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29
An Efficient Coq Tactic for Deciding Kleene Algebras
, 2009
"... We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations almost instantaneously. The corresponding decision procedure was ..."
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We present a reflexive tactic for deciding the equational theory of Kleene algebras in the Coq proof assistant. This tactic relies on a careful implementation of efficient finite automata algorithms, so that it solves casual equations almost instantaneously. The corresponding decision procedure was proved correct and complete; correctness is established w.r.t. any model (including binary relations), by formalising Kozen’s initiality theorem.
On Automating the Calculus of Relations
 In: Proc. IJCAR. Vol. 5195. LNCS
, 2008
"... Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This ..."
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Abstract. Relation algebras provide abstract equational axioms for the calculus of binary relations. They name an established area of mathematics with various applications in computer science. We prove more than hundred theorems of relation algebras with offtheshelf automated theorem provers. This yields a basic calculus from which more advance applications can be explored. Here, we present two examples from the formal methods literature. Our experiments not only further underline the feasibility of automated deduction in complex algebraic structures and provide theorem proving benchmarks, they also pave the way for lifting established formal methods such as B or Z to a new level of automation. 1
Algebraic Separation Logic
, 2010
"... We present an algebraic approach to separation logic. In particular, we give an algebraic characterisation for assertions of separation logic, discuss different classes of assertions and prove abstract laws fully algebraically. After that, we use our algebraic framework to give a relational semantic ..."
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Cited by 12 (7 self)
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We present an algebraic approach to separation logic. In particular, we give an algebraic characterisation for assertions of separation logic, discuss different classes of assertions and prove abstract laws fully algebraically. After that, we use our algebraic framework to give a relational semantics of the commands of the simple programming language associated with separation logic. On this basis we prove the frame rule in an abstract and concise way. We also propose a more general version of separating conjunction which leads to a frame rule that is easier to prove. In particular, we show how to algebraically formulate the requirement that a command does not change certain variables; this is also expressed more conveniently using the generalised separating conjunction. The algebraic view does not only yield new insights on separation logic but also shortens proofs due to a point free representation. It is largely firstorder and hence enables the use of offtheshelf automated theorem provers for verifying properties at a more abstract level.
Automated engineering of relational and algebraic methods in Isabelle/HOL  (invited tutorial
 In Proc. RAMICS, volume 6663 of Lecture Notes in Computer Science
, 2011
"... Abstract. We present a new integration of relational and algebraic methods in the Isabelle/HOL theorem proving environment. It consists of a fine grained hierarchy of algebraic structures based on Isabelle's type classes and locales, and a repository of more than 800 facts obtained by automate ..."
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Abstract. We present a new integration of relational and algebraic methods in the Isabelle/HOL theorem proving environment. It consists of a fine grained hierarchy of algebraic structures based on Isabelle's type classes and locales, and a repository of more than 800 facts obtained by automated theorem proving. We demonstrate further benefits of Isabelle for hypothesis learning, duality reasoning, theorem instantiation, and reasoning across models and theories. Our work forms the basis for a reference repository and a program development environment based on algebraic methods. It can also be used by mathematicians for exploring and integrating new variants.
Deciding Kleene Algebras in Coq
 Logical Methods in Computer Science
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 4 (0 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Deciding regular expressions (in)equivalence in Coq
 Proc. RAMiCS 2012, volume 7560 of LNCS
, 2012
"... Abstract. This work presents a mechanically verified implementation of an algorithm for deciding regular expression (in)equivalence within the Coq proof assistant. This algorithm decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivati ..."
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Abstract. This work presents a mechanically verified implementation of an algorithm for deciding regular expression (in)equivalence within the Coq proof assistant. This algorithm decides regular expression equivalence through an iterated process of testing the equivalence of their partial derivatives and also does not construct the underlying automata. Our implementation has a refutation step that improves the general efficiency of the decision procedure by enforcing the inequivalence of regular expressions at early stages of computation. Recent theoretical and experimental research provide evidence that this method is, on average, more efficient than the classical methods based in automata. We present some performance tests and comparisons with similar approaches.
http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva207378 Program Analysis and Verification based on Kleene Algebra in Isabelle/HOL
"... N.B. When citing this work, cite the original published paper. Permanent link to this version: ..."
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N.B. When citing this work, cite the original published paper. Permanent link to this version:
Simplifying Pointer Kleene Algebra
"... Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving s ..."
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Pointer Kleene algebra has proved to be a useful abstraction for reasoning about reachability properties and correctly deriving pointer algorithms. Unfortunately it comes with a complex set of operations and defining (in)equations which exacerbates its practicability with automated theorem proving systems but also its use by theory developers. Therefore we provide an easier access to this approach by simpler axioms and laws which also are more amenable to automatic theorem proving systems. 1