The complexity of linear problems in fields
Journal of Symbolic Computation
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
A Quantifier Elimination Algorithm for Linear Real Arithmetic
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
Handbook of Practical Logic and Automated Reasoning
Handbook of Practical Logic and Automated Reasoning
Constructive type classes in Isabelle
TYPES'06 Proceedings of the 2006 international conference on Types for proofs and programs
Isabelle/HOL: a proof assistant for higher-order logic
Isabelle/HOL: a proof assistant for higher-order logic
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MKM'06 Proceedings of the 5th international conference on Mathematical Knowledge Management
Verifying and reflecting quantifier elimination for presburger arithmetic
LPAR'05 Proceedings of the 12th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Verifying mixed real-integer quantifier elimination
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Proving bounds for real linear programs in Isabelle/HOL
TPHOLs'05 Proceedings of the 18th international conference on Theorem Proving in Higher Order Logics
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CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
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FOPARA'11 Proceedings of the Second international conference on Foundational and Practical Aspects of Resource Analysis
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This paper presents verified quantifier elimination procedures for dense linear orders (two of them novel), for real and for integer linear arithmetic. All procedures are defined and verified in the theorem prover Isabelle/HOL, are executable and can be applied to HOL formulae themselves (by reflection). The formalization of the different theories is highly modular.