Algebraic specification
Topological models for boundary representation: a comparison with n-dimensional generalized maps
Computer-Aided Design - Beyond solid modelling
Algebraic specification of a 3D-modeler based on hypermaps
CVGIP: Graphical Models and Image Processing
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
Formal Specification and Theorem Proving Breakthroughs in Geometric Modeling
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Synthesizing Proofs from Programs in the Calculus of Inductive Constructions
MPC '95 Mathematics of Program Construction
Higher-Order Intuitionistic Formalization and Proofs in Hilbert's Elementary Geometry
ADG '00 Revised Papers from the Third International Workshop on Automated Deduction in Geometry
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An innovative attempt to integrate formal program development in geometric modeling is reported through the axiomatization of model of the combinatorial maps in the Calculus of Inductive Constructions. A hierarchical specification of ordered sorts is validated in the Coq prover by inductive proofs, and the automatic extraction of a prototype. Classical difficulties - like cohabitation of hierarchized objects, smooth handling of subtyping, and completion of partial relations - are addressed both from theorem proving and prototyping viewpoint.