W.K.-S. Phoa. Building domains from graph models. Math. Struct. in Comp. Sci., 2:277-299, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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Computational Adequacy for Recursive Types in Models of.. - Simpson (2002) (Correct)
.... cpos [3] More generally, axiomatic domain theory has successfully abstracted the particularities of domains to provide a host of neo classical models [3, 6] A very di erent type of model is given by game theoretic semantics [25] Finally, there are a variety of models based on realizability [11, 28, 29, 30, 21, 22, 35]. What has been missing hitherto is a single unifying treatment accounting for the existence of all these types of model. In this paper, we provide the axiomatic basis for such a treatment. In a follow up paper [44] we shall demonstrate how the various types of model are incorporated within our ....
....by Proposition 14.3, because it holds that the numerals RC(A) 1;N) Mod(A) 1;N) are standard. Thus, by Theorem 2, the interpretation of FPC in Mod(A) is computationally adequate. This gives the rst proof of computational adequacy for an interpretation of FPC in the realizability models of [11, 28, 29, 30, 21, 22]. 15.2 Models of axiomatic domain theory In [3, Def. 8.3.1] an axiomatization of a general categorical notion of model for FPC is given. Moreover, as Theorem 9.2.19 of op. cit. computational adequacy is proved for any nontrivial model satisfying two further conditions: i) the model is ....
W.K.-S. Phoa. Building domains from graph models. Math. Struct. in Comp. Sci., 2:277-299, 1992.
Computational Adequacy for Recursive Types in Models of.. - Simpson (2002) (Correct)
.... a host of neo classical models [2, 4] A quite different type of model is given by gametheoretic semantics [18] Finally, while the structure has not previously been exhibited in the form above, it has long been known that there should be a variety of models based on realizability semantics [9, 20, 21, 22, 17]. What has been missing hitherto is a single unifying treatment accounting for the existence of all these types of model. In this paper, we provide such a treatment. In [28] Dana Scott observed that categories of domains can live as full subcategories of models of intuitionistic set theory. We ....
....models, such as the category of #cpos, and their generalizations [2, 4] all embed in Grothendieck toposes [3, 5] and hence, by [15, Ch. IV] in categories with class structure. Moreover, under mild conditions, Axiom N is satisfied. Also, by their very definition, realizability models [9, 20, 21, 22, 16, 17] embed in realizability toposes [10, 12] and hence in categories with class structure [15, Ch. IV] Again, Axiom N is satisfied. Thus, Theorem 1 gives an account of the construction of solutions to recursive domain equations that applies simultaneously to domain theoretic and to realizability ....
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W.K.-S. Phoa. Building domains from graph models. Math. Struct. in Comp. Sci., 2:277--299, 1992.
A Uniform Approach to Domain Theory in Realizability Models - Longley, Simpson (1996) (5 citations) (Correct)
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W.K.-S. Phoa. Building domains from graph models. Math. Structures in Computer Science, 2, 1992.
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