exercise_3_1 : THEORY
BEGIN

  D : real = 5*1852 % [m] 
  T : real = 5*60   % [s]

  IMPORTING CDR2D[D,T]

  Identifier : TYPE = string

  %
  % Exercise 1
  %

  % Define a type of aircraft with an identifier, a 2D position, and a 2D velocity
  AircraftXY : TYPE % = ...

  % Define an example of an AircraftXYZ
  
  ac0 : AircraftXY % = ... 

  IMPORTING NAS[Identifier,AircraftXY]

  % Define cdnas such that it returns true if there is a traffic aircraft
  % that is in conflict_ever with the ownship
  cdnas(ownid:Identifier,nas:(exists?(ownid))) : bool % = ...

END exercise_3_1

exercise_3_2 : THEORY
BEGIN

  %
  % Exercise 2
  %

  D : real = 5*1852 % [m] 
  T : real = 5*60   % [s]

  IMPORTING CDR2D[D,T]

  Identifier : TYPE = string

  AircraftGeo : TYPE = [#
    id   : Identifier,
    lat  : {x:real | -90 <= x AND x <= 90},
    lon  : {x:real | abs(x) < 360},
    gs   : posreal, % Ground speed [m/s] 
    trk  : {x:real | abs(x) < 360} % Track [True North]
  #] 

  IMPORTING vectors@ECEF,
            vectors@vect3_basis,
            vectors@trackAngles_2D

  % Radius of the earth
  R : posreal = 6353000 % [m]

  geo2sxy(lat_ref,lon_ref:real)(lat,lon:real) : Position =
   LET midlat = (lat_ref+lat)/2,
       midlon = (lon_ref+lon)/2,
       refxyz = spherical2xyz(R,midlat,midlon),
       pxyz   = spherical2xyz(R,lat,lon) IN
   sphere_to_2D_plane(refxyz)(pxyz)

  gstrk2vxy(gs:posreal,trk:real): AbsVelocity = 
    v_from(trk,gs)

  IMPORTING NAS[Identifier,AircraftGeo]

  % Define cdnas such that it returns true if there is a traffic aircraft
  % that is in conflict_ever with the ownship
  cdnas(ownid:Identifier,nas:(exists?(ownid))) : bool % = ...

END exercise_3_2