V. Danos and R. Harmer. Probabilistic game semantics. ACM Trans. Comput. Log., 3(3):359--382, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... of observational equivalence for programming languages with a variety of features (purely functional call byname PCF [6, 64] PCF with control [78] call by value languages [8, 59] Idealized Algol with active [7] and passive expressions [9] nite non determinism [51] probabilistic languages [32], languages with local exceptions [79] The rst of these results solved a long standing open problem of nding a fully abstract semantics for PCF. In this chapter we apply game semantic techniques to light ane logic. The models possess the categorical structure described in Chapter 5 and will ....

V. Danos and R. Harmer. Probabilistic game semantics. In Proc. IEEE Symposium on Logic in Computer Science. Computer Science Society, 2000.

....languages and logical systems. It has been used to construct the first syntax independent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with non functional features such as control operators and locally scoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6] Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in ....

V. Danos and R. Harmer. Probabilistic game semantics. In Proc. IEEE Symposium on Logic in Computer Science, Santa Barbara, June,

....constructions that Girard performed in [Gir86] for qualitative domains and coherence spaces. 1 Or successively; the multiset can be interpreted (e.g. in the forthcoming example) as giving the different values taken by the argument during the computation. In the non deterministic game model of [DH00] the same information is made available, but moreover, the temporal scheduling (the order in which these values are taken) is specified. 2 This property is not only mathematically appealing, but it also plays a crucial technical role in many aspects of the theory of coherence space models (for ....

.... of the fixpoint operator in the co Kleisli category of the purely relational model of linear logic, which is a category (the order relation between morphisms being of course the inclusion) Our negative argument is based on a PCF term which has already been considered by Danos and Harmer in [DH00]. Using the least fixpoint operator, we construct f N ( N as follows: f = Y N(N )gn ( Case N )n)m 1 (g) m 1) 0 8 otherwise stated, f is defined recursively as f = n ifn = 0 then 0 else1 (f)n : Then f(k[1] 0] k) j k 2 Ng f and therefore f(f0; 1g ) N, whereas f0; 1g ....

Vincent Danos and Russell Harmer. Probabilistic game semantics. In Proceedings of the fifteenth Symposium on Logic in Computer Science. IEEE Computer Society Press, 2000.

.... have already been presented, by Girard [Gir99] and Blute [Blu96] in a setting considered rst by Barr in [Bar79, Bar90] Other semantics of typed lambda calculi with real coecients have been considered, among which we would like to mention in particular Danos and Harmer s probabilistic games [DH00], whose non deterministic character seems to be very much in the spirit of the model presented here. We propose a quite concrete approach based on a standard notion in the theory of locally convex topological vector spaces (lcs for short) the notion of K othe sequence spaces (see [K ot66] These ....

Vincent Danos and Russell Harmer. Probabilistic game semantics. In Proceedings of the fteenth Symposium on Logic in Computer Science. IEEE Computer Society Press, 2000.

.... 9) # V :# Prob(M, V ) #) #(V ) # V :# Prob(M, V ) V ] #) An adequacy theorem for FPC with probabilistic choice was already proved in [13] FPC can be viewed as an extension of our PCF with recursive types) for work on call by name and probabilistic nondeterminism see [6]. 7 Conclusions It is interesting to work out other examples. Printing provides one example, where one has a unary operation print a for each symbol a of an alphabet A, and for Set one can take the (non commutative) monad T (X) A # X, which is, in fact, the free # algebra over X; for Dcpo one ....

V. Danos and R. Harmer, Probabilistic Game Semantics, in Proc. 15th LICS, pp. 204--213, Washington: IEEE Press, 2000.

....language. We then present an appropriate de nition of probabilistic non interference for this language. Section 4 presents the three stages of our analysis and we conclude with the statement of correctness. 2 Probabilistic Algol In this paper, we consider a Probabilistic Idealised Algol (PA) [1]. Idealized Algol is a language developed by Reynolds [5] which extends the simply typed calculus with imperative features. The result is a prototype language combining block structured imperative programming and elements of higher order functional programming. The basic phrase types of PA are ....

V. Danos and R. Harmer. Probabilistic game semantics. In Proc. the Thirteenth Annual IEEE Symposium on on Logic in Computer Science. IEEE Computer Society Press, 2000. To appear.

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V. Danos and R. Harmer. Probabilistic game semantics. ACM Trans. Comput. Log., 3(3):359--382, 2002.

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V. Danos and R. Harmer, Probabilistic Game Semantics, in Proc. 15th LICS, pp. 204--213, Washington: IEEE Press, 2000.

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