A. D. Ker, H. Nickau, and C.-H. L. Ong. A universal innocent game model of the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL, Madrid, Spain, September  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in general, a monotone strategy cannot be approximated by a chain of nite and monotone strategies. This shortage of nite strategies is necessary in order to have a full de nability result. In game semantics the interpretation of a solvable term is always an in nite object. In [KNO00,KNO99] the semantic interpretations of terms are characterised as almost everywhere copy cat strategies. On the game models we are going to construct, the condition of monotonicity essentially forces the behaviour of strategies to be almost everywhere copy cat strategies. The equivalence relation ....

A. D. Ker, H. Nickau, and C. H. L. Ong. A universal innocent game model for the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL Madrid, Spain, volume 1683 of Lecture Notes in Computer Science, pages 405-419. Springer, September 1999.

....necessary to model di erent theories. This appears to be rather problematic, since we feel that head reduction is intrinsic to games for which we can observe only interactions with the environment. This hypothesis seems to be con rmed also by the recent results presented in the related works [KNO00,KNO99], in the slight di erent game semantics paradigm of Hyland and Ong [HO00] There, two particular games models are built and it is proved, using techniques quite di erent from ours, that the two models induce respectively the theories H and B. The present paper is organized as follows. In ....

A. D. Ker, H. Nickau, and C. H. L. Ong. A universal innocent game model for the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL Madrid, Spain, volume 1683 of Lecture Notes in Computer Science, pages 405-419. Springer-Verlag, September 1999.

....They show that all their models induce the same theory H and have asked for new techniques for overcoming this apparent rigidity of game models . This paper answers that question by constructing a universal game model for the B ohm tree theory. An extended abstract of this work [KNO99] (in which the model DXA was called M) was presented at the European Association for Computer Science Logic conference in Madrid, in September 1999. The work presented in this paper was undertaken as part of the rst named author s EPSRC funded doctoral research (the results appear in [Ker01] 3 ....

A. D. Ker, H. Nickau, and C.-H. L. Ong. A universal innocent game model of the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL, Madrid, Spain, September

....for composition Unfortunately regular strategies cannot be composed. This section is concerned with a notion of strategies that are good for composition. Good strategies are generated from regular ones by a process of copycat expansion, which is essentially a semantic form of expansion [8, 10]. We shall see that good strategies compose by the standard mechanism of parallel composition with hiding [2] De nition 5 (Good strategies) Take a regular strategy = f;F . The good strategy generated from , written , is de ned by the following algorithm: Suppose the odd length position ....

Ker, A. D., Nickau, H., Ong, C.-H. L.: A universal innocent game model for the Bohm tree lambda theory. In Proceedings of the 8th Annual Conference on the EACSL, Madrid, Spain, September

....copycat strategies, at every sequence where the composite strategy is de ned. The algorithm and the proof, which take some six pages when written out in full, are very technical, and some care is needed in the case analysis. As this paper has a sequel [13] an extended abstract appears as [12]) in which we develop the idea of almost everywhere copycat strategies in more depth, to obtain a universal model for the B ohm tree theory, it seems to us more sensible to present the material there as part of a systematic account. A full version of the proof can also be found in the rst ....

....to the structure, in particular using di erent objects. One consequence is that there is not an object U with U = U ) U , which one would hope for in the light of the comments below) The details of this construction are to presented in a sequel, 13] of which an extended abstract appears as [12]. This makes a ner distinction between strategies, because given a threshold at a P view of an EAC strategy it is still valid to claim any higher threshold. In terms of terms this is because for any term s [ s] x:sx] for fresh x. So two strategies which have the same moves may be di erent ....

A. Ker, H. Nickau, and C.-H. L. Ong. A universal innocent game model of the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL, Madrid, Spain, September 1999, number 1683 in Lecture Notes in Computer Science, pages 405-419. Springer-Verlag, 1999.

....for composition Unfortunately regular strategies cannot be composed. This section is concerned with a notion of strategies that are good for composition. Good strategies are generated from regular ones by a process of copycat expansion, which is essentially a semantic form of expansion [8, 10]. We shall see that good strategies compose by the standard mechanism of parallel composition with hiding [2] De nition 5 (Good strategies) Take a regular strategy = f;F . The good strategy generated from , written , is de ned by the following algorithm: Suppose the odd length position ....

A. D. Ker, H. Nickau, and C.-H. L. Ong. A universal innocent game model for the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference on the EACSL Madrid, Spain, September 1999, pages 405 {

....copycat strategies, at every sequence where the composite strategy is de ned. The algorithm and the proof, which take some six pages when written out in full, are very technical, and some care is needed in the case analysis. As this paper has a sequel [KNO99b] an extended abstract appears as [KNO99a]) in which we develop the idea of almost everywhere copycat strategies in more depth, to obtain a universal model for the B ohm tree theory, it seems to us more sensible to present the material there as part of a systematic account. A full version of the proof can also be found in the rst ....

....to the structure, in particular using di erent objects. One consequence is that there is not an object U with U = U ) U , which one would hope for in the light of the comments below) The details of this construction are to presented in a sequel, KNO99b] of which an extended abstract appears as [KNO99a]. This makes a ner distinction between strategies, because given a threshold at a P view of an EAC strategy it is still valid to claim any higher threshold. In terms of terms this is because for any term s [ s] x:sx] for fresh x. So two strategies which have the same moves may be di erent ....

A. Ker, H. Nickau, and C.-H. L. Ong. A universal innocent game model of the Bohm tree lambda theory. In Computer Science Logic: Proceedings of the 8th Annual Conference of the EACSL, Madrid, Spain, September 1999, number 1683 in Lecture Notes in Computer Science, pages 405-419. Springer-Verlag, 1999.

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