Higher-order intuitionistic formalization and proofs in Hilbert’s elementary geometry

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2061, Issue , 2001, Pages 306-323

  Dehlinger, Christophe ^a   Dufourd, Jean François ^a   Schreck, Pascal ^a  

^a UNIVERSITÉ DE STRASBOURG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; FORMAL LOGIC; THEOREM PROVING;

AXIOMATICS; CALCULUS OF INDUCTIVE CONSTRUCTIONS; ELEMENTARY GEOMETRY; GEOMETRIC ALGORITHM; GEOMETRIC CONCEPTS; HIGHER-ORDER; LOGICAL FRAMEWORKS; PRIMITIVE OPERATIONS;

GEOMETRY;

EID: 81755166754     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45410-1_17     Document Type: Conference Paper

References (23)

1. Balbiani, P., Dugat, V., Farinas del Cerro, L., Lopez, A.: Eléments de Géométrie Mécanique. Hermes (1994).
2. Barras, B. et al.: The Coq Proof Assistant Reference Manual (Version 6.3.1). INRIA (1999), http://pauillac.inria.fr/coq/doc/main.html
3. Chou, S.-C.: Mechanical Geometry Theorem Proving. D. Reidel (1988).
4. Coquand, T., Huet, G.: Constructions: A higher order proof system for mechanizing mathematics. EUROCAL’85, Linz, LNCS 203, Springer-Verlag (1985), 151–184.
5. Coquand, T., Paulin, C.: Inductively defined types. P. Martin-Lof and G. Mints, editors, COLOG-88, LNCS 417, Springer-Verlag (1990), 50–66.
6. Dufourd, J.-F., Mathis, P., Schreck, P.: Geometric construction by assembling solved subfigures. Artificial Intelligence 99 (1998), 73–119.
7. Dufourd, J.-F., Puitg, F.: Functional specification and prototyping with combinatorial maps. Computational Geometry — Theory and Applications 16 (2000), 129–156.
8. Essert-Villard, C., Schreck, P., Dufourd, J.-F.: Sketch-based pruning of a solution space within a formal geometric constraint solver. Submitted (2000).
9. Gelernter, H.: Realization of a geometry theorem proving machine. Computers and Thought, Mac Graw Hill (1963), 134–163.
10. Girard, J.-Y., Lafont, Y., Taylor, P.: Proofs and Types. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press (1989).
11. Heyting, A.: Intuitionism — An Introduction. North Holland (1956).
12. Heyting, A.: Axioms for intuitionistic plane affine geometry. Proceedings of an International Symposium on the Axiomatic Method with Special Reference to Geometry and Physics (1959), 160–173.
13. Hilbert, D.: Fondations de la Géométrie—Edition critique préparée par P. Rossier, CNRS, Dunod (1971).
14. Knuth, D.E.: Axioms and Hulls. LNCS 606, Springer-Verlag (1992).
15. Paulin-Mohring, C.: Inductive Definition in the System Coq — Rules and Properties. Typed Lambda-Calculi and Applications, LNCS 664, Springer-Verlag (1993).
16. Toussaint, G.: A new look at Euclid’s second proposition. Technical Report No SOCS 90.21 (1990).
17. von Plato, J.: The axioms of constructive geometry. Annals of Pure and Applied Logic 76 (1995), 169–200.
18. von Plato, J.: Organization and development of a constructive axiomatization. LNCS 1158, Springer-Verlag (1996), 288–296.
19. von Plato, J.: A constructive theory of ordered affine geometry. Indagationes Mathematicae N.S. 9(4) (1998), 549–562.
20. Puitg, F., Dufourd J.-F.: Formal program development in geometric modelling. Current Trends in Applied Formal Methods, Boppard, LNCS 1641, Springer- Verlag (1998), 62–76.
21. Puitg, F., Dufourd J.-F.: Formal specifications and theorem proving breakthroughs in geometric modelling. Theorem Proving in Higher Order Logics, Canberra, LNCS 1479, Springer-Verlag (1998), 401–427.
22. Puitg, F., Dufourd J.-F.: Formalizing mathematics in higher logic: A case study in geometric modelling. Theoretical Computer Science 234 (M. Nivat, ed.), Elsevier Science (2000), 1–57.
23. Wu, W.-T.: Mechanical Theorem Proving in Geometries. Springer-Verlag (1994).