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Extending the HOL theorem prover with a Computer Algebra System to Reason about the Reals
 Higher Order Logic Theorem Proving and its Applications (HUG `93
, 1993
"... In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from ..."
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Cited by 33 (4 self)
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In this paper we describe an environment for reasoning about the reals which combines the rigour of a theorem prover with the power of a computer algebra system. 1 Introduction Computer theorem provers are a topic of research interest in their own right. However much of their popularity stems from their application in computeraided verification, i.e. proving that designs of electronic or computer systems, programs, protocols and cryptosystems satisfy certain properties. Such proofs, as compared with the proofs one finds in mathematics books, usually involve less sophisticated central ideas, but contain far more technical Supported by the Science and Engineering Research Council, UK. y Supported by SERC grant GR/G 33837 and a grant from DSTO Australia. details and therefore tend to be much more difficult for humans to write or check without making mistakes. Hence it is appealing to let computers help. Some fundamental mathematical theories, such as arithmetic, are usually requi...
Reasoning About the Reals: the marriage of HOL and Maple
, 1993
"... . Computer algebra systems are extremely powerful and flexible, but often give results which require careful interpretation or are downright incorrect. By contrast, theorem provers are very reliable but lack the powerful specialized decision procedures and heuristics of computer algebra systems. In ..."
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Cited by 10 (0 self)
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. Computer algebra systems are extremely powerful and flexible, but often give results which require careful interpretation or are downright incorrect. By contrast, theorem provers are very reliable but lack the powerful specialized decision procedures and heuristics of computer algebra systems. In this paper we try to get the best of both worlds by careful exploitation of a link between a theorem prover and a computer algebra system. 1 Motivation In the HOL theorem prover[5], a theory of real numbers has been developed, using a rigorous definition in terms of Dedekind cuts [8]. It is therefore possible to apply HOL to areas traditionally within the purview of Computer Algebra Systems (CASs). This offers two main benefits. Firstly, theorem provers are designed to manipulate proofs and theorems in a coherent and structured way, with all concepts clearly defined. By contrast, most CASs have no concept of `logic' as such  they usually take an algebraic expression and return another pur...
“But you have to remember P. J. Daniell of Sheffield”
"... Abstract: P. J. Daniell is a mysterious figure who appears at several turns in the history of mathematics in the 20th century, in the fields of integration, stochastic processes, statistics, control engineering and even in the history of English mathematical education. The main focus of this paper i ..."
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Abstract: P. J. Daniell is a mysterious figure who appears at several turns in the history of mathematics in the 20th century, in the fields of integration, stochastic processes, statistics, control engineering and even in the history of English mathematical education. The main focus of this paper is on Daniell’s work in relation to the development of probability in the twentieth century. But as it seems that no survey of his work and life has been attempted for 60 years I try to consider all his contributions and place them in an appropriate historical context. Résumé: P. J. Daniell est un personnage mystérieux qui apparaît à plusieurs moments clefs de l’histoire des mathématiques du 20ème siècle, dans le domaine de l’intégration, des processus stochastiques, des statistiques, de la commande optimale et même dans l’histoire de l’éducation mathématique en Angleterre. Ce papier se concentre sur le travail de Daniell en relation avec le développement des probabilités au vingtième siècle. Comme aucune description de sa vie et de son œuvre n’a sembletil été réalisée depuis 60 ans, nous essayons de dresser un tableau de l’ensemble de ses contributions et de les placer dans un contexte historique approprié.