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Geometrical Specification using Dependent Types in PVS Mauricio Ayala-Rincon

Summary: Geometrical Specification using Dependent Types in PVS
Mauricio Ayala-Rinc´on
, Valnei A. Fernandes and Andr´e L. Galdino
Grupo de Teoria da Computac¸~ao, Departamento de Matem´atica
Universidade de Bras´ilia, 70910-900 Bras´ilia D.F., Brasil
Abstract. We point out the importance of the use of the refined dependent types avail-
able in the proof assistant PVS for the correct specification of a geometrical approach
to solve the problem of air traffic conflict detection and resolution (between two air-
crafts in mid air). A correct PVS specification which completely solves this problem
giving a triplet which consists of escape trajectory, recovery trajectory, switching
time and whose first component allows exclusively changes in a unique of the pa-
rameters ground speed, heading and vertical speed is partially extended in such a
way that the formulated escape maneuvers may combine changes in two of these pa-
rameters: ground speed and heading.
Keywords: Type Theory, Dependent Types, PVS, Geometric Specification, Air Traf-
fic Conflict Detection and Resolution.
1. Introduction
Dependent types have been shown of great usefulness in programming languages for detect-


Source: Ayala-Rincón, Mauricio - Departamento de Matemática, Universidade de Brasília


Collections: Mathematics