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29
Coinductive proof principles for stochastic processes
 Proc. 21st Symp. Logic in Computer Science (LICS’06
, 2006
"... Vol. 3 (4:8) 2007, pp. 1–14 ..."
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Open Maps as a Bridge Between Algebraic Observational Equivalence and Bisimilarity
, 1997
"... There are two widely accepted notions of behavioural equivalence, formalizing the idea of observational indistinguishability: observational equivalence for algebras (which are models for sequential systems) and bisimulation equivalence (bisimilarity) for concurrent processes. In this paper we show t ..."
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There are two widely accepted notions of behavioural equivalence, formalizing the idea of observational indistinguishability: observational equivalence for algebras (which are models for sequential systems) and bisimulation equivalence (bisimilarity) for concurrent processes. In this paper we show that the observational equivalences for standard, partial and regular algebras are bisimulation equivalences. This is done in the setting of open maps, proposed in [JNW93] as an abstract approach to behavioural equivalences of processes. The main advantage of the results is capturing the models for sequential and concurrent systems in a uniform framework. In such an abstract setting we formulate the property of determinism, shared by all the algebras considered in this paper, and identify some interesting facts about bisimilarity in the deterministic case. All the results for standard, regular and partial algebras are obtained by the applications of a general machinery developed in the pape...
Reasoning with Actions
 Dept. of Computer Science, Univ. of Aarhus
"... Action semantics is a semantic description framework with very good pragmatic properties but a rather weak theory for reasoning about programs. A strong action theory would be of great practical use, however. It would make it possible to reason about the large class of programming languages that can ..."
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Action semantics is a semantic description framework with very good pragmatic properties but a rather weak theory for reasoning about programs. A strong action theory would be of great practical use, however. It would make it possible to reason about the large class of programming languages that can be described in action semantics. This paper develops the foundations for a richer action theory, by bringing together concepts and techniques from testing theory for processes and from work on operational reasoning about functional programs. Semantic preorders and equivalences in the action semantics setting are studied and a useful operational technique for establishing testing equivalences is presented. 1 Introduction In this paper we develop a richer theory for reasoning about programs in action semantics (AS). Because AS is a general semantic description framework, our work has a great practical scope. A strong action theory would offer techniques for reasoning about programs in any p...
Stream Differential Equations: concrete formats for coinductive definitions
, 2011
"... In this article we give an accessible introduction to stream differential equations, ie., equations that take the shape of differential equations from analysis and that are used to define infinite streams. Furthermore we discuss a syntactic format for stream differential equations that ensures that ..."
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In this article we give an accessible introduction to stream differential equations, ie., equations that take the shape of differential equations from analysis and that are used to define infinite streams. Furthermore we discuss a syntactic format for stream differential equations that ensures that any system of equations that fits into the format has a unique solution. It turns out that the stream functions that can be defined using our format are precisely the causal stream functions. Finally, we are going to discuss nonstandard stream calculus that uses basic (co)operations different from the usual head and tail operations in order to define and to reason about streams and stream functions. 1
Program Equivalence in Linear Contexts
"... Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at contextual equivalence in the usual (nonlinear) functional l ..."
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Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at contextual equivalence in the usual (nonlinear) functional languages, and fail in capturing nontrivial equivalent programs in linear contexts, particularly when nondeterminism is present. We propose the notion of linear contextual equivalence to formally characterize such program equivalence, as well as a novel and general approach to studying it in higherorder languages, based on labeled transition systems specifically designed for functional languages. We show that linear contextual equivalence indeed coincides with trace equivalence. We illustrate our technique in both deterministic (a linear version of PCF) and nondeterministic (linear PCF in Moggi’s framework) functional languages.
Implicit Programming and the Logic of Constructible Duality
, 1998
"... We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a selfdual logic constructible duality. We develop a selfdual model by considering an interval of worlds in an intuitionistic Kripk ..."
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We present an investigation of duality in the traditional logical manner. We extend Nelson's symmetrization of intuitionistic logic, constructible falsity, to a selfdual logic constructible duality. We develop a selfdual model by considering an interval of worlds in an intuitionistic Kripke model. The duality arises through how we judge truth and falsity. Truth is judged forward in the Kripke model, as in intuitionistic logic, while falsity is judged backwards. We develop a selfdual algebra such that every point in the algebra is representable by some formula in the logic. This algebra arises as an instantiation of a Heyting algebra into several categorical constructions. In particular, we show that this algebra is an instantiation of the Chu construction applied to a Heyting algebra, the second Dialectica construction applied to a Heyting algebra, and as an algebra for the study of recursion and corecursion. Thus the algebra provides a common base for these constructions, and suggests itself as an important part of any constructive logical treatment of duality. Implicit programming is suggested as a new paradigm for computing with constructible duality as its formal system. We show that all the operators that have computable least fixed points are definable explicitly and all operators with computable optimal fixed points are definable implicitly within constructible duality. Implicit programming adds a novel definitional mechanism that allows functions to be defined implicitly. This new programming feature is especially useful for programming with corecursively defined datatypes such as circular lists.
Implicit programming and Computable Optimal Fixed Points. available from http://wwwformal.Stanford.EDU/annap
, 1997
"... ..."
Relative Equational Specification and Semantics
, 1997
"... Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modula ..."
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Abstract: Standard concepts of initial and final algebra semantics are generalised in a modular hierarchical manner. The resulting relative formalism allows a unified view on the relationship between initial and final algebra semantics and gives a dualised notion of consistency. Using this, a modular hierarchical approach to proof by consistency is taken by which only toplevel equations need be considered at any level. The formalism also allows nonhomogeneous specification schemes and different proof methods at each level.
MSc in Logic at the Universiteit van Amsterdam.
, 2012
"... Interaction, observation and denotation A study of dialgebras for program semantics ..."
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Interaction, observation and denotation A study of dialgebras for program semantics