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44
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 298 (31 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
Automata and coinduction (an exercise in coalgebra
 LNCS
, 1998
"... The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which ..."
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Cited by 62 (16 self)
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The classical theory of deterministic automata is presented in terms of the notions of homomorphism and bisimulation, which are the cornerstones of the theory of (universal) coalgebra. This leads to a transparent and uniform presentation of automata theory and yields some new insights, amongst which coinduction proof methods for language equality and language inclusion. At the same time, the present treatment of automata theory may serve as an introduction to coalgebra.
Semantics of Types for Mutable State
, 2004
"... Proofcarrying code (PCC) is a framework for mechanically verifying the safety of machine language programs. A program that is successfully verified by a PCC system is guaranteed to be safe to execute, but this safety guarantee is contingent upon the correctness of various trusted components. For in ..."
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Cited by 55 (5 self)
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Proofcarrying code (PCC) is a framework for mechanically verifying the safety of machine language programs. A program that is successfully verified by a PCC system is guaranteed to be safe to execute, but this safety guarantee is contingent upon the correctness of various trusted components. For instance, in traditional PCC systems the trusted computing base includes a large set of lowlevel typing rules. Foundational PCC systems seek to minimize the size of the trusted computing base. In particular, they eliminate the need to trust complex, lowlevel type systems by providing machinecheckable proofs of type soundness for real machine languages. In this thesis, I demonstrate the use of logical relations for proving the soundness of type systems for mutable state. Specifically, I focus on type systems that ensure the safe allocation, update, and reuse of memory. For each type in the language, I define logical relations that explain the meaning of the type in terms of the operational semantics of the language. Using this model of types, I prove each typing rule as a lemma. The major contribution is a model of System F with general references — that is, mutable cells that can hold values of any closed type including other references, functions, recursive types, and impredicative quantified types. The model is based on ideas from both possible worlds and the indexed model of Appel and McAllester. I show how the model of mutable references is encoded in higherorder logic. I also show how to construct an indexed possibleworlds model for a von Neumann machine. The latter is used in the Princeton Foundational PCC system to prove type safety for a fullfledged lowlevel typed assembly language. Finally, I present a semantic model for a region calculus that supports typeinvariant references as well as memory reuse. iii
Circular Coinductive Rewriting
 In Proceedings of Automated Software Engineering 2000
, 2000
"... Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples ..."
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Cited by 46 (11 self)
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Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.
A Stratified Semantics of General References Embeddable in HigherOrder Logic (Extended Abstract)
, 2002
"... Amal J. Ahmed Andrew W. Appel # Roberto Virga Princeton University {amal,appel,rvirga}@cs.princeton.edu Abstract We demonstrate a semantic model of general references  that is, mutable memory cells that may contain values of any (staticallychecked) closed type, including other references. Our mo ..."
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Cited by 30 (8 self)
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Amal J. Ahmed Andrew W. Appel # Roberto Virga Princeton University {amal,appel,rvirga}@cs.princeton.edu Abstract We demonstrate a semantic model of general references  that is, mutable memory cells that may contain values of any (staticallychecked) closed type, including other references. Our model is in terms of execution sequences on a von Neumann machine
A Fast Bisimulation Algorithm
 PROC. OF INT. CONFERENCE ON COMPUTER AIDED VERIFICATION (CAV’01), VOLUME 2102 OF LNCS
, 2000
"... In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure. ..."
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Cited by 29 (15 self)
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In this paper we propose an efficient algorithmic solution to the problem of determining a Bisimulation Relation on a finite structure.
From Settheoretic Coinduction to Coalgebraic Coinduction: some results, some problems
, 1999
"... ..."
Dynamic Odds & Ends
 Ethics
, 1998
"... Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of f ..."
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Cited by 13 (2 self)
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Modal logic becomes action logic by adding programs as in propositional dynamic logic or the µ calculus. Modal languages can be seen as decidable fragments of firstorder logic that admit a natural bisimulation, and hence enjoy a good model theory. Recently, much stronger 'guarded fragments' of firstorder logic have been identified that enjoy the same pleasant features. The latter can serve as richer action languages as well. We will develop the logic of guarded fragments as a form of process theory. ln particular, moving from sequential to parallel process operations correlates with moving to firstorder fragments that are close to, or perhaps just over the decidableundecidable fence. 1 The modal dynamics of actions We will start by reviewing the basics. Standard polymodal logic is a decidable fragment of the firstorder logic of process graphs (labeled transition systems, Kripke models). It can be characterized semantically as consisting, up to logical equivalence, of those firs...
On Bounded Set Theory
"... We consider some Bounded Set Theories (BST), which are analogues to Bounded Arithmetic. Corresponding provablyrecursive operations over sets are characterized in terms of explicit definability and PTIME or LOGSPACEcomputability. We also present some conservativity results and describe a relation ..."
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Cited by 11 (1 self)
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We consider some Bounded Set Theories (BST), which are analogues to Bounded Arithmetic. Corresponding provablyrecursive operations over sets are characterized in terms of explicit definability and PTIME or LOGSPACEcomputability. We also present some conservativity results and describe a relation between BST, possibly with AntiFoundation Axiom, and a Logic of Inductive Definitions (LID) and Finite Model Theory.