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49
Selection Functions, Bar Recursion and Backward Induction
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE, 20, PP 127168
, 2010
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Categorical Modelling of Structural Operational Rules  Case Studies
, 1997
"... . This paper aims at substantiating a recently introduced categorical theory of `wellbehaved' operational semantics. A variety of concrete examples of structural operational rules is modelled categorically illustrating the versatility and modularity of the theory. Further, a novel functorial n ..."
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Cited by 8 (4 self)
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. This paper aims at substantiating a recently introduced categorical theory of `wellbehaved' operational semantics. A variety of concrete examples of structural operational rules is modelled categorically illustrating the versatility and modularity of the theory. Further, a novel functorial notion of guardedness is introduced which allows for a general and formal treatment of guarded recursive programs. Introduction The predominant approach to operational semantics is Plotkin's SOS [13], which is based on structural rules. One finds in the literature various formats of structural rules which guarantee a good behaviour such as having adequate denotational models and behavioural equivalence (eg bisimulation) being a congruence. In [17], it is shown that the rules in the best known of these formats, namely GSOS [5], are in 11 correspondence with natural transformations of a suitable type, depending on specific functorial notions of syntax and behaviour. This led to studying abstract ...
On the construction of free algebras for equational systems
 IN: SPECIAL ISSUE FOR AUTOMATA, LANGUAGES AND PROGRAMMING (ICALP 2007). VOLUME 410 OF THEORETICAL COMPUTER SCIENCE
, 2009
"... The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop the finitary and transfinite construction of free algebras for equational systems; and to illustrate the use of equational systems as needed in modern applica ..."
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Cited by 5 (4 self)
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The purpose of this paper is threefold: to present a general abstract, yet practical, notion of equational system; to investigate and develop the finitary and transfinite construction of free algebras for equational systems; and to illustrate the use of equational systems as needed in modern applications.
Restriction categories III: colimits, partial limits, and extensivity
 Mathematical Structures in Computer Science
, 2007
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Coalgebras and Monads in the Semantics of Java
 Theoretical Computer Science
, 2002
"... This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at th ..."
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Cited by 4 (0 self)
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This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at the University of Nijmegen. It is shown how the monadic perspective gives rise to the relevant computational structure in Java (composition, extension and repetition), and how the coalgebraic perspective o#ers an associated program logic (with invariants, bisimulations, and Hoare logics) for reasoning about the computational structure provided by the monad.
An Equational Notion of Lifting Monad
 TITLE WILL BE SET BY THE PUBLISHER
, 2003
"... We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category ..."
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Cited by 4 (1 self)
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We introduce the notion of an equational lifting monad: a commutative strong monad satisfying one additional equation (valid for monads arising from partial map classifiers). We prove that any equational lifting monad has a representation by a partial map classifier such that the Kleisli category of the former fully embeds in the partial category of the latter. Thus equational lifting monads precisely capture the equational properties of partial maps as induced by partial map classifiers. The representation theorem also provides a tool for transferring nonequational properties of partial map classifiers to equational lifting monads. It is proved using a direct axiomatization of Kleisli categories of equational lifting monads. This axiomatization is of interest in its own right. 1
What is a Data Type?
, 1996
"... A program derivation is said to be polytypic if some of its parameters are data types. Polytypic program derivations necessitate a general, noninductive definition of `data type'. Here we propose such a definition: a data type is a relator that has membership. It is shown how this definition i ..."
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Cited by 4 (1 self)
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A program derivation is said to be polytypic if some of its parameters are data types. Polytypic program derivations necessitate a general, noninductive definition of `data type'. Here we propose such a definition: a data type is a relator that has membership. It is shown how this definition implies various other properties that are shared by all data types. In particular, all data types have a unique strength, and all natural transformations between data types are strong. 1 Introduction What is a data type? It is easy to list a number of examples: pairs, lists, bags, finite sets, possibly infinite sets, function spaces . . . but such a list of examples hardly makes a definition. The obvious formalisation is a definition that builds up the class of data types inductively; such an inductive definition, however, leads to cumbersome proofs if we want to prove a property of all data types. Here we aim to give a noninductive characterisation, defining a data type as a mathematical object...
A linear logic model of state
 Manuscript
, 1993
"... We propose an abstract formal model of state manipulation in the framework of Girard’s linear logic. Two issues motivate this work: how to describe the semantics of higherorder imperative programming languages and how to incorporate state manipulation in functional programming languages. The centra ..."
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We propose an abstract formal model of state manipulation in the framework of Girard’s linear logic. Two issues motivate this work: how to describe the semantics of higherorder imperative programming languages and how to incorporate state manipulation in functional programming languages. The central idea is that a state is linear and “regenerative”, where the latter is the property of a value that generates a new value upon each use. Based on this, we define a type constructor for states and a “modality” type constructor for regenerative values. Just as Girard’s “of course ” modality allows him to express static values and intuitionistic logic within the framework of linear logic, our regenerative modality allows us to express dynamic values and imperative programs within the same framework. We demonstrate the expressiveness of the model by showing that a higherorder Algollike language can be embedded in it. 1
Universal properties of Span
 in The Carboni Festschrift, Theory and Applications of Categories 13 (2005
"... Abstract. We give two related universal properties of the span construction. The first involves sinister morphisms out of the base category and sinister transformations. The second involves oplax morphisms out of the bicategory of spans having an extra property; we call these “jointed ” oplax morphi ..."
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Cited by 4 (2 self)
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Abstract. We give two related universal properties of the span construction. The first involves sinister morphisms out of the base category and sinister transformations. The second involves oplax morphisms out of the bicategory of spans having an extra property; we call these “jointed ” oplax morphisms.
A separation logic for refining concurrent objects
, 2010
"... Finegrained concurrent data structures are crucial for gaining performance from multiprocessing, but their design is a subtle art. Recent literature has made large strides in verifying these data structures, using either atomicity refinement or separation logic with relyguarantee reasoning. In thi ..."
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Cited by 3 (1 self)
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Finegrained concurrent data structures are crucial for gaining performance from multiprocessing, but their design is a subtle art. Recent literature has made large strides in verifying these data structures, using either atomicity refinement or separation logic with relyguarantee reasoning. In this paper we show how the ownership discipline of separation logic can be used to enable atomicity refinement, and we develop a new relyguarantee method that is localized to the definition of a data structure. We present the first semantics of separation logic that is sensitive to atomicity, and show how to control this sensitivity through ownership. The result is a logic that enables compositional reasoning about atomicity and interference, even for programs that use finegrained synchronization and dynamic memory allocation.