Algorithm Synthesis by Lazy Thinking: Examples and Implementation in Theorema

Recently, we proposed a systematic method for top-down synthesis and verification of lemmata and algorithms called “lazy thinking method” as a part of systematic mathematical theory exploration (mathematical knowledge management). The lazy thinking method is characterized: •by using a library of the...

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Bibliographic Details
Published in:Electronic notes in theoretical computer science Vol. 93; pp. 24 - 59
Main Authors: Buchberger, Bruno, Crăciun, Adrian
Format: Journal Article
Language:English
Published: Elsevier B.V 18.02.2004
Subjects:
algorithm correctness
algorithm invention
algorithm schemes
algorithm verification
conjecture generation
didactics of programming
lazy thinking
learning from failure
mathematical knowledge management
mathematical knowledge retrieval
merge-sort
merging
program synthesis
re-usable algorithms
requirement engineering
sorting
Theorema
requirement engineering
merging
merge-sort
algorithm verification
program synthesis
re-usable algorithms
lazy thinking
algorithm schemes
learning from failure
didactics of programming
Theorema
mathematical knowledge retrieval
sorting
algorithm invention
algorithm correctness
conjecture generation
mathematical knowledge management
ISSN:1571-0661, 1571-0661
Online Access:Get full text
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Summary:Recently, we proposed a systematic method for top-down synthesis and verification of lemmata and algorithms called “lazy thinking method” as a part of systematic mathematical theory exploration (mathematical knowledge management). The lazy thinking method is characterized: •by using a library of theorem and algorithm schemes•and by using the information contained in failing attempts to prove the schematic theorem or the correctness theorem for the algorithm scheme for inventing lemmata or requirements for subalgorithms, respectively. In this paper, we give a couple of examples for algorithm synthesis using the lazy thinking paradigm. These examples illustrate how the synthesized algorithm depends on the algorithm scheme used. Also, we give details about the implementation of the lazy thinking algorithm synthesis method in the frame of the Theorema system. In this implementation, the synthesis of the example algorithms can be carried out completely automatically, i.e. without any user interaction.
ISSN:1571-0661
1571-0661
DOI:10.1016/j.entcs.2003.12.027