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Equational Reasoning in Algebraic Structures: a Complete Tactic
"... We present rational, a Coq tactic for equational reasoning in abelian groups, commutative rings, and fields. We give an mathematical description of the method that this tactic uses, which abstracts from Coq specifics. We prove that the method that rational uses is correct, and that it is complete fo ..."
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We present rational, a Coq tactic for equational reasoning in abelian groups, commutative rings, and fields. We give an mathematical description of the method that this tactic uses, which abstracts from Coq specifics. We prove that the method that rational uses is correct, and that it is complete for groups and rings. Completeness means that the method succeeds in proving an equality if and only if that equality is provable from the the group/ring axioms. Finally we characterize in what way our method is incomplete for fields.
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"... We present rational, a Coq tactic for equational reasoning in abelian groups, commutative rings, and fields. We give an mathematical description of the method that this tactic uses, which abstracts from Coq specifics. We prove that the method that rational uses is correct, and that it is complete fo ..."
Abstract
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We present rational, a Coq tactic for equational reasoning in abelian groups, commutative rings, and fields. We give an mathematical description of the method that this tactic uses, which abstracts from Coq specifics. We prove that the method that rational uses is correct, and that it is complete for groups and rings. Completeness means that the method succeeds in proving an equality if and only if that equality is provable from the the group/ring axioms. Finally we characterize in what way our method is incomplete for fields.