Mathematical Knowledge Management: Second International by Andrew A. Adams (auth.), Andrea Asperti, Bruno Buchberger,

By Andrew A. Adams (auth.), Andrea Asperti, Bruno Buchberger, James Harold Davenport (eds.)

This booklet constitutes the refereed lawsuits of the second one overseas convention on Mathematical wisdom administration, MKM 2003, held in Betinoro, Italy, in February 2003.

The sixteen revised complete papers offered including an invited paper have been conscientiously reviewed and chosen for presentation. one of the issues addressed are digitization, illustration, formalization, facts assistants, disbursed libraries of arithmetic, NAG library, LaTeX, MathML, arithmetic markup, theorem description, question languages for mathematical metadata, mathematical info retrieval, XML-based mathematical wisdom processing, semantic internet, mathematical content material administration, formalized arithmetic repositories, theorem proving, and evidence theory.

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Extra resources for Mathematical Knowledge Management: Second International Conference, MKM 2003 Bertinoro, Italy, February 16–18, 2003 Proceedings

Example text

Variable A : Prop. Variable B : Prop. Definition H1 : Prop := A /\ B. Theorem T1 : H1 -> A. Proof. Qed. End S. (* Here the type of H1 and T1 are different. See code fragment below *) Theorem T2 : True /\ True -> True. Proof. Exact (T1 True False (I,I)). Qed. The previous fragment should be equivalent, from a logic point of view, to the following input: 7 8 This information is required for managing explicit substitutions that are needed to allow reduction of terms with metavariables.

Nothing is done to speed up instantiation, that becomes a seldom required operation. The two possibilities requires different data-structures and representation of metavariables. Moreover, for technical reasons, in Coq there is a further distinction between full-fledged metavariables (called existential variables and use to represent holes in the type of other metavariables) and restricted metavariables that are used to represent just the open goals. The first time we exported from Coq, we did not change the Coq representation.

Since different tools may require different subsets of the whole knowledge and since you are likely to change the DTDs and the documents often, insulating the tools from changes in other parts of the library is almost mandatory. It is not unusual to find out later that the grain was not fine enough. Example: not every operation that is applied to a theorem requires both the statement and the proof. Finding out which lemma can be applied, for instance, just requires the statement or, even better, the list of its hypotheses and the conclusion.

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