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Conference Papers Year : 2010

A formal quantifier elimination for algebraically closed fields

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Abstract

We prove formally that the first order theory of algebraically closed fields enjoy quantifier elimination, and hence is decidable. This proof is organized in two modular parts. We first reify the first order theory of rings and prove that quantifier elimination leads to decidability. Then we implement an algorithm which constructs a quantifier free formula from any first order formula in the theory of ring. If the underlying ring is in fact an algebraically closed field, we prove that the two formulas have the same semantic. The algorithm producing the quantifier free formula is programmed in continuation passing style, which leads to both a concise program and an elegant proof of semantic correctness.
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Dates and versions

inria-00464237 , version 1 (16-03-2010)
inria-00464237 , version 2 (19-03-2010)
inria-00464237 , version 3 (29-03-2010)

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Cyril Cohen, Assia Mahboubi. A formal quantifier elimination for algebraically closed fields. Symposium on the Integration of Symbolic Computation and Mechanised Reasoning, Calculemus, Jul 2010, Paris, France. pp.189-203, ⟨10.1007/978-3-642-14128-7_17⟩. ⟨inria-00464237v3⟩
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