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AlgorithmSupported Mathematical Theory Exploration: A Personal View and Strategy
, 2004
"... We present a personal view and strategy for algorithmsupported mathematical theory exploration and draw some conclusions for the desirable functionality of future mathematical software systems. The main points of emphasis are: The use of schemes for bottomup mathematical invention, the algorit ..."
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Cited by 18 (5 self)
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We present a personal view and strategy for algorithmsupported mathematical theory exploration and draw some conclusions for the desirable functionality of future mathematical software systems. The main points of emphasis are: The use of schemes for bottomup mathematical invention, the algorithmic generation of conjectures from failing proofs for topdown mathematical invention, and the possibility to program new reasoners within the logic on which the reasoners work ("metaprogramming").
Algorithm Synthesis by Lazy Thinking: Using Problem Schemes
 In [66
, 2004
"... Recently, as part of a general formal (i.e. logic based) methodology for mathematical knowledge management we also introduced a method for the automated synthesis of correct algorithms, which we called the lazy thinking method. For a given concrete problem specification (in predicate logic), the ..."
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Cited by 4 (0 self)
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Recently, as part of a general formal (i.e. logic based) methodology for mathematical knowledge management we also introduced a method for the automated synthesis of correct algorithms, which we called the lazy thinking method. For a given concrete problem specification (in predicate logic), the method tries out various algorithm schemes and derives specifications for the subalgorithms in the algorithm scheme.
Providing a Formal Linkage between MDG and HOL
, 2002
"... We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interface ..."
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Cited by 2 (2 self)
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We describe an approach for formally verifying the linkage between a symbolic state enumeration system and a theorem proving system. This involves the following three stages of proof. Firstly we prove theorems about the correctness of the translation part of the symbolic state system. It interfaces between low level decision diagrams and high level description languages. We ensure that the semantics of a program is preserved in those of its translated form. Secondly we prove linkage theorems: theorems that justify introducing a result from a state enumeration system into a proof system. Finally we combine the translator correctness and linkage theorems. The resulting new linkage theorems convert results to a high level language from the low level decision diagrams that the result was actually proved about in the state enumeration system.They justify importing lowlevel external verification results into a theorem prover. We use a linkage between the HOL system and a simplified version of the MDG system to illustrate the ideas and consider a small example that integrates two applications from MDG and HOL to illustrate the linkage theorems.
Formal mathematical theory exploration in theorema (4 lectures
 Invited talk at Summer School on Theoretical Computer Science
, 2005
"... ..."
1.1 Aims of Theorema: A Brief Overview
"... Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theoremasupported mathematical theory exploration by a case study (the automated synthesis of an algorithm fo ..."
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Theorema is a project that aims at supporting the entire process of mathematical theory exploration within one coherent logic and software system. This survey paper illustrates the style of Theoremasupported mathematical theory exploration by a case study (the automated synthesis of an algorithm for the construction of Gröbner Bases) and gives an overview on some reasoners and organizational tools for theory exploration developed in the Theorema project.