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14
Kleene Algebra with Domain
, 2003
"... We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We ..."
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Cited by 41 (29 self)
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We propose Kleene algebra with domain (KAD), an extension of Kleene algebra with two equational axioms for a domain and a codomain operation, respectively. KAD considerably augments the expressibility of Kleene algebra, in particular for the specification and analysis of state transition systems. We develop the basic calculus, discuss some related theories and present the most important models of KAD. We demonstrate applicability by two examples: First, an algebraic reconstruction of Noethericity and wellfoundedness. Second, an algebraic reconstruction of propositional Hoare logic.
Semantic Types: A Fresh Look at the Ideal Model for Types
, 2004
"... We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact tha ..."
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Cited by 23 (2 self)
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We present a generalization of the ideal model for recursive polymorphic types. Types are defined as sets of terms instead of sets of elements of a semantic domain. Our proof of the existence of types (computed by fixpoint of a typing operator) does not rely on metric properties, but on the fact that the identity is the limit of a sequence of projection terms. This establishes a connection with the work of Pitts on relational properties of domains. This also suggests that ideals are better understood as closed sets of terms defined by orthogonality with respect to a set of contexts.
Reasoning With Taxonomies
, 1996
"... Taxonomies are prevalent in a multitude of fields, including ecology, linguistics, programming languages, databases, and artificial intelligence. In this thesis, we focus on several aspects of reasoning with taxonomies, including the management of taxonomies in computers, extensions of partial ord ..."
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Cited by 19 (1 self)
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Taxonomies are prevalent in a multitude of fields, including ecology, linguistics, programming languages, databases, and artificial intelligence. In this thesis, we focus on several aspects of reasoning with taxonomies, including the management of taxonomies in computers, extensions of partial orders to enhance the taxonomic information that can be represented, and novel uses of taxonomies in several applications. The first part of the thesis deals with theoretical and implementational aspects of representing, or encoding, taxonomies. Our contributions include (i) a formal abstraction of encoding that encompasses all current techniques; (ii) a generalization of the technique of modulation that enhances the efficiency of this strategy for encoding and reduces its brittleness for dynamic taxonomies; (iii) the development of sparse logical terms as a universal implementation for ...
Type Elaboration and Subtype Completion for Java Bytecode
 IN PROCEEDINGS 27TH ACM SIGPLANSIGACT SYMPOSIUM ON PRINCIPLES OF PROGRAMMING LANGUAGES
, 1999
"... Java source code is strongly typed, but the translation from Java source to bytecode omits much of the type information originally contained within methods. Type elaboration is a technique for reconstructing strongly typed programs from incompletely typed bytecode by inferring types for local variab ..."
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Cited by 16 (0 self)
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Java source code is strongly typed, but the translation from Java source to bytecode omits much of the type information originally contained within methods. Type elaboration is a technique for reconstructing strongly typed programs from incompletely typed bytecode by inferring types for local variables. There are situations where, technically, there are not enough types in the original type hierarchy to type a bytecode program. Subtype completion is a technique for adding necessary types to an arbitrary type hierarchy to make type elaboration possible for all verifiable Java bytecode. Type elaboration with subtype completion has been implemented as part of the Marmot Java compiler.
Abstract Interpretation of Linear Logic Programming
 IN PROC. OF ILPS'93
, 1993
"... Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear Lo ..."
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Cited by 14 (2 self)
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Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear Logic. A proof normalization procedure, called "focusing", has been proposed to make the problem of proof search tractable. Correspondingly, there is a normalization procedure mapping formulae of Linear Logic into a syntactic fragment of that logic, called LinLog, and in which the focusing normalization for proofs can be most conveniently expressed. In this paper, we propose to push this compilation/normalization process further, by applying abstract interpretation and partial evaluation techniques to (focused) proofs in LinLog. These techniques provide information concerning the evolution of the computational resources (formulae) during the execution (proof construction). The practical outcome that we expect from this theoretical effort is the definition of a general tool for statically analyzing and reasoning about the runtime behavior of programs in frameworks where computations can be accounted for in terms of proof search in Linear Logic.
Modal Kleene Algebra And Applications  A Survey
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey ..."
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Cited by 11 (5 self)
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Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. They provide a concise and convenient algebraic framework that subsumes various other calculi and allows treating quite a variety of areas. We survey
Termination in Modal Kleene Algebra
 EXPLORING NEW FRONTIERS OF THEORETICAL INFORMATICS. IFIP INTERNATIONAL FEDERATION FOR INFORMATION PROCESSING SERIES 155. KLUWER 2004, 653–666
, 2004
"... Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspond ..."
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Cited by 9 (8 self)
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Modal Kleene algebras are Kleene algebras with forward and backward modal operators defined via domain and codomain operations. The paper investigates the algebraic structure of modal operators. It studies and compares different notions of termination in this class, including an algebraic correspondence proof of Lob's formula from modal logic. It gives calculational proofs of two fundamental statements from rewriting theory that involve termination: Bachmair's and Dershowitz's wellfounded union theorem and Newman's lemma. These results are also of general interest for the termination analysis of programs and state transition systems.
Invertibility of Functional Galois Connections
, 2002
"... We consider equations of the form Bf = g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferenti ..."
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Cited by 5 (3 self)
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We consider equations of the form Bf = g, where B is a Galois connection between lattices of functions. This includes the case where B is the Fenchel transform, or more generally a Moreau conjugacy. We characterize the existence and uniqueness of a solution f in terms of generalized subdifferentials, which extends K. Zimmermann's covering theorem for maxplus linear equations. c 2002 Academie des sciences/ Editions scientifiques et medicales Elsevier SAS Inversibilit e des correspondances de Galois fonctionnelles R esum e. On considere des equations de la forme Bf = g, ou B est une correspondance de Galois entre des treillis de fonctions, ce qui inclut le cas ou B est la transformation de Fenchel, ou plus generalement une conjugaison de Moreau. Nous caracterisons l'existence et l'unicite d'une solution f , en termes de sousdifferentiels generalises, et etendons ainsi le theoreme de couverture de K. Zimmermann pour les equations lineaires maxplus. c 2002 Academie des sciences/ Editions scientifiques et medicales Elsevier SAS Version francaise abr eg ee Soient (F ; F ) et (G ; G ) deux ensembles partiellement ordonnes, et B : F ! G , C : G ! F . On dit que (B; C) est une correspondance de Galois si la propriete (7b) cidessous est satisfaite. L'application C, qui est unique, est notee B . On dit aussi que B et C sont des correspondances de Galois. On s'interesse au cas ou F = sci(Y; R) est l'ensemble des fonctions semicontinues inferieurement d'un espace topologique separe Y dans R, et ou G = R , pour un espace topologique separe X . On montre en particulier que B et B s'ecrivent sous la forme (8), ou b et b sont des applications X Y R ! R, et ou pour tout x 2 X; y 2 Y , (b(x; y; ); b (x; y; )) est une correspondance de Galois....
Refinement in Ergo
, 1995
"... Refinement is a mathematicallybased technique for developing a program from an abstract specification so that the program satisfies the specification. The aim of the Program Refinement Tool project is to develop a generic refinement tool suitable for supporting a methodology for the interactive ..."
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Cited by 4 (1 self)
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Refinement is a mathematicallybased technique for developing a program from an abstract specification so that the program satisfies the specification. The aim of the Program Refinement Tool project is to develop a generic refinement tool suitable for supporting a methodology for the interactive development of programs based on the refinement calculus. This report summarizes our investigation into how the Ergo theorem prover can be used to model the refinement calculus and form the basis of this tool.
The Testing Paradigm Applied to Network Structure
 Eindhoven University of Technology
, 1994
"... The testing paradigm provides a simple framework for comparing networks of processes. To apply the testing paradigm, one needs a suite of tests and a test criterion expressing when a network passes a test. Two networks are considered testing equivalent when they pass the same tests. In all applicat ..."
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Cited by 1 (0 self)
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The testing paradigm provides a simple framework for comparing networks of processes. To apply the testing paradigm, one needs a suite of tests and a test criterion expressing when a network passes a test. Two networks are considered testing equivalent when they pass the same tests. In all applications of the testing paradigm that we have seen, tests "probe" (some of) the behavior of the process network under test. Network structure, however, is mostly handled in an ad hoc way. In this note, we use the testing paradigm to compare structural aspects of process networks. Central to our approach are the following three ingredients: (i) Tests are drawn from the set of process networks, that is, each test is itself just a process network. (ii) A (global) correctness concern, in the form of a predicate, expresses when a network is correct as an autonomous system. (iii) A network passes a test (by another network) when the composition of two networks involved is a correct (autonomous) system. Our approach has several merits. It allows a uniform treatment of structure and behavior. Structural and behavioral correctness concerns can be varied independently within the same framework. Structural correctness concerns can be made explicit at the very beginning, and need not appear implicitly as an unmotivated afterthought. Several phenomena, such as nondeterminism, can be illustrated solely in terms of structure, without getting bogged down by behavioral complications. For one particular choice of (structural) correctness concerns, we work out a model in full detail. We briefly investigate alternative correctness concerns. CONTENTS ii Contents 1