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General Formal Ontology (GFO): A Foundational Ontology Integrating
 Objects and Processes. Part I: Basic Principles’, Research Group Ontologies in Medicine (OntoMed) Technical Report Version 1.0.1, Accessed 24
, 2007
"... Research in ontology has in recent years become widespread in the field of information systems, in distinct areas of sciences, in business, in economy, and in industry. The importance of ontologies is increasingly recognized in fields diverse as in ecommerce, semantic web, enterprise, information in ..."
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Cited by 27 (5 self)
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Research in ontology has in recent years become widespread in the field of information systems, in distinct areas of sciences, in business, in economy, and in industry. The importance of ontologies is increasingly recognized in fields diverse as in ecommerce, semantic web, enterprise, information integration, qualitative modelling of physical
From coinductive proofs to exact real arithmetic
"... Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresp ..."
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Cited by 8 (6 self)
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Abstract. We give a coinductive characterisation of the set of continuous functions defined on a compact real interval, and extract certified programs that construct and combine exact real number algorithms with respect to the binary signed digit representation of real numbers. The data type corresponding to the coinductive definition of continuous functions consists of finitely branching nonwellfounded trees describing when the algorithm writes and reads digits. This is a pilot study in using prooftheoretic methods for obtaining certified algorithms in exact real arithmetic. 1
Proofs, programs, processes
"... Abstract. We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming la ..."
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Cited by 3 (2 self)
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Abstract. We study a realisability interpretation for inductive and coinductive definitions and discuss its application to program extraction from proofs. A speciality of this interpretation is that realisers are given by terms that correspond directly to programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. to the binary signed digit representation. 1
Realisability and adequacy for (co)induction
"... Abstract. We prove the correctness of a formalised realisability interpretation of extensions of firstorder theories by inductive and coinductive definitions in an untyped λcalculus with fixedpoints. We illustrate the use of this interpretation for program extraction by some simple examples in th ..."
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Cited by 1 (1 self)
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Abstract. We prove the correctness of a formalised realisability interpretation of extensions of firstorder theories by inductive and coinductive definitions in an untyped λcalculus with fixedpoints. We illustrate the use of this interpretation for program extraction by some simple examples in the area of exact real number computation, and hint at further nontrivial applications in computable analysis. 1
Minlog A Tool for Program Extraction Supporting Algebras and Coalgebras
"... Abstract. Minlog is an interactive system which implements prooftheoretic methods and applies them to verification and program extraction. We give an overview of Minlog and demonstrate how it can be used to exploit the computational content in (co)algebraic proofs and to develop correct and efficien ..."
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Cited by 1 (0 self)
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Abstract. Minlog is an interactive system which implements prooftheoretic methods and applies them to verification and program extraction. We give an overview of Minlog and demonstrate how it can be used to exploit the computational content in (co)algebraic proofs and to develop correct and efficient programs. We illustrate this by means of two examples: one about parsing, the other about exact real numbers in signed digit representation. 1
PreProceedings of the Ninth International Workshop on Automated Verification of Critical Systems
"... AVOCS, the workshop on Automated Verification of Critical Systems, is an annual meeting that brings together researchers and practitioners to exchange new results on tools and techniques for the verification of critical systems. Topics of interest cover all aspects of automated verification, includi ..."
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AVOCS, the workshop on Automated Verification of Critical Systems, is an annual meeting that brings together researchers and practitioners to exchange new results on tools and techniques for the verification of critical systems. Topics of interest cover all aspects of automated verification, including model checking, theorem proving, abstract interpretation, and refinement pertaining to various types of critical systems (safetycritical, securitycritical, businesscritical, performancecritical, etc.). Contributions that describe different techniques, or industrial case studies are encouraged.
Author manuscript, published in "Science of Computer Programming (2009)" DOI: 10.1016/j.scico.2007.09.002 Proofs of randomized algorithms in Coq
, 2009
"... Randomized algorithms are widely used for finding efficiently approximated solutions to complex problems, for instance primality testing and for obtaining good average behavior. Proving properties of such algorithms requires subtle reasoning both on algorithmic and probabilistic aspects of programs. ..."
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Randomized algorithms are widely used for finding efficiently approximated solutions to complex problems, for instance primality testing and for obtaining good average behavior. Proving properties of such algorithms requires subtle reasoning both on algorithmic and probabilistic aspects of programs. Thus, providing tools for the mechanization of reasoning is an important issue. This paper presents a new method for proving properties of randomized algorithms in a proof assistant based on higherorder logic. It is based on the monadic interpretation of randomized programs as probabilistic distributions (Giry, 1982; Ramsey and Pfeffer, 2002). It does not require the definition of an operational semantics for the language nor the development of a complex formalization of measure theory. Instead it uses functional and algebraic properties of unit interval. Using this model, we show the validity of general rules for estimating the probability for a randomized algorithm to satisfy specified properties. This approach addresses only discrete distributions and gives rules for analysing general recursive functions. We apply this theory to the formal proof of a program implementing a Bernoulli distribution from a coin flip and to the (partial) termination of several programs. All the theories and results presented in this paper have been fully formalized and proved in the Coq proof assistant. Key words: randomized algorithms, proof of partial and total correctness, functional language, axiomatic semantics, probability framing, callbyvalue, monadic interpretation
DOI 10.1007/s0022401193258 Proofs, Programs, Processes
, 2011
"... Abstract The objective of this paper is to provide a theoretical foundation for program extraction from inductive and coinductive proofs geared to practical applications. The novelties consist in the addition of inductive and coinductive definitions to a realizability interpretation for firstorder ..."
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Abstract The objective of this paper is to provide a theoretical foundation for program extraction from inductive and coinductive proofs geared to practical applications. The novelties consist in the addition of inductive and coinductive definitions to a realizability interpretation for firstorder proofs, a soundness proof for this system, and applications to the synthesis of nontrivial provably correct programs in the area of exact real number computation. We show that realizers, although per se untyped, can be assigned polymorphic recursive types and hence represent valid programs in a lazy functional programming language such as Haskell. Programs extracted from proofs using coinduction can be understood as perpetual processes producing infinite streams of data. Typical applications of such processes are computations in exact real arithmetic. As an example we show how to extract a program computing the average of two real numbers w.r.t. the binary signed digit representation.