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Effective Applicative Structures
 In: Proceedings of the 6th biennial conference on Category Theory in Computer Science (CTCS'95). SpringerVerlag Lecture Notes in Computer Science 953 8195
, 1995
"... S. All local authors can be reached viaemail at theaddress lastname@cs.unibo.it. Written requests and comments should be addressed to tradmin@cs.unibo.it. UBLCS Technical Report Series 9320 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 9321 A Classifica ..."
Abstract

Cited by 8 (2 self)
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S. All local authors can be reached viaemail at theaddress lastname@cs.unibo.it. Written requests and comments should be addressed to tradmin@cs.unibo.it. UBLCS Technical Report Series 9320 An Information Flow Security Property for CCS, R. Focardi, R. Gorrieri, October 1993. 9321 A Classification of Security Properties, R. Focardi, R. Gorrieri, October 1993. 9322 Real Time Systems: A Tutorial, F. Panzieri, R. Davoli, October 1993. 9323 A Scalable Architecture for Reliable Distributed Multimedia Applications, F. Panzieri, M. Roccetti, October 1993. 9324 WideArea Distribution Issues in Hypertext Systems, C. Maioli, S. Sola, F. Vitali, October 1993. 9325 On Relating Some Models for Concurrency, P. Degano, R. Gorrieri, S. Vigna, October 1993. 9326 Axiomatising ST Bisimulation Equivalence, N. Busi, R. van Glabbeek, R. Gorrieri, December 1993. 9327 A Theory of Processeswith Durational Actions, R. Gorrieri, M. Roccetti, E. Stancampiano, December1993. 941 Further Modifications t...
On Completability of Partial
"... A Partial Combinatory Algebra is completable if it can be extended to a total one. Klop [11, 12] gave a sufficient condition for completability of a PCA M = (M,·,K,S) in the form of ten axioms (inequalities) on terms of M. We prove that Klop’s sufficient condition is equivalent to the existence of a ..."
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A Partial Combinatory Algebra is completable if it can be extended to a total one. Klop [11, 12] gave a sufficient condition for completability of a PCA M = (M,·,K,S) in the form of ten axioms (inequalities) on terms of M. We prove that Klop’s sufficient condition is equivalent to the existence of an injective smn function over M (that in turns is equivalent to the Padding Lemma). This is proved by working with an alternative characterization of PCA’s, recently introduced by the authors (Effective Applicative Structures). As a corollary, we show that nine of Klop’s ten axioms are actually redundant (the so called Barendregt’s axiom is enough to guarantee completability). Moreover, we prove that any Uniformly Reflexive Structure [17, 18, 16] is completable. 1
Synthetic Computability
"... ◮ Suppose we want to study mathematical structures forming a category C, such as: ◮ smooth manifolds and differentiable maps ◮ topological spaces and continuous maps ◮ computable sets and computable maps ◮ Classical approach: objects are sets equipped with extra structure, morphisms preserve the str ..."
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◮ Suppose we want to study mathematical structures forming a category C, such as: ◮ smooth manifolds and differentiable maps ◮ topological spaces and continuous maps ◮ computable sets and computable maps ◮ Classical approach: objects are sets equipped with extra structure, morphisms preserve the structure. ◮ Synthetic approach: embed C in a suitable mathematical universe E (a model of intuitionistic set theory) and view structures as ordinary sets and morphisms as ordinary maps inside E. A synthetic universe for computability theory ◮ M. Hyland’s effective topos Eff is the mathematical universe suitable for computability theory. ◮ In Eff all objects and morphisms are equipped with