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24
Intuitionistic Reasoning about Shared Mutable Data Structure
 Millennial Perspectives in Computer Science
, 2000
"... Drawing upon early work by Burstall, we extend Hoare's approach to proving the correctness of imperative programs, to deal with programs that perform destructive updates to data structures containing more than one pointer to the same location. The key concept is an "independent conjunction" P & ..."
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Cited by 107 (5 self)
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Drawing upon early work by Burstall, we extend Hoare's approach to proving the correctness of imperative programs, to deal with programs that perform destructive updates to data structures containing more than one pointer to the same location. The key concept is an "independent conjunction" P & Q that holds only when P and Q are both true and depend upon distinct areas of storage. To make this concept precise we use an intuitionistic logic of assertions, with a Kripke semantics whose possible worlds are heaps (mapping locations into tuples of values).
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 36 (8 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
Reasoning about local variables with operationallybased logical relations
 In LICS
, 1996
"... A parametric logical relation between the phrases of an Algollike language is presented. Its definition involves the structural operational semantics of the language, but was inspired by recent denotationallybased work of O’Hearn and Reynolds on translating Algol into a predicatively polymorphic l ..."
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Cited by 32 (3 self)
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A parametric logical relation between the phrases of an Algollike language is presented. Its definition involves the structural operational semantics of the language, but was inspired by recent denotationallybased work of O’Hearn and Reynolds on translating Algol into a predicatively polymorphic linear lambda calculus. The logical relation yields an applicative characterisation of contextual equivalence for the language and provides a useful (and complete) method for proving equivalences. Its utility is illustrated by giving simple and direct proofs of some contextual equivalences, including an interesting equivalence due to O’Hearn which hinges upon the undefinability of ‘snapback ’ operations (and which goes beyond the standard suite of ‘MeyerSieber ’ examples). Whilst some of the mathematical intricacies of denotational semantics are avoided, the hard work in this operational approach lies in establishing the ‘fundamental property’ for the logical relation—the proof of which makes use of a compactness property of fixpoint recursion with respect to evaluation of phrases. But once this property has been established, the logical relation provides a verification method with an attractively low mathematical overhead. 1.
Objects and classes in Algollike languages
 Information and Computation
, 2002
"... Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and ..."
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Cited by 22 (5 self)
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Many objectoriented languages used in practice descend from Algol. With this motivation, we study the theoretical issues underlying such languages via the theory of Algollike languages. It is shown that the basic framework of this theory extends cleanly and elegantly to the concepts of objects and classes. An important idea that comes to light is that classes are abstract data types, whose theory corresponds to that of existential types. Equational and Hoarelike reasoning methods, and relational parametricity provide powerful formal tools for reasoning about Algollike objectoriented programs. 1
The RegularLanguage Semantics of SecondOrder Idealized ALGOL
, 2003
"... We explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a nontrivial fragment of Idealized Algol (IA) by expressing sets of complete plays as regular languages. Being derived directly from the fully abstract game semantics for IA, our model inh ..."
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Cited by 20 (8 self)
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We explain how recent developments in game semantics can be applied to reasoning about equivalence of terms in a nontrivial fragment of Idealized Algol (IA) by expressing sets of complete plays as regular languages. Being derived directly from the fully abstract game semantics for IA, our model inherits its good theoretical properties; in fact, for secondorder IA taken as a standalone language the regular language model is fully abstract. The method is algorithmic and formal, which makes it suitable for automation. We show how reasoning is carried out using a metalanguage of extended regular expressions, a language for which equivalence is decidable.
Objects, Interference, and the Yoneda Embedding
, 1995
"... We present a new semantics for Algollike languages that combines methods from two prior lines of development: ffl the objectbased approach of [21,22], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functorcategory approach initiat ..."
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Cited by 16 (7 self)
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We present a new semantics for Algollike languages that combines methods from two prior lines of development: ffl the objectbased approach of [21,22], where the meaning of an imperative program is described in terms of sequences of observable actions, and ffl the functorcategory approach initiated by Reynolds [24], where the varying nature of the runtime stack is explained using functors from a category of store shapes to a category of cpos. The semantics
Abstract Models of Storage
, 2000
"... This note is a historical survey of Christopher Strachey's influence on the development of semantic models of assignment and storage management in procedural languages. ..."
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Cited by 8 (0 self)
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This note is a historical survey of Christopher Strachey's influence on the development of semantic models of assignment and storage management in procedural languages.
Note on Algol and Conservatively Extending Functional Programming
, 1995
"... A simple Idealized Algol is considered, based on Reynolds's "essence of Algol." It is shown that observational equivalence in this language conservatively extends observational equivalence in its assignmentfree functional sublanguage. 1 Introduction In "The essence of Algol," Reynolds (1981) prese ..."
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Cited by 4 (0 self)
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A simple Idealized Algol is considered, based on Reynolds's "essence of Algol." It is shown that observational equivalence in this language conservatively extends observational equivalence in its assignmentfree functional sublanguage. 1 Introduction In "The essence of Algol," Reynolds (1981) presents a view of Algol as a callbyname language based on the typed calculus, with "imperative" primitive types. A central feature of the design is the interaction between assignment and procedures. Side effects are wholly isolated in a primitive type comm of commands, and do not occur when computing a value of functional type. That is to say, side effects in procedures are latent, in the sense that an effect occurs only by evaluating a procedure call as a term of type comm. As a result, function types retain a genuine "functional character." For instance, the full fi and j laws are valid equivalences in Algollike languages. This functional aspect of Algol has been emphasized strongly by Reyn...
Syntactic Control of Interference for Separation Logic
"... Separation Logic has witnessed tremendous success in recent years in reasoning about programs that deal with heap storage. Its success owes to the fundamental principle that one should keep separate areas of the heap storage separate in program reasoning. However, the way Separation Logic deals with ..."
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Cited by 4 (1 self)
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Separation Logic has witnessed tremendous success in recent years in reasoning about programs that deal with heap storage. Its success owes to the fundamental principle that one should keep separate areas of the heap storage separate in program reasoning. However, the way Separation Logic deals with program variables continues to be based on traditional Hoare Logic without taking any benefit of the separation principle. This has led to unwieldy proof rules suffering from lack of clarity as well as questions surrounding their soundness. In this paper, we extend the separation idea to the treatment of variables in Separation Logic, especially Concurrent Separation Logic, using the system of Syntactic Control of Interference proposed by Reynolds in 1978. We extend the original system with permission algebras, making it more powerful and able to deal with the issues of concurrent programs. The result is a streamined presentation of Concurrent Separation Logic, whose rules are memorable and soundness obvious. We also include a discussion of how the new rules impact the semantics and devise static analysis techniques to infer the required permissions automatically. Categories and Subject Descriptors D.3.1 [Programming Languages]: