Real algebraic strategies for metitarski proofs

Authors:
Grant Olney Passmore;Lawrence C. Paulson;Leonardo de Moura
Affiliations:
Computer Laboratory, University of Cambridge, UK, LFCS, University of Edinburgh, UK;Computer Laboratory, University of Cambridge, UK;Microsoft Research, Redmond
Venue:
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
Year:
2012

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Abstract

MetiTarski [1] is an automatic theorem prover that can prove inequalities involving sin, cos, exp, ln, etc. During its proof search, it generates a series of subproblems in nonlinear polynomial real arithmetic which are reduced to true or false using a decision procedure for the theory of real closed fields (RCF). These calls are often a bottleneck: RCF is fundamentally infeasible. However, by studying these subproblems, we can design specialised variants of RCF decision procedures that run faster and improve MetiTarski's performance.