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Formal specification and theorem proving breakthroughs in geometric modeling

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Theorem Proving in Higher Order Logics (TPHOLs 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1479))

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Abstract

An innovative attempt to develop formal techniques in geometric modeling is reported through the axiomatization of the combinatorial maps in the Calculus of Inductive Constructions. A hierarchical specification of ordered sorts is presented and validated by inductive proofs of consistency and completeness in the Coq prover. Classical difficulties in theorem proving like cohabitation of objects with their generalization, smooth handling of subtyping, completion of partial relations or objects, observationality v. constructivism, and symmetry of relations, are addressed. Geometrical modeling issues are thus solved in a new and unquestionable fashion, giving a great insight on the domain and a deep understanding of the model, and so validating the methodology.

This work is supported by the GDR-PRC of Programmation, and the GDR-PRC of Algorithmique, Modèles et Infographie (MENRT, CNRS, France).

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Authors and Affiliations

  1. Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection LSIIT, UPRES-A 7005, PÔle API, boulevard S. Brant, F-67400, Illkirch Cedex, France

    FranÇois Puitg & Jean -FranÇois Dufourd

Authors
  1. FranÇois Puitg
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  2. Jean -FranÇois Dufourd
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Jim Grundy Malcolm Newey

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© 1998 Springer-Verlag Berlin Heidelberg

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Puitg, F., Dufourd, J.F. (1998). Formal specification and theorem proving breakthroughs in geometric modeling. In: Grundy, J., Newey, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1998. Lecture Notes in Computer Science, vol 1479. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055149

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  • DOI: https://doi.org/10.1007/BFb0055149

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64987-8

  • Online ISBN: 978-3-540-49801-8

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