A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des Sciences Mathematiques du Quebec, Vol I, no 4, pp.46-52, 1977.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a number of researchers have recently examined categories of games, or at least categories with some game theoretic flavour, it seems worthwhile to make some explicit comparisons. 6. 1 Conway games As far as we know, the first person to make a category of games and winning strategies was Joyal [Joy77]. His category was based on Conway games [Con76] with Conway s addition of games as the tensor product. Conway s formalization of games differs from ours in that he presents the tree of positions directly, rather than via an underlying set of moves. This means that strategies must be formalized as ....

....of this, we have the following Proposition. Proposition 17 Let C be the category of Conway games, with our definition of tensor product, and the consequent notion of morphism from A to B as a winning strategy in A GammaffiB = So, in particular, this is not the category studied by Joyal [Joy77]. G is a full subcategory of C. If A is a Conway game, let A be the game in G obtained by deleting all non strictly alternating sequences in PA (and correspondingly pruning WA ) Then A in C; so G C. Moreover, B) alt Omega . The upshot of this Proposition is that, once our ....

A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des sciences mathematiques du Quebec, 1(4), 1977.

....fully abstract model. PCF is a higher order functional programming language that essentially is a fragment of any programming language with higher order procedures (for instance any expressive enough object oriented programming language) Precursors to these game theoretical models can be seen in [Jo77], where for the first time a category of games is defined, and in the work of Kleene on recursive functionals, and of Berry and Curien on sequential algorithms in [BeCu82] In another line of research, game semantical methods have so far had a number of other applications, including in [AbrJag94] ....

A. Joyal, Remarques sur la theorie des jeux a deux personnes, Gazette des sciences mathematiques du Quebec 1,4 (1977), p. ???

....in the 1950 s [Lor60] The basic idea is to interpret a formula as a two person game (played between the Proponent asserting the thesis, and the Opponent seeking to refute it) and a proof of the formula as a winning strategy for Proponent. Significant further contributions were made by Joyal [Joy77], who organized Conway s games into a category, and by Blass [Bla93] who gave a game semantics for Girard s Linear Logic. 1 In joint work with Radha Jagadeesan in 1992 [AJ92] a number of key ideas were introduced: ffl A dictionary between the concepts of game semantics, and those of process ....

A. Joyal. Remarques sur la th'eorie des jeux a deux personnes. Gazette des sci. math. du Quebec, 1,4 1977.

....is a proof net. By (2) this implies that the proof structure ( Gamma; OE oe ) is in fact a proof net. 5 Further Directions Extension to Infinite Games [Preliminary calculations suggest that the obvious extension of the definition works ] Big gaps here. Related Work Old work: Con76] [Joy77], Hyl90] LS91] Lamarche: Lam93] Concrete Data Structure and Sequential Algorithms: Cur93] Acknowledgements We would like to thank members of the Cambridge Imperial Joint Seminars on Game Semantics for helpful discussions. ....

A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des Sciences Mathematiques du Quebec, 1(4), 1977.

....a number of researchers have recently examined categories of games, or at least categories with some game theoretic flavour, it seems worthwhile to make some explicit comparisons. 6. 1 Conway games As far as we know, the first person to make a category of games and winning strategies was Joyal [Joy77]. His category was based on Conway games [Con76] with Conway s addition of games as the tensor product. Conway s formalization of games differs from ours in that he presents the tree of positions directly, rather than via an underlying set of moves. This means that strategies must be formalized as ....

....the following Proposition. Proposition 17 Let C be the category of Conway games, with our definition of tensor product, and the consequent notion of morphism from A to B as a winning strategy in A GammaffiB = A Omega B ) So, in particular, this is not the category studied by Joyal [Joy77]. G is a full subcategory of C. If A is a Conway game, let A alt be the game in G obtained by deleting all non strictly alternating sequences in PA (and correspondingly pruning WA ) Then A = A alt in C; so G C. Moreover, A Omega B) alt = A alt Omega B alt . The upshot of ....

A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des sciences mathematiques du Quebec, 1(4), 1977.

....a number of researchers have recently examined categories of games, or at least categories with some game theoretic flavour, it seems worthwhile to make some explicit comparisons. 6. 1 Conway games As far as we know, the first person to make a category of games and winning strategies was Joyal [Joy77]. His category was based on Conway games [Con76] with Conway s addition of games as the tensor product. Conway s formalization of games differs from ours in that he presents the tree of positions directly, rather than via an underlying set of moves. This means that strategies must be formalized as ....

....the following Proposition. Proposition 17 Let C be the category of Conway games, with our definition of tensor product, and the consequent notion of morphism from A to B as a winning strategy in A GammaffiB = A Omega B ) So, in particular, this is not the category studied by Joyal [Joy77]. G is a full subcategory of C. If A is a Conway game, let A alt be the game in G obtained by deleting all non strictly alternating sequences in PA (and correspondingly pruning WA ) Then A = A alt in C; so G C. Moreover, A Omega B) alt = A alt Omega B alt . The upshot of ....

A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des sciences mathematiques du Quebec, 1(4), 1977.

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A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des Sciences Mathematiques du Quebec, Vol I, no 4, pp.46-52, 1977.

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A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des Sciences Mathematiques du Quebec, Vol I, no 4, pp.46-52, 1977. 51

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A. Joyal. Remarques sur la theorie des jeux a deux personnes. Gazette des Sciences Mathematiques du Quebec, Vol I, no 4, pp.46-52, 1977.

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A. Joyal, Remarques sur la theorie des jeux a deux personnes, Gazette des sciences mathematiques du Quebec 1,4 (1977), p. ???

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