H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Ph.D. Thesis, Siegen University, Aachen: Shaker Verlag, 1996.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....linear logic was given in [Lam94] while the ones in [LafStr91] or [Mey94] the latter for predicate logic without contractions) are not intensional. Subsequently this lead in 1993 to the development of intensional game theoretical models in the semantics of programming languages independently by [AbrJagMal94, HylOng1, Ni96]. These models proved to be very useful and provided e.g. a solution for the probably best known open problem in the semantics of programming languages, the Full Abstractness Problem for the programming language PCF [Pl77] by giving the first syntaxindependent fully abstract model. PCF is a ....

H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Dissertation, Universitat Gesamthochschule Siegen, 1996

.... We can give continuation semantics for CBPV, and recover the CBV semantics of [26, 5] and the CBN semantics of [14, 37] NB not that of [26] which is not strictly speaking CBN, as it does not validate the j law) We can give game semantics for CBPV, and recover the CBN game semantics of [11, 23] and the CBV game semantics of [2, 10] We can give an equational theory for CBPV. The equations that this gives us for CBN include the fi and j laws for functions, which generally fail in CBV. The equations that we obtain for CBV include for example Gamma; x : bool M = if x then M ....

Hanno Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen.

....rise to the fully abstract model is known as the full abstraction problem. The aim is to find a presentation of the fully abstract model that is, as far as possible, presented in a manner that is both concrete and independent of syntax. Recently, several solutions to this problem have been given [1, 4, 10, 11]. However, the problem as posed is not precisely defined; there is no clear mathematical definition of what separates Milner s syntactical construction from the more semantical constructions that the full abstraction problem asks for. In particular, it is not entirely clear in what sense, if any, ....

Hanno Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Doctoral Dissertation. Shaker Verlag, 1996.

....and PCF, respectively. They have natural submodels C o and S o consisting of those elements definable in, respectively, PCF and PCF; equivalently, these are the submodels of the effective elements. Instead of Milner s model we might have used (the extensional collapse of) the games model [AJM95, HO94, Nic96]. There is little to choose between the two; Milner s model is, perhaps, a little more convenient as it is known to be cpo enriched; the more pressing issue here is to settle the well known open question as to whether the collapse of the games model is cpo enriched if so, it is isomorphic to ....

H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Ph.D. Thesis, Siegen University, Aachen: Shaker Verlag, 1996.

.... CBPV, and recover the CBV semantics of [26, 5] and the CBN semantics of [15, 37] NB not that of [26] which is not strictly speaking CBN, as it does not validate the j law) Call By Push Value: A Subsuming Paradigm 3 We can give game semantics for CBPV, and recover the CBN game semantics of [12, 23] and the CBV game semantics of [2, 11] We can give an equational theory for CBPV. The equations that this gives us for CBN include the fi and j laws for functions, which generally fail in CBV. The equations that we obtain for CBV include for example Gamma; x : bool M = if x then M ....

H. Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen.

....collapsing certain sets of strategies. There have been two proposals: the first one is based on the idea of history free strategies [1] according to the second one players move depending on views of the play: let us call view games and view strategies games and strategies as defined in [5, 6]. In [4] a different notion of game, originally introduced by Novikoff, is used to give an intuitionistic explanation of the classical notion of truth. As it will be apparent from sections 2 and 3 of the present paper, view games are a particular case of Novikoff Coquand games: the former can be ....

....2 To the time moves are meaningless so that we forget about their actual form. We defer to section 3 and to example 3.3 the explanation about their interpretation. U cut free (pre) plays is the terminology of [4] If a pre play has finite length then the previous definition is a generalization of [6], definition 3.1.3. Observe that in a U cut free pre play, U is the unique player allowed to play at limit points. Because of the finite depth of R and clauses (P 3) P 4) for all length(p) there exists a (unique) n such that r n ( 0. It follows that turn is redundant (but useful in ....

[Article contains additional citation context not shown here]

H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Shaker Verlag, Achen 1996.

....by extensionally collapsing certain sets of strategies. There have been two proposals: the first one is based on the idea of history free strategies [3] according to the second one players move depending on views of the play: these are called dialog games and innocent strategies, as defined in [10, 11]. In [7] an apparently different notion of game, originally introduced by Novikoff, is used to give an intuitionistic explanation of the classical notion of truth. As it will be explained in sections 2 and 3 of the present paper, dialog games and Novikoff Coquand games are closely related: the ....

....of view strategies (called innocent in [10] having a simple inductive definition: view(U; p; i) ae fi Gamma 1g [ view(U; p; i Gamma 1) if turn(i) U fr(i)g [ view(U; p; r(i) if turn(i) 6= U . This is the standard notion of visibility in dialog games: it is defined in this way both in [10, 11] and in [7] the case of plays of possibly transfinite length has been considered for the first time in [5] from which we borrow the axiomatic definition of Vis. Definition above does not tell, explicitly, who is the player on turn at a limit point 2 I, nor his views. The main theorem 4, ....

[Article contains additional citation context not shown here]

H. Nickau, Hereditarily Sequential Functionals: A Game- Theoretic Approach to Sequentiality, Shaker Verlag, Achen 1996.

.... We aim to construct a universal model (i.e. every element of the model is the denotation of some term) of the pure untyped calculus which induces the B ohm tree theory B, by building on the game models presented in [KNO01] Although the general approach is innocent in the sense of [HO00] and [Nic96], the two player games we use are simpler and can be considered a special case where moves are neither questions nor answers but simply declarations . A notable feature of game semantics is that the de nable strategies are e ective methods for copying moves uniformly from one component of the ....

.... s is said to be well formed if it satis es the following properties 2 : Alternation: Elements of s alternate between P moves and O moves. Justi cation: If m is justi ed by m then the move m is directly beneath m in the tree of the arena. 2 The no dangling question mark condition in [HO00, Nic96] (equivalently the well bracketing condition) is redundant for our arenas. 5 Henceforth all justi ed sequences are assumed to be well formed. The P view of a justi ed sequence s, written p s q , is given recursively by: p q = for initial moves p s m q = p s q m for m a P move p ....

Hanno Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen. 40

....Hanno Nickau and C. H. Luke Ong Oxford University Computing Laboratory, Parks Road, Oxford. OX1 3QD Abstract We present a new denotational model for the untyped calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [9] and Nickau [17], but the traditional distinction between question and answer moves is removed. We rst construct models D and DREC as global sections of a re exive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible ....

....that a player may not take into account any irrelevant preceding moves. Furthermore, strategies may be composed , if they are strategies for arenas of appropriate type. All of these de nitions are standard. Another familiar idea is that of an innocent function, which is the presentation used in [17]. Instead of considering a strategy to be the set of all possible sequences of moves, we de ne a function telling a player how to react in every possible situation. Innocent strategies work particularly simply in this form because we de ne the function to map from views to (justi ed) moves and no ....

[Article contains additional citation context not shown here]

H. Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen. Shaker-Verlag, 1996. 54

....Computing Laboratory, Parks Road, Oxford. OX1 3QD November 1998, revised September 1999 Abstract We present a new denotational model for the untyped calculus, using the techniques of game semantics. The strategies used are innocent in the sense of Hyland and Ong [HO94] and Nickau [Nic96], but the traditional distinction between question and answer moves is removed. We rst construct models D and DREC as global sections of a re exive object in the categories A and A REC of arenas and innocent and recursive innocent strategies respectively. We show that these are sensible ....

....that a player may not take into account any irrelevant preceding moves. Furthermore, strategies may be composed , if they are strategies for arenas of appropriate type. All of these de nitions are standard. Another familiar idea is that of an innocent function, which is the presentation used in [Nic96]. Instead of considering a strategy to be the set of all possible sequences of moves, we de ne a function telling a player how to react in every possible situation. Innocent strategies work particularly simply in this form because we de ne the function to map from views to (justi ed) moves and no ....

[Article contains additional citation context not shown here]

H. Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen. Shaker-Verlag, 1996.

....z Oxford University Computing Laboratory, Parks Road, Oxford. OX1 3QD November 1998 Abstract This paper is a detailed description of the application of games to the construction of models of pure untyped calculus. The strategies used are innocent in the sense of Hyland and Ong [HO94] and Nickau [Nic96]. The games used, however, are made up solely of declarations, and there is no sense of question and answer. We first construct models D and DREC as global sections of a reflexive object in the categories A I and A I REC of arenas and innocent and recursive innocent strategies respectively. We ....

....that a player may not take into account any irrelevant preceeding moves. Furthermore, strategies may be composed , if they are strategies for arenas of appropriate type. All of these definitions are standard. Another familiar idea is that of an innocent function, which is the presentation used in [Nic96]. Instead of considering a strategy to be the set of all possible sequences of moves, we define a function telling a player how to react in every possible situation. Innocent strategies work particularly simply in this form because we define the function to map from views to (justified) moves and ....

[Article contains additional citation context not shown here]

Hanno Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen.

.... We aim to construct a universal model (i.e. every element of the model is the denotation of some term) of the pure untyped calculus which induces the Bohm tree theory B, by building on the game models presented in [KNO98] Although the general approach is innocent in the sense of [HO94] and [Nic96], the two player games we use are simpler and can be considered a special case where moves are neither questions nor answers but simply declarations . A notable feature of game semantics is that the definable strategies are effective methods for copying moves uniformly from one component of ....

....p s q = p t q ) t Delta m 2 oe and the moves m are justified by moves which are identical in the P view p s q = p t q . i.e. P s next move, and its justification, at each stage depends only on the P view up to that point. An 1 The no dangling question mark condition in [HO94, Nic96] (equivalently the well bracketing condition) is redundant for our arenas. important fact is that composition of innocent strategies is well defined (for a proof see [HO94, x5.3] if oe is an innocent strategy on A ) B and an innocent strategy on B ) C then oe; is an innocent strategy on ....

Hanno Nickau. Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality. Shaker-Verlag, 1996. Dissertation, Universitat Gesamthochschule Siegen.

No context found.

H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Ph.D. Thesis, Siegen University, Aachen: Shaker Verlag, 1996.

No context found.

H. Nickau, Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality, Dissertation, Universitat Gesamthochschule Siegen, 1996

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC