M. P. Fiore. An enrichment theorem for an axiomatisation of categories of domains and continuous functions. Math. Structures Comput. Sci., 7:591--618, 1997  Home/Search   Document Details and Download   Summary   Related Articles   Check

....and functional programming languages, e.g. 1, 38, 45] in which one evaluates arguments before applying them to a concerned procedure. The semantics of higher order computation based on call by value evaluation has been widely studied by many researchers in the context of domain theory, cf. [44, 45, 29, 40, 17, 51, 14, 15], through which it has become clear that the semantic framework needed to capture the call by value computation has a basic difference from the one for call by name computation (see [21, 53] for basic introduction to the topic) The difference between the semantics of call by value and that of ....

....which have arisen through the categorical analysis of 1 There is an independent and concurrent similar result by Riecke and Sandholm [50] which however does not use game semantics. See Section 7 for discussions. domain theoretic universes for call by value, or partial, computation, cf.[46, 39, 40, 15], though with a strong intensional flavour. In particular each of the intensional category and its extensional quotient is isomorphic to the Kleisli category of a strong monad on the respective subcategory of total maps, from which such notions as pairing and exponentiation arise (which reminds us ....

Fiore, M., An Enrichment Theorem for an Axiomatisation of Categories of Domains and Continuous Functions, Math. Struct. in Comp. Science, 1996.

....and functional programming languages, e.g. 1, 40, 47] in which one evaluates arguments before applying them to a concerned procedure. The semantics of higher order computation based on call by value evaluation has been widely studied by many researchers in the context of domain theory, cf. [46, 47, 31, 42, 19, 53, 16, 17], through which it has become clear that the semantic framework needed to capture the call by value computation has a basic difference from the one for call by name computation (see [23, 55] for basic introduction to the topic) The difference between the semantics of call by value and that of ....

....which have arisen through the categorical analysis of 1 There is an independent and concurrent similar result by Riecke and Sandholm [52] which however does not use game semantics. See Section 7 for discussions. domain theoretic universes for call by value, or partial, computation, cf.[48, 41, 42, 17], though with a strong intensional flavour. In particular each of the intensional category and its extensional quotient is isomorphic to the Kleisli category of a strong monad on the respective subcategory of total maps, from which such notions as pairing and exponentiation arise (which reminds us ....

Fiore, M., An Enrichment Theorem for an Axiomatisation of Categories of Domains and Continuous Functions, Math. Struct. in Comp. Science, 1996.

.... is an orthogonality condition: an object is Sigma separated if and only if it is internally orthogonal to the unique mediating map s in 2 po d d fflffl Sigma fflffl id Sigma id D s OEOE Sigma , cf. 8] 3 Consider the following notion, used implicitly in [5, 6]: an object is path transitive when it is internally orthogonal to the unique mediating map t in 1 po fflffl Sigma fflffl j Sigma Sigma L , Sigma Sigma t G G G G G Sigma 2 . Examples of path transitive objects are the simplicial sets Y(P ) for every poset P . The ....

.... chain hx i i in OA , F A hx i i is an upper bound. Proof: For k 2 N, consider the path hk; 1i: Sigma . Then, x k = hx i i ffi k = hx i i ffi hk; 1i ffi vA hx i i ffi hk; 1i ffi = hx i i ffi 1 = F A hx i i 2 Moreover, the operator F A satisfies the following properties, cf. [5, 6]. Proposition 4.2 (Constant) For x 2 jAj, we have that F A hx vA : vA x vA : i = x. Monotonicity) If hx i i and hy j i are chains in OA such that x k vA y k for all k 2 N, then F A hx i i vA F A hy j i. Finality) If hx i i is an chain in OA and f : is monotone and ....

M. P. Fiore. An enrichment theorem for an axiomatisation of categories of domains and continuous functions. Math. Structures Comput. Sci., 7:591--618, 1997

....In particular, part of our agenda is to establish a representation theory for domains. Here, as a first step, we concentrate on the enrichment of models of ADT. The intention is that the enriched Yoneda Grothendieck Dedekind Cayley embedding [27] will provide the desired representation (c.f. [15, 11]) Axiomatic versions of various traditional results in domain theory can be found in e.g. 39, 16, 17, 38, 13, 9, 11, 32] For instance, in [39] the crucial role Research supported by EPSRC grant GR J84205, Frameworks for Programming Language Semantics and Logic. y Research supported by an ....

....a first step, we concentrate on the enrichment of models of ADT. The intention is that the enriched Yoneda Grothendieck Dedekind Cayley embedding [27] will provide the desired representation (c.f. 15, 11] Axiomatic versions of various traditional results in domain theory can be found in e.g. [39, 16, 17, 38, 13, 9, 11, 32]. For instance, in [39] the crucial role Research supported by EPSRC grant GR J84205, Frameworks for Programming Language Semantics and Logic. y Research supported by an EPSRC Senior Fellowship. of Cpo enrichment in the solution of recursive domain equations was recognised and made the central ....

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M.P. Fiore. An enrichment theorem for an axiomatisation of categories of domains and continuous functions. To appear in Mathematical Structures in Computer Science ---Proceedings of the Workshop LDPL'95, 1997.

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