Automatic Synthesis of Decision Procedures: A Case Study of Ground and Linear Arithmetic

Authors:
Predrag Janičić;Alan Bundy
Affiliations:
Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 Belgrade, Serbia;School of Informatics, University of Edinburgh, Appleton Tower, Crichton St, Edinburgh EH8 9LE, UK
Venue:
Calculemus '07 / MKM '07 Proceedings of the 14th symposium on Towards Mechanized Mathematical Assistants: 6th International Conference
Year:
2007

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Abstract

We address the problem of automatic synthesis of decision procedures. Our synthesis mechanism consists of several stages and sub-mechanisms and is well-suited to the proof-planning paradigm. The system (adeptus), that we present in this paper, synthesised a decision procedure for ground arithmetic completely automatically and it used some specific method generators in generating a decision procedure for linear arithmetic, in only a few seconds of cputime. We believe that this approach can lead to automated assistance in constructing decision procedures and to more reliable implementations of decision procedures.