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Geometrical Specification using Dependent Types in PVS Mauricio AyalaRinc on # , Valnei A. Fernandes and Andr e L. Galdino
 

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

  

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

 

Collections: Mathematics