Details:

Title	Integrating Computer Algebra into Proof Planning
Author(s)	Manfred Kerber, Michael Kohlhase, Volker Sorge
Type	Article in Journal
Abstract	Mechanized reasoning systems and computer algebra systems have different objectives. Their integration is highly desirable, since formal proofs often involve both of the two different tasks proving and calculating. Even more important, proof and computation are often interwoven and not easily separable. In this article we advocate an integration of computer algebra into mechanized reasoning systems at the proof plan level. This approach allows us to view the computer algebra algorithms as methods, that is, declarative representations of the problem-solving knowledge specific to a certain mathematical domain. Automation can be achieved in many cases by searching for a hierarchic proof plan at the method level by using suitable domain-specific control knowledge about the mathematical algorithms. In other words, the uniform framework of proof planning allows us to solve a large class of problems that are not automatically solvable by separate systems. Our approach also gives an answer to the correctness problems inherent in such an integration. We advocate an approach where the computer algebra system produces high-level protocol information that can be processed by an interface to derive proof plans. Such a proof plan in turn can be expanded to proofs at different levels of abstraction, so the approach is well suited for producing a high-level verbalized explication as well as for a low-level, machine-checkable, calculus-level proof. We present an implementation of our ideas and exemplify them using an automatically solved example.
Keywords	mechanised reasoning, computer algebra, hierarchical proof planning, proof checking
Length	29
File
URL	dx.doi.org/10.1023/A:1006059810729
Language	English
Journal	Journal of Automated Reasoning
Volume	21
Number	3
Pages	327-355
Year	1998
Month	December
Translation	No
Refereed	No