Reasoning about local variables with operationally-based logical relations

Pitts, Andrew M.

doi:10.1109/lics.1996.561314

Cited by 26 publications

(33 citation statements)

References 16 publications

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“…We use it to obtain a straightforward and apparently quite powerful method for proving properties of Morris-style contextual equivalence of types and terms involving impredicative polymorphism and fixpoint recursion; and one which is based only upon the syntax and operational semantics of the language. (See (Pitts 1997b;Pitts and Stark 1998) for previous results of this kind. )…”

Section: Introductionmentioning

confidence: 93%

Parametric polymorphism and operational equivalence

Pitts

2000

Math. Struct. Comp. Sci.

129

185

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Studies of the mathematical properties of impredicative polymorphic types have for the most part focused on the polymorphic lambda calculus of Girard-Reynolds, which is a calculus of total polymorphic functions. This paper considers polymorphic types from a functional programming perspective, where the partialness arising from the presence of fixpoint recursion complicates the nature of potentially infinite ('lazy') data types. An approach to Reynolds' notion of relational parametricity is developed which works directly on the syntax of a programming language, using a novel closure operator to relate operational behaviour to parametricity properties of types. Working with an extension of Plotkin's PCF with ∀-types, lazy lists and existential types, we show by example how the resulting logical relation can be used to prove properties of polymorphic types up to operational equivalence.

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Section: Introductionmentioning

confidence: 93%

Parametric polymorphism and operational equivalence

Pitts

2000

Math. Struct. Comp. Sci.

129

185

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“…To avoid such issues, which raise the complexity of our presentation but are ultimately irrelevant to the matter of predicate abstraction, we impose some restrictions on the way variables and labels can be used in the language by disallowing variable and label-typed terms in the language. Variables and labels are "named constants" rather than programming language identifiers [13]. We disallow recursion and higher-order functions because they introduce infinite-state models in a way that is not related to the store.…”

Section: The Languagementioning

confidence: 99%

Compositional Predicate Abstraction from Game Semantics

Bakewell

Ghica

2009

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. We introduce a technique for using conventional predicate abstraction methods to reduce the state-space of models produced using game semantics. We focus on an expressive procedural language that has both local store and local control, a language which enjoys a simple game-semantic model yet is expressive enough to allow non-trivial examples. Our compositional approach allows the verification of incomplete programs (e.g. libraries) and offers the opportunity for new heuristics for improved efficiency. Game-semantic predicate abstraction can be embedded in an abstraction-refinement cycle in a standard way, resulting in an improved version of our experimental model-checking tool Mage, and we illustrate it with several toy examples.

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“…For first order imperative programs the topic is thoroughly surveyed in the textbook by de Roever et al [19]. Object oriented programs have features in common with higher order imperative programs, for which representation independence is nontrivial owing to semantic difficulties [42,46,39]. Two sources of complication in object oriented programs are inheritance and the ubiquitous use of recursive classes; these were addressed by Cavalcanti and the author [15] -under the drastic simplification that copying is used instead of sharing.…”

Section: Pointer Confinement and Simulationmentioning

confidence: 99%