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Formal Proof Sketches
 In Proceedings of TYPES’03, volume 3085 of LNCS
, 2002
"... We de ne the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants. 1 ..."
Abstract

Cited by 22 (3 self)
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We de ne the notion of formal proof sketch for the mathematical language Mizar. We show by examples that formal proof sketches are very close to informal mathematical proofs. We discuss some ways in which formal proof sketches might be used to improve mathematical proof assistants. 1
Textbook proofs meet formal logic  the problem of underspecification and granularity
 Proceedings of MKM’05, volume 3863 of LNAI, IUB
, 2006
"... Abstract. Unlike computer algebra systems, automated theorem provers have not yet achieved considerable recognition and relevance in mathematical practice. A significant shortcoming of mathematical proof assistance systems is that they require the fully formal representation of mathematical content, ..."
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Cited by 7 (3 self)
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Abstract. Unlike computer algebra systems, automated theorem provers have not yet achieved considerable recognition and relevance in mathematical practice. A significant shortcoming of mathematical proof assistance systems is that they require the fully formal representation of mathematical content, whereas in mathematical practice an informal, naturallanguagelike representation where obvious parts are omitted is common. We aim to support mathematical paper writing by integrating a scientific text editor and mathematical assistance systems such that mathematical derivations authored by human beings in a mathematical document can be automatically checked. To this end, we first define a calculusindependent representation language for formal mathematics that allows for underspecified parts. Then we provide two systems of rules that check if a proof is correct and at an acceptable level of granularity. These checks are done by decomposing the proof into basic steps that are then passed on to proof assistance systems for formal verification. We illustrate our approach using an example textbook proof. 1