally integrated are 3 invited talks. The papers conceal a variety of themes within the conception, logics and functions of coalgebras.

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Additional info for Coalgebraic Methods in Computer Science: 12th IFIP WG 1.3 International Workshop, CMCS 2014, Colocated with ETAPS 2014, Grenoble, France, April 5-6, 2014, Revised Selected Papers

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Pp. 237–246. IEEE Computer Society (2011) 13. : Generic trace semantics via coinduction. Log. Methods Comput. Sci. 3(4:11), 1–36 (2007) 14. : An axiomatic basis for computer programming. Commun. ACM, 12, 576–580, 583 (1969) 15. : Categorical Logic and Type Theory. North Holland, Amsterdam (1999) 16. : New directions in categorical logic, for classical, probabilistic and quantum logic. 3940 17. : Measurable spaces and their effect logic. In: LICS. pp. 83–92. IEEE Computer Society (2013) 18. : Probabilistic non-determinism.

N , Xn ) ∈ X} · – (MA , g, id ) is a λ-bialgebra for λ : GF → F G distributive law defined by λA : (MnA × P<κ (MA × A)) → P<κ (MA × n≥1 (MnA × A)) n≥1 λA (X1 , . . , Xn+1 ) = {(α1 + . . + αk ,X1 , . . , Xn+1 ) | k ≥ 1 & α1 , Xi1 ∈ Xi1 , . . , αk , Xik ∈ Xik & 1 ≤ i1 , . . , ik ≤ n & ∀j ∈ {1, . . , n} \ {i1 , . . , ik }. Xj = Xj } . 3 Operations on Polarized Multigames Notice that polarized multigames are not closed under the operations defined above. However, one can define corresponding sums and linear implications on polarized multigames, simply by “pruning” the graphs of the resulting multigames.

D, 1, τtotal , Cv, ρinf ) thus obtained is a 2-player PT situation. The resulting logic PK (τtotal , ρinf ) is as follows. Given a postcondition q : Y → D1 and a computation f : X → U DCvF DY , the weakest precondition is PK (τtotal , ρinf )(f )(q)(x) = inf y∈Y d(y) · q(y) d ∈ f (x) . (20) Here d is a subdistribution chosen by Opponent; and the value y∈Y d(y)·q(y) is the expected value of the random variable q under the distribution d. Therefore the weakest precondition computed above is the least expected value of q when Opponent picks a distribution in harm’s way.

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