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503
Full Abstraction for PCF
 INFORMATION AND COMPUTATION
, 1996
"... An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable i ..."
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Cited by 205 (15 self)
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An intensional model for the programming language PCF is described, in which the types of PCF are interpreted by games, and the terms by certain "historyfree" strategies. This model is shown to capture definability in PCF. More precisely, every compact strategy in the model is definable in a certain simple extension of PCF. We then introduce an intrinsic preorder on strategies, and show that it satisfies some remarkable properties, such that the intrinsic preorder on function types coincides with the pointwise preorder. We then obtain an orderextensional fully abstract model of PCF by quotienting the intensional model by the intrinsic preorder. This is the first syntaxindependent description of the fully abstract model for PCF. (Hyland and Ong have obtained very similar results by a somewhat different route, independently and at the same time.) We then consider the effective version of our model, and prove a Universality Theorem: every element of the effective extensional model is definable in PCF. Equivalently, every recursive strategy is definable up to observational equivalence.
Linearity, Sharing and State: a fully abstract game semantics for Idealized Algol with active expressions
 ALGOLLIKE LANGUAGES
, 1997
"... The manipulation of objects with state which changes over time is allpervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses ..."
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Cited by 105 (19 self)
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The manipulation of objects with state which changes over time is allpervasive in computing. Perhaps the simplest example of such objects are the program variables of classical imperative languages. An important strand of work within the study of such languages, pioneered by John Reynolds, focusses on "Idealized Algol", an elegant synthesis of imperative and functional features. We present a novel semantics for Idealized Algol using games, which is quite unlike traditional denotational models of state. The model takes into account the irreversibility of changes in state, and makes explicit the difference between copying and sharing of entities. As a formal measure of the accuracy of our model, we obtain a full abstraction theorem for Idealized Algol with active expressions.
Constructive Design of a Hierarchy of Semantics of a Transition System by Abstract Interpretation
, 2002
"... We construct a hierarchy of semantics by successive abstract interpretations. Starting from the maximal trace semantics of a transition system, we derive the bigstep semantics, termination and nontermination semantics, Plotkin’s natural, Smyth’s demoniac and Hoare’s angelic relational semantics and ..."
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Cited by 103 (18 self)
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We construct a hierarchy of semantics by successive abstract interpretations. Starting from the maximal trace semantics of a transition system, we derive the bigstep semantics, termination and nontermination semantics, Plotkin’s natural, Smyth’s demoniac and Hoare’s angelic relational semantics and equivalent nondeterministic denotational semantics (with alternative powerdomains to the EgliMilner and Smyth constructions), D. Scott’s deterministic denotational semantics, the generalized and Dijkstra’s conservative/liberal predicate transformer semantics, the generalized/total and Hoare’s partial correctness axiomatic semantics and the corresponding proof methods. All the semantics are presented in a uniform fixpoint form and the correspondences between these semantics are established through composable Galois connections, each semantics being formally calculated by abstract interpretation of a more concrete one using Kleene and/or Tarski
FreshML: Programming with Binders Made Simple
, 2003
"... FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving binding operations. Userdeclared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming boun ..."
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Cited by 81 (24 self)
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FreshML extends ML with elegant and practical constructs for declaring and manipulating syntactical data involving binding operations. Userdeclared FreshML datatypes involving binders are concrete, in the sense that values of these types can be deconstructed by matching against patterns naming bound variables explicitly. Such matching may have a computational effect in which bound names get swapped with freshly generated names. Previous work on FreshML used a complicated static type system inferring information about the `freshness' of names for expressions in order to tame such effects. The main contribution of this paper is to show (perhaps surprisingly) that a much simpler type system without freshness inference, coupled with name swapping and a conventional treatment of fresh name generation, suffices for FreshML's crucial correctness propertynamely that values of datatypes involving binders are operationally equivalent if and only if they represent #equivalent pieces of objectlevel syntax. This correctness result is established via a novel denotational semantics. FreshML without static freshness inference is no more impure than ML and our experiences programming in it show that it supports a programming style pleasingly close to informal practice when it comes to dealing with syntax modulo #equivalence.
Structural Induction and Coinduction in a Fibrational Setting
 Information and Computation
, 1997
"... . We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for in ..."
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Cited by 70 (15 self)
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. We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coinductively defined types. Our main results provide sufficient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle for terminal coalgebras is admissible. After giving an alternative formulation of induction in terms of binary relations, we combine both principles and obtain a mixed induction/coinduction principle which allows us to reason about minimal solutions X = oe(X) where X may occur both positively and negatively in the type constructor oe. We further strengthen these logical principles to deal with contexts and prove that such strengthening is valid when the (abstract) logic we consider is contextually/functionally complete. All the main results follow from a basic result about adjunc...
Dynamical systems, Measures and Fractals via Domain Theory
 Information and Computation
, 1995
"... We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f:X X on a metric space X, we study the extended dynamical systems (l/X,l/f), (UX, U f) and (LX, Lf) where 1/, U and L ar ..."
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Cited by 70 (20 self)
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We introduce domain theory in dynamical systems, iterated function systems (fractals) and measure theory. For a discrete dynamical system given by the action of a continuous map f:X X on a metric space X, we study the extended dynamical systems (l/X,l/f), (UX, U f) and (LX, Lf) where 1/, U and L are respectively the Vietoris hyperspace, the upper hyperspace and the lower hyperspace functors. We show that if (X, f) is chaotic, then so is (UX, U f). When X is locally compact UX, is a continuous bounded complete dcpo. If X is second countable as well, then UX will be omegacontinuous and can be given an effective structure. We show how strange attractors, attractors of iterated function systems (fractals) and Julia sets are obtained effectively as fixed points of deterministic functions on UX or fixed points of nondeterministic functions on CUX where C is the convex (Plotkin) power domain. We also show that the set, M(X), of finite Borel measures on X can be embedded in PUX, where P is the probabilistic power domain. This provides an effective framework for measure theory. We then prove that the invariant measure of an hyperbolic iterated function system with probabilities can be obtained as the unique fixed point of an associated continuous function on PUX.
On probabilistic model checking
, 1996
"... Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative ..."
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Cited by 67 (12 self)
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Abstract. This tutorial presents an overview of model checking for both discrete and continuoustime Markov chains (DTMCs and CTMCs). Model checking algorithms are given for verifying DTMCs and CTMCs against specifications written in probabilistic extensions of temporal logic, including quantitative properties with rewards. Example properties include the probability that a fault occurs and the expected number of faults in a given time period. We also describe the practical application of stochastic model checking with the probabilistic model checker PRISM by outlining the main features supported by PRISM and three realworld case studies: a probabilistic security protocol, dynamic power management and a biological pathway. 1
Weak Bisimulation for Fully Probabilistic Processes
, 1999
"... Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisi ..."
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Cited by 62 (9 self)
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Bisimulations that abstract from internal computation have proven to be useful for verification of compositionally defined transition systems. In the literature of probabilistic extensions of such transition systems, similar bisimulations are rare. In this paper, we introduce weak and branching bisimulation for fully probabilistic systems, transition systems where nondeterministic branching is replaced by probabilistic branching. In contrast to the nondeterministic case, both relations coincide. We give an algorithm to decide weak (and branching) bisimulation with a time complexity cubic in the number of states of the fully probabilistic system. This meets the worst case complexity for deciding branching bisimulation in the nondeterministic case. In addition, the relation is shown to be a congruence with respect to the operators of PLSCCS , a lazy synchronous probabilistic variant of CCS. We illustrate that due to these properties, weak bisimulation provides all the crucial ingredients...
Domain Theory and Integration
 Theoretical Computer Science
, 1995
"... We present a domaintheoretic framework for measure theory and integration of bounded realvalued functions with respect to bounded Borel measures on compact metric spaces. The set of normalised Borel measures of the metric space can be embedded into the maximal elements of the normalised probabilis ..."
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Cited by 60 (13 self)
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We present a domaintheoretic framework for measure theory and integration of bounded realvalued functions with respect to bounded Borel measures on compact metric spaces. The set of normalised Borel measures of the metric space can be embedded into the maximal elements of the normalised probabilistic power domain of its upper space. Any bounded Borel measure on the compact metric space can then be obtained as the least upper bound of an !chain of linear combinations of point valuations (simple valuations) on the upper space, thus providing a constructive setup for these measures. We use this setting to define a new notion of integral of a bounded realvalued function with respect to a bounded Borel measure on a compact metric space. By using an !chain of simple valuations, whose lub is the given Borel measure, we can then obtain increasingly better approximations to the value of the integral, similar to the way the Riemann integral is obtained in calculus by using step functions. ...