Results 1 
5 of
5
Collapsing Partial Combinatory Algebras
 HigherOrder Algebra, Logic, and Term Rewriting
, 1996
"... Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a pca. We establish several facts concerning final collapses (maximal identification of elements). `En passant' we find another example of a pca that cannot be extended to a total one. 1
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 7 (2 self)
 Add to MetaCart
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...
Completing Partial Combinatory Algebras with Unique HeadNormal Forms
, 1996
"... In this note, we prove that having unique headnormal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CLterms as well as the pca of natural numbers with partial recursive function application can be exte ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
In this note, we prove that having unique headnormal forms is a sufficient condition on partial combinatory algebras to be completable. As application, we show that the pca of strongly normalizing CLterms as well as the pca of natural numbers with partial recursive function application can be extended to total combinatory algebras. 1.
Extending Partial Combinatory Algebras
, 1999
"... Introduction Consider a structure A = hA; s; k; \Deltai, where A is some set containing the distinguished elements s; k, equipped with a binary operation \Delta on A, called application, which may be partial. Notation 1.1. 1 Instead of a \Delta b we write ab; and in writing applicative expression ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Introduction Consider a structure A = hA; s; k; \Deltai, where A is some set containing the distinguished elements s; k, equipped with a binary operation \Delta on A, called application, which may be partial. Notation 1.1. 1 Instead of a \Delta b we write ab; and in writing applicative expressions, the usual convention of association to the left is employed. So for elements a; b; c 2 A, the expression aba(ac) is short for ((a \Delta b) \Delta a) \Delta (a \Delta c). 2 ab # will mean that ab is defined; ab " means that ab is not defined. Obviously, an applicative expression
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 ..."
Abstract
 Add to MetaCart
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