Sands, D.: Improvement Theory and Its Applications, in: Higher Order Operational Techniques in Semantics (A. Gordon, A. Pitts, Eds.), Cambridge University Press, 1998, 275--306.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....not immediate how to ex tend any of these methods to the fair non determinism exhibited by McCarthy s amb. Here we extend these methods by using an alternative to Howe s relational construction (from [9] and by introducing costs (following Sands improvement theory for deterministic languages [18]) The unique fixed point induction rule is adapted from [18] Our adaption inspired a similar rule in [15] where it is used in an extensive treatment of a theory for erratic choice (that respects sharing) for the Fudgets stream processor calculus. This paper reports on results from the ....

....non determinism exhibited by McCarthy s amb. Here we extend these methods by using an alternative to Howe s relational construction (from [9] and by introducing costs (following Sands improvement theory for deterministic languages [18] The unique fixed point induction rule is adapted from [18]. Our adaption inspired a similar rule in [15] where it is used in an extensive treatment of a theory for erratic choice (that respects sharing) for the Fudgets stream processor calculus. This paper reports on results from the authors dissertations [10, 13] Mostly, proofs are sketched or ....

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D. Sands. Improvement theory and its applications. In Gordon and Pitts [6], pages 275--306.

....M has been slowed down by k ticks. As an example of a cost equivalence involving the tick, we have the following: x:M) y : 2X M [ y = x ] Now we are in a position to state the unique xed point induction principle, which is a variation on the proof rule of improvement up to context [San98] and Lassen and Moran s cost equivalence induction [LM98,Mor98] Theorem 1 (Unique Fixed Point Induction) For any M , N , C, and substitution , the following proof rule is sound: M : X C[M ] N : X C[N ] M : N The proof is given in appendix . It may seem at rst sight ....

D. Sands, Improvement theory and its applications, In Gordon and Pitts

....has been slowed down by k ticks. As an example of a cost equivalence involving the tick, we have the following: x:M) y : 2X M [ y = x ] Now we are in a position to state the unique xed point induction principle, which is a variation on the proof rule of improvement up to context [San98b] and Lassen and Moran s cost equivalence induction [LM99,Mor98] Theorem 6 (Unique Fixed Point Induction) For any M , N , C, and substitution , the following proof rule is sound: M : X C[M ] N : X C[N ] M : N The proof is given in section 6. It may seem at rst sight that cost ....

D. Sands, Improvement theory and its applications, In Gordon and Pitts

....has been slowed down by k ticks. As an example of a cost equivalence involving the tick, we have the following: x:M) y : 2X M [ y = x ] fi) Now we are in a position to state the unique fixed point induction principle, which is a variation on the proof rule of improvement up to context [San98b] and Lassen and Moran s cost equivalence induction [LM98,Mor98] Theorem 1 (Unique Fixed Point Induction) For any M , N , C, and substitution oe, the following proof rule is sound: M : X C[M oe] N : X C[N oe] M : N The proof is given in appendix B. It may seem at first sight ....

D. Sands, Improvement theory and its applications, In Gordon and Pitts

....completeness are somewhat diOEcult to establish, although for the special case of operational approximation completeness amounts to showing that there are suOEciently many idestructorsj for each constructor see [How96] for a precise formulation. Bisimulation upto Improvement and Context In [San97] we described a bisimulation like proof technique for equivalence based on the Improvement Theorem of [San96b] with something of the AEavour of Sangiorgi s ibisimulation up to context and up to expansionj for the pi calculus [San95b, San94] where iexpansionj is analogous to an improvement ....

....with something of the AEavour of Sangiorgi s ibisimulation up to context and up to expansionj for the pi calculus [San95b, San94] where iexpansionj is analogous to an improvement relation based on the number of silent transitions a process can perform. It seems that a similar development to [San97] can be carried out in the setting of a well founded gdsos, and roughly speaking, amounts to generalising the improvement induction principle from a pair of expressions to a possibly in nite set of pairs. Such a development would put improvement induction on a bisimulation like footing, but we ....

D. Sands. Improvement theory and its applications. In A. Gordon and A. Pitts, editors, Higher-Order operational Techniques in Semantics. Cambridge University Press, 1997. (to appear).

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Sands, D.: Improvement Theory and Its Applications, in: Higher Order Operational Techniques in Semantics (A. Gordon, A. Pitts, Eds.), Cambridge University Press, 1998, 275--306.

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D. Sands. Improvement theory and its applications. In A. D. Gordon and A. M. Pitts, editors, Higher Order Operational Techniques in Semantics, Publications of the Newton Institute, pages 275--306. Cambridge University Press, 1998.

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