Adjunct elimination in Context Logic for trees
Cristiano Calcagno,Thomas Dinsdale-Young,Philippa Gardner +2 more
- Vol. 208, Iss: 5, pp 474-499
TLDR
This work proves adjunct-elimination results for Context Logic applied to trees for multi-holed Context Logic, following previous results by Lozes for Separation Logic and Ambient Logic.Abstract:
We study adjunct-elimination results for Context Logic applied to trees, following previous results by Lozes for Separation Logic and Ambient Logic. In fact, it is not possible to prove such elimination results for the original single-holed formulation of Context Logic. Instead, we prove our results for multi-holed Context Logic.read more
Citations
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DissertationDOI
Local reasoning about Web programs
TL;DR: This thesis makes use of recent developments in program reasoning using context logic to provide the first formal, compositional specification for the Fundamental Interfaces of DOM Core Level 1, presenting both a bigstep operational semantics for the necessary operations of the library and a context logic for reasoning about programs which use the library.
Book ChapterDOI
Small specifications for tree update
Philippa Gardner,Mark Wheelhouse +1 more
TL;DR: This work introduces Segment Logic, which provides a more fine-grained analysis of the tree structure and yields small specifications, as well as being aesthetically pleasing, small specifications are important for reasoning about concurrent tree update.
Proceedings Article
An Algebraic Glimpse at Bunched Implications and Separation Logic
Peter Jipsen,Tadeusz Litak +1 more
TL;DR: The logic of Bunched Implications (BI) and Separation Logic is overviewed from a perspective inspired by Hiroakira Ono's algebraic approach to substructural logics and an algebraic proof of cut elimination in the setting of residuated frames of Galatos and Jipsen is presented.
DissertationDOI
Structural separation logic
TL;DR: This thesis presents structural separation Logic, a novel program reasoning approach for software that manipulates both standard heaps and structured data such as lists and trees, and presents an axiomatic semantics for the Document Object Model in structural separation logic.
Book ChapterDOI
DOM: Specification and Client Reasoning
TL;DR: An axiomatic specification of a key fragment of DOM using structural separation logic allows us to develop modular reasoning about client programs that call the DOM.
References
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Proceedings ArticleDOI
Separation logic: a logic for shared mutable data structures
TL;DR: An extension of Hoare logic that permits reasoning about low-level imperative programs that use shared mutable data structure is developed, including extensions that permit unrestricted address arithmetic, dynamically allocated arrays, and recursive procedures.
Journal ArticleDOI
The logic of bunched implications.
Peter W. O'Hearn,David J. Pym +1 more
TL;DR: A logic BI in which a multiplicative (or linear) and an additive (or intuitionistic) implication live side-by-side is introduced and computational interpretations, based on sharing, at both the propositional and predicate levels are discussed.
Journal ArticleDOI
BI as an assertion language for mutable data structures
Samin Ishtiaq,Peter W. O'Hearn +1 more
TL;DR: A model in which the law of the excluded middle holds is given, thus showing that the approach to logic BI of bunched implications of O'Hearn and Pym is compatible with classical logic.
Proceedings ArticleDOI
Anytime, anywhere: modal logics for mobile ambients
Luca Cardelli,Andrew D. Gordon +1 more
TL;DR: In order to describe properties of mobile computations the authors devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model.
Book ChapterDOI
A Semantic Basis for Local Reasoning
Hongseok Yang,Peter W. O'Hearn +1 more
TL;DR: A semantic analysis of a recently proposed formalism for local reasoning, where a specification can concentrate on only those cells that a program accesses, shows the soundness and completeness of a rule that allows frame axioms, which describe invariant properties of portions of heap memory, to be inferred automatically.