By Pierre-Louis Curien (auth.), G Q Zhang, J. Lawson, Y.-M. Liu, M.-K. Luo (eds.)
Domains are mathematical constructions for info and approximation; they mix order-theoretic, logical, and topological rules and supply a common framework for modelling and reasoning approximately computation. the idea of domain names has proved to be a great tool for programming languages and different parts of machine technological know-how, and for purposes in arithmetic.
Included during this court cases quantity are chosen papers of unique learn offered on the second overseas Symposium on area conception in Chengdu, China. With authors from France, Germany, nice Britain, eire, Mexico, and China, the papers hide the most recent examine in those sub-areas: domain names and computation, topology and convergence, domain names, lattices, and continuity, and representations of domain names as occasion and logical constructions.
Researchers and scholars in theoretical computing device technological know-how may still locate this a useful resource of reference. The survey papers before everything will be of specific curiosity to those that desire to achieve an realizing of a few normal rules and strategies during this area.
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Extra info for Domain Theory, Logic and Computation: Proceedings of the 2nd International Symposium on Domain Theory, Sichuan, China, October 2001
In fact, it turns out that there is a mathematically natural class of sequentially computable functionals with many attractive properties. These are known in [Lo02] as the (eﬀective) sequentially realizable (or SR) functionals, and are closely akin to the strongly stable functionals of Bucciarelli and Ehrhard [BE91]. One of the main results of [Lo02] is that in the category constituted by the SR functionals, the object [N N⊥N → N⊥ ] is universal. Since this object is the denotation of the call-by-value type (nat → nat) → nat (call this type 2), we may state this fact as follows: for any call-byvalue type σ, its denotation [[ σ ]] in the category of SR functionals is a retract of [[ 2 ]].
PCF with parallel functions We now consider the well known extension of PCF with “parallel” computable functionals discovered by Plotkin [Pl77] and Sazonov [Sa76]. Here it suits our purposes to work with the call-by-value version. n for n = 0, 1, . t). It is well known that a fully abstract and complete model for PCF++ is provided by the category of eﬀective Scott domains and computable maps (see [Pl77]), or indeed by its full subcategory Coh eﬀ of eﬀective coherent domains. It is also known that the object T ω = 2N ⊥ is a universal object in this category, and indeed that Coh eﬀ is equivalent to the 43 Universal types Karoubi envelope of the corresponding λ-algebra T ωeﬀ (see [Pl78]).
2 For one or more types σ (called program types), a set of special closed terms V : σ called values, an evaluation relation M ⇒ V between closed terms and values, and a function Obs σ mapping values V : σ to some set Oσ of observations. ) 3 A category C with ﬁnite products. 4 An interpretation [[ − ]] of L in C, assigning to each type σ an object σ; to each environment Γ = (x1 : σ1 , . . , xn : σn ) the object [[ Γ ]] = [[ σ1 ]]×· · ·×[[ σn ]] ; and to each typing judgement Γ M : σ a morphism [[ M ]]Γ : [[ Γ ]] → [[ σ ]].
Domain Theory, Logic and Computation: Proceedings of the 2nd International Symposium on Domain Theory, Sichuan, China, October 2001 by Pierre-Louis Curien (auth.), G Q Zhang, J. Lawson, Y.-M. Liu, M.-K. Luo (eds.)