Results 1  10
of
10
Final Semantics for a Higher Order Concurrent Language
 CAAP'96 Conference Proceedings, H.Kirchner ed., Springer LNCS
, 1995
"... We show that adequate semantics can be provided for imperative higher order concurrent languages simply using syntactical final coalgebras. In particular we investigate and compare various behavioural equivalences on higher order processes defined by finality using hypersets and c.m.s.'s. Correspond ..."
Abstract

Cited by 15 (11 self)
 Add to MetaCart
We show that adequate semantics can be provided for imperative higher order concurrent languages simply using syntactical final coalgebras. In particular we investigate and compare various behavioural equivalences on higher order processes defined by finality using hypersets and c.m.s.'s. Correspondingly, we derive various coinduction and mixed inductioncoinduction proof principles for establishing these equivalences.
From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
"... ..."
A Small Final Coalgebra Theorem
 Theoretical Computer Science
, 1998
"... This paper presents an elementary and selfcontained proof of an existence theorem of final coalgebras for endofunctors on the category of sets and functions. ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
This paper presents an elementary and selfcontained proof of an existence theorem of final coalgebras for endofunctors on the category of sets and functions.
Semantics for Finite Delay
 Theoretical Computer Science
, 1997
"... We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Aczel's s ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We produce a fully abstract model for a notion of process equivalence taking into account issues of fairness, called by Milner fair bisimilarity. The model uses Aczel's antifoundation axiom and it is constructed along the lines of the antifounded model for SCCS given by Aczel. We revisit Aczel's semantics for SCCS where we prove a unique fixpoint theorem under the assumption of guarded recursion. Then we consider Milner's extension of SCCS to include a finite delay operator ". Working with fair bisimilarity we construct a fully abstract model, which is also fully abstract for fortification. We discuss the solution of recursive equations in the model. The paper is concluded with an investigation of the algebraic theory of fair bisimilarity. Keywords: fairness, antifoundation, finite delay, parallelism, fair bisimilarity, fortification. This paper was composed while I was unemployed and an unofficial visitor at the Department of Mathematics, University of Ioannina, Greece. My than...
Axiomatic Characterizations of Hyperuniverses and Applications
 University of Southern
, 1996
"... Hyperuniverses are topological structures exhibiting strong closure properties under formation of subsets. They have been used both in Computer Science, for giving denotational semantics `a la Scottde Bakker, and in Mathematical Logic, in order to show the consistency of set theories which do not a ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Hyperuniverses are topological structures exhibiting strong closure properties under formation of subsets. They have been used both in Computer Science, for giving denotational semantics `a la Scottde Bakker, and in Mathematical Logic, in order to show the consistency of set theories which do not abide by the "limitation of size" principle. We present correspondences between settheoretic properties and topological properties of hyperuniverses. We give existence theorems and discuss applications and generalizations to the non compact case. Work partially supported by 40% and 60% MURST grants, CNR grants, and EEC Science MASK, and BRA Types 6453 contracts. y Member of GNSAGA of CNR. z The main results of this paper have been communicated by this author at the "11 th Summer Conference on General Topology and Applications" August 1995, Portland, Maine. Introduction Natural frameworks for dicussing Selfreference and other circular phenomena are extremely useful in areas such ...
Coinductive Characterizations of Applicative Structures
 MATH. STRUCTURES IN COMP. SCI. 9(4):403–435
, 1998
"... We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
We discuss new ways of characterizing, as maximal fixed points of monotone operators, observational congruences on terms and, more in general, equivalences on applicative structures. These characterizations naturally induce new forms of coinduction principles, for reasoning on program equivalences, which are not based on Abramsky's applicative bisimulation. We discuss in particular, what we call, the cartesian coinduction principle, which arises when we exploit the elementary observation that functional behaviours can be expressed as cartesian graphs. Using the paradigm of final semantics, the soundness of this principle over an applicative structure can be expressed easily by saying that the applicative structure can be construed as a strongly extensional coalgebra for the functor (P( \Theta )) \Phi (P( \Theta )). In this paper, we present two general methods for showing the soundenss of this principle. The first applies to approximable applicative structures. Many c.p.o. models in...
Final Semantics for the picalculus
, 1998
"... In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This i ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
In this paper we discuss final semantics for the calculus, a process algebra which models systems that can dynamically change the topology of the channels. We show that the final semantics paradigm, originated by Aczel and Rutten for CCSlike languages, can be successfully applied also here. This is achieved by suitably generalizing the standard techniques so as to accommodate the mechanism of name creation and the behaviour of the binding operators peculiar to the calculus. As a preliminary step, we give a higher order presentation of the calculus using as metalanguage LF , a logical framework based on typed calculus. Such a presentation highlights the nature of the binding operators and elucidates the role of free and bound channels. The final semantics is defined making use of this higher order presentation, within a category of hypersets.
Final Semantics for untyped λcalculus
 IN LNCS, VOLUME 902
, 1995
"... Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principl ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principles arise naturally as coinduction principles, when the observational equivalences are shown to be induced by the unique mapping into a final Fcoalgebra, for a suitable functor F . This is achieved either by induction on computation steps or exploiting the properties of some, computationally adequate, inverse limit denotational model. The final F coalgebras cannot be given, in general, the structure of a "denotational" λmodel. Nevertheless the "final semantics" can count as compositional in that it induces a congruence. We utilize the intuitive categorical setting of hypersets and functions. The importance of the principles introduced in this paper lies in the fact that they often allow...
A Complete Coinductive Logical System for Bisimulation Equivalence on Circular Objects
 in FoSSaCS'99 (ETAPS) Conf. Proc., W.Thomas ed., Springer LNCS 1578
, 1983
"... We introduce a coinductive logical system à la Gentzen for establishing bisimulation equivalences on circular nonwellfounded regular objects, inspired by work of Coquand, and of Brandt and Henglein. In order to describe circular objects, we utilize a typed language, whose coinductive types involve ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
We introduce a coinductive logical system à la Gentzen for establishing bisimulation equivalences on circular nonwellfounded regular objects, inspired by work of Coquand, and of Brandt and Henglein. In order to describe circular objects, we utilize a typed language, whose coinductive types involve disjoint sum, cartesian product, and finite powerset constructors. Our system is shown to be complete with respect to a maximal fixed point semantics. It is shown to be complete also with respect to an equivalent final semantics. In this latter semantics, terms are viewed as points of a coalgebra for a suitable endofunctor on the category Set of nonwellfounded sets. Our system subsumes an axiomatization of regular processes, alternative to the classical one given by Milner.
Coalgebraic Coinduction in (Hyper)settheoretic Categories
, 2000
"... This paper is a contribution to the foundations of coinductive types and coiterative functions, in (Hyper)settheoretical Categories, in terms of coalgebras. We consider atoms as first class citizens. First of all, we give a sharpening, in the way of cardinality, of Aczel's Special Final Coalgebra ..."
Abstract
 Add to MetaCart
This paper is a contribution to the foundations of coinductive types and coiterative functions, in (Hyper)settheoretical Categories, in terms of coalgebras. We consider atoms as first class citizens. First of all, we give a sharpening, in the way of cardinality, of Aczel's Special Final Coalgebra Theorem, which allows for good estimates of the cardinality of the final coalgebra. To these end, we introduce the notion of Y uniform functor, which subsumes Aczel's original notion. We give also an nary version of it, and we show that the resulting class of functors is closed under many interesting operations used in Final Semantics. We define also canonical wellfounded versions of the final coalgebras of functors uniform on maps. This leads to a reduction of coiteration to ordinal induction, giving a possible answer to a question raised by Moss and Danner. Finally, we introduce a generalization of the notion of F bisimulation inspired by Aczel's notion of precongruence, and we show t...