Proofs of equalities may be built from assumptions using proof rules for reflexivity, symmetry, and transitivity. Reflexivity is an axiom proving x=x for any x; symmetry is a 1-p...
It is a well-known fact that algorithms are often hidden inside mathematical proofs. If these proofs are formalized inside a proof assistant, then a mechanism called extraction ca...
Abstract. The theorem prover Isabelle is used to formalise and reproduce some of the styles of reasoning used by Newton in his Principia. The Principia's reasoning is resolute...
Abstract. We have argued previously that the e ectiveness of a veri cation system derives not only from the power of its individual features for expression and deduction, but from ...
Abstract. In this work we study the problem of reconstructing an image from a perceptual segmentation based on a geometric classification of its points using non-linear curvature f...