Abstract
We propose the basis of a higher-order logical framework to axiomatize and build proofs in Hilbert’s elementary geometry in which intuitionistic aspects are emphasized. More precisely, we use the Calculus of inductive constructions and the system Coq to specify geometric concepts and to study and interactively handle proofs for the first two groups of Hilbert’s axiomatics. It is the first step to a formalization well adapted to the definition of primitive operations that are used in many different geometric algorithms.
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Dehlinger, C., Dufourd, JF., Schreck, P. (2001). Higher-Order Intuitionistic Formalization and Proofs in Hilbert’s Elementary Geometry. In: Richter-Gebert, J., Wang, D. (eds) Automated Deduction in Geometry. ADG 2000. Lecture Notes in Computer Science(), vol 2061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45410-1_17
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DOI: https://doi.org/10.1007/3-540-45410-1_17
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