Book ChapterDOI
A Spatial Logic for Concurrency (Part II)
Luís Caires,Luca Cardelli +1 more
- pp 209-225
TLDR
Modal logic for describing the spatial organization and the behavior of distributed systems is presented, including spatial operations corresponding to process composition and name hiding, and a fresh quantifier.Abstract:
We present a modal logic for describing the spatial organization and the behavior of distributed systems. In addition to standard logical and temporal operators, our logic includes spatial operations corresponding to process composition and name hiding, and a fresh quantifier.read more
Citations
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Journal ArticleDOI
Nominal Logic: A First Order Theory of Names and Binding
TL;DR: Nominal Logic is introduced, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping, for freshness of names, and for name-binding, and its axioms express properties of these constructs satisfied by the FM-sets model of syntax involving binding.
Proceedings ArticleDOI
A sequent calculus for nominal logic
Murdoch J. Gabbay,James Cheney +1 more
TL;DR: In this article, a new logic called fresh logic (FL) admits cut-elimination, which is a proof-theoretic foundation for nominal logic programming and shows how to interpret FO/spl lambda lambda//spl nabla/, another logic with a self-dual quantifier, within FL.
Journal ArticleDOI
A spatial logic for concurrency (part I)
Luís Caires,Luca Cardelli +1 more
TL;DR: A logic that can express properties of freshness, secrecy, structure, and behavior of concurrent systems is presented, which includes spatial operations corresponding to composition, local name restriction, and a primitive fresh name quantifier.
Journal ArticleDOI
Nominal unification
TL;DR: A generalisation of first-order unification to the practically important case of equations between terms involving binding operations, which retains the latter's pleasant properties: unification problems involving α-equivalence and freshness are decidable; and solvable problems possess most general solutions.
Proceedings ArticleDOI
FreshML: programming with binders made simple
TL;DR: This paper is to show that a standard type system without freshness inference suffices for FreshML's crucial correctness property that values of datatypes involving binders are operationally equivalent if and only if they represent a-equivalent pieces of object-level syntax.
References
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Book
Communicating and Mobile Systems: the Pi-Calculus
TL;DR: Communicating Systems: Behaviour of automata and Observation equivalence: theory, examples, and Discussion and related work Bibliography Index.
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
Results on the propositional μ-calculus
TL;DR: A propositional μ-calculus L μ is defined and study, which consists essentially of propositional modal logic with a least fixpoint operator that is syntactically simpler yet strictly more expressive than Propositional Dynamic Logic (PDL).
Journal ArticleDOI
Algebraic laws for nondeterminism and concurrency
Matthew Hennessy,Robin Milner +1 more
TL;DR: The paper demonstrates, for a sequence of simple languages expressing finite behaviors, that in each case observation congruence can be axiomatized algebraically and the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties.
Book
Basic proof theory
TL;DR: N- systems and H-systems and Gentzen systems, proof theory of arithmetic, second-order logic, and solutions to selected exercises.