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The Isabelle Collections Framework
"... The Isabelle Collections Framework (ICF) provides a unified framework for using verified collection data structures in Isabelle/HOL formalizations and generating efficient functional code in ML, Haskell, and OCaml. Thanks to its modularity, it is easily extensible and supports switching to differen ..."
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The Isabelle Collections Framework (ICF) provides a unified framework for using verified collection data structures in Isabelle/HOL formalizations and generating efficient functional code in ML, Haskell, and OCaml. Thanks to its modularity, it is easily extensible and supports switching to different data structures any time. For good integration with applications, a data refinement approach separates the correctness proofs from implementation details. The generated code based on the ICF lies in better complexity classes than the one that uses Isabelle’s default setup (logarithmic vs. linear time). In a case study with tree automata, we demonstrate that the ICF is easy to use and efficient: An ICF based, verified tree automata library outperforms the unverified Timbuk/Taml library by a factor of 14.
The MyhillNerode Theorem based on Regular Expressions
 The Archive of Formal Proofs. http://afp.sourceforge.net/develentries/ MyhillNerode.shtml
, 2011
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
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Cited by 14 (3 self)
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Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode theorem—can be recreated using only regular expressions. 1
Verified Decision Procedures for MSO on Words Based on Derivatives of Regular Expressions
"... Monadic secondorder logic on finite words (MSO) is a decidable yet expressive logic into which many decision problems can be encoded. Since MSO formulas correspond to regular languages, equivalence of MSO formulas can be reduced to the equivalence of some regular structures (e.g. automata). This pa ..."
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Monadic secondorder logic on finite words (MSO) is a decidable yet expressive logic into which many decision problems can be encoded. Since MSO formulas correspond to regular languages, equivalence of MSO formulas can be reduced to the equivalence of some regular structures (e.g. automata). This paper presents a verified functional decision procedure for MSO formulas that is not based on automata but on regular expressions. Functional languages are ideally suited for this task: regular expressions are data types and functions on them are defined by pattern matching and recursion and are verified by structural induction. Decision procedures for regular expression equivalence have been formalized before, usually based on Brzozowski derivatives. Yet, for a straightforward embedding of MSO formulas into regular expressions an extension of regular expressions with a projection operation is required. We prove total correctness and completeness of an equivalence checker for regular expressions extended in that way. We also define a languagepreserving translation of formulas into regular expressions with respect to two different semantics of MSO. Our results have been formalized and verified in the theorem prover Isabelle. Using Isabelle’s code generation facility, this yields purely functional, formally verified programs that decide equivalence of MSO formulas.
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, 2008
"... Abstract Based on inductive definitions, we develop a tool that automates the definition of partial recursive functions in higherorder logic (HOL) and provides appropriate proof rules for reasoning about them. Termination is modeled by an inductive domain predicate which follows the structure of th ..."
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Abstract Based on inductive definitions, we develop a tool that automates the definition of partial recursive functions in higherorder logic (HOL) and provides appropriate proof rules for reasoning about them. Termination is modeled by an inductive domain predicate which follows the structure of the recursion. Since a partial induction rule is available immediately, partial correctness properties can be proved before termination is established. It turns out that this modularity also facilitates termination arguments for total functions, in particular for nested recursions. Our tool is implemented as a definitional package extending Isabelle/HOL. Various extensions provide convenience to the user: pattern matching, default values, tail recursion,
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, 2010
"... This work presents a formalization of a library for automata on bit strings. It forms the basis of a reflectionbased decision procedure for Presburger arithmetic, which is efficiently executable thanks to Isabelle’s code generator. With this work, we therefore provide a mechanized proof of a wellk ..."
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This work presents a formalization of a library for automata on bit strings. It forms the basis of a reflectionbased decision procedure for Presburger arithmetic, which is efficiently executable thanks to Isabelle’s code generator. With this work, we therefore provide a mechanized proof of a wellknown connection between logic and automata
Verified Synthesis of KnowledgeBased Programs in Finite Synchronous Environments
, 2013
"... Knowledgebased programs (KBPs) are a formalism for directly relating an agent’s knowledge and behaviour. Here we present a general scheme for compiling KBPs to executable automata with a proof of correctness in Isabelle/HOL. We develop the algorithm topdown, using Isabelle’s locale mechanism to st ..."
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Knowledgebased programs (KBPs) are a formalism for directly relating an agent’s knowledge and behaviour. Here we present a general scheme for compiling KBPs to executable automata with a proof of correctness in Isabelle/HOL. We develop the algorithm topdown, using Isabelle’s locale mechanism to structure these proofs, and show that two classic examples
Theoretical Informatics and Applications Informatique Théorique et Applications Will be set by the publisher A FORMALISATION OF THE MYHILLNERODE THEOREM BASED ON REGULAR EXPRESSIONS ∗
"... Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is th ..."
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Abstract. There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOLbased theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none of which are inductive datatypes. Also convenient operations for disjoint unions of graphs, matrices and functions are not easily formalisiable in HOL. In contrast, regular expressions can be defined conveniently as a datatype and a corresponding reasoning infrastructure comes for free. We show in this paper that a central result from formal language theory—the MyhillNerode Theorem—can be recreated using only regular expressions. From this theorem many closure properties of regular languages follow. 1991 Mathematics Subject Classification. 68Q45. 1.
Noname manuscript No. (will be inserted by the editor)
"... Abstract This paper presents a probabilistic relational modelling (implementation) of the major probabilistic retrieval models. Such a highlevel implementation is useful since it supports the ranking of any object, it allows for the reasoning across structured and unstructured data, and it gives th ..."
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Abstract This paper presents a probabilistic relational modelling (implementation) of the major probabilistic retrieval models. Such a highlevel implementation is useful since it supports the ranking of any object, it allows for the reasoning across structured and unstructured data, and it gives the software (knowledge) engineer control over ranking and thus supports customisation. The contributions of this paper include the specification of probabilistic SQL (PSQL) and probabilistic relational algebra (PRA), a new relational operator for probability estimation (the relational Bayes), the probabilistic relational modelling of retrieval models, a comparison of modelling retrieval with traditional SQL versus modelling retrieval with PSQL, and a comparison of the performance of probability estimation with traditional SQL versus PSQL. The main findings are that the PSQL/PRA paradigm allows for the description of advanced retrieval models, is suitable for solving largescale retrieval tasks, and outperforms traditional SQL in terms of abstraction and performance regarding probability estimation.
devant le jury composé de:
, 2006
"... dans l’école doctorale de Mathématiques, Sciences et Technologies de ..."
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