W.K.-S. Phoa. E ective domains and intrinsic structure. In Proc. 5th IEEE Symposium on Logic in Computer Science, pages 366-377, 1990. 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 ....
....argument using classical logic, cannot be full subcategories of the category of sets. In [38] Dana Scott showed that such categories can nonetheless live as full subcategories of models of intuitionistic set theory, an observation that led to the subsequent development of synthetic domain theory [36, 14, 28, 46, 22, 40, 35, 27, 7]. In this paper, we exploit this idea to obtain algebraically compact categories in a uniform way. Roughly speaking, we start o with a category S of intuitionistic sets that satis es one simple axiom, Axiom 1 of Section 2. From any such category S, we extract a full subcategory of predomains, ....
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W.K.-S. Phoa. E ective domains and intrinsic structure. In Proc. 5th IEEE Symposium on Logic in Computer Science, pages 366-377, 1990.
Solving Recursive Domain Equations in Models of Intuitionistic.. - Simpson (2001) (Correct)
....of predomains within realizability models [15, 17] arise as full subcategories of realizability toposes [8, 10] Thus, one maintains generality by asking for categories of predomains to come embedded within elementary toposes. At this point, one can use the techniques of synthetic domain theory [21, 20, 9, 18, 26, 23, 17], in which (pre)domains are viewed as special sets within an intuitionistic set theory (for example, the internal logic of a topos) Dana Scott originally proposed synthetic domain theory as a possible framework for developing a nave set theoretic approach to reasoning about domains [21] Here, ....
W.K.-S. Phoa. E#ective domains and intrinsic structure. In Proceedings of 5th Annual Symposium on Logic in Computer Science, 1990.
Geometric And Higher Order Logic In Terms Of Abstract Stone Duality - Taylor (2000) (Correct)
....M of supports, each class possibly being classi ed by some object M . 2.13. Remark. Many of the ideas in this paper evolved from synthetic domain theory, a model of which is a topos (with a classi er for all monos) that also has a classi er for recursively enumerable subsets [Ros86, Pho90a, Pho90b, Hyl91, Tay91, FR97, BR98] In this case, is a subsemilattice of Such models exist wherein the full subcategory of replete objects satis es the monadicity property discussed in this paper for , in addition to that for the whole category for [RT97] A distilled account of repleteness and ....
Wesley Phoa. E ective domains and intrinsic structure. In Logic in Computer Science 5, pages 366-377. IEEE Computer Society Press, 1990.
A General Semantics for Evaluation Logic - Moggi (1994) (4 citations) (Correct)
....EL T , whenever one starts from a semantics of PL in D 1 given via translation into a metalanguage for Denotational Semantics. Remark 5. 2 In the literature there are several ways of constructing D from C: the category of complete extensional PERs of [3, 21] the category of complete spaces of [16], the category of replete objects (see [7, 23] Example 5.3 We show that the category ExP of complete extensional PERs can be turned into a full re ective sub bration of Set bered over itself. Consider the small category PER of partial equivalence relations (PERs) and its full re ective ....
W. Phoa. E ective domains and intrinsic structure. In 5th LICS Conf. IEEE, 1990.
The S-replete construction - Hyland, Moggi (1995) (Correct)
....that e 2 M. e is weak X iso, because e is S iso and X 2 S f 1 ; e is split mono, because 9 g:e; g = id X ; e 2 M, because (E ; M) is proper. Remark 3. 7 The above result can be reformulated as every brewise S replete object is an S space , where X is an S space ( X 2 M (see [Pho90]) In proving the internal version referred to above, one has to rely on further properties of S spaces. Given X 2 C 1 , de ne R(X) fX 0 M S 2 (X)jX 0 brewise S replete and X (X) X 0 g and let r X : X RX be the factorization of X through RX , S 2 (X) Theorem 3.8 The re ....
W. Phoa. E ective domains and intrinsic structure. In 5th LICS Conf. IEEE, 1990.
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