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Summary: Geometrical Specification using Dependent Types in PVS
Mauricio AyalaRinc’ on # , Valnei A. Fernandes and Andr’ e L. Galdino
1 Grupo de Teoria da Computac› ”
ao, Departamento de Matem’atica
Universidade de Bras’lia, 70910900 Bras’lia D.F., Brasil
{ayala,galdino,valnei}@mat.unb.br
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
ing errors of programs by type checking even during compilation. In fact dependent types can
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