MACHINE
  LeftTurnAssist
REFINES
  ControlledSystem
SEES
  LeftTurnAssistCtx
VARIABLES
  t
  x_s
  ppov
  psv
  vsv
  vpov
  asv
INVARIANTS
  inv1: ppov : RRealPlus --> RReal
  inv2: psv : RRealPlus --> RReal
  inv3: vsv : RRealPlus --> RReal
  inv4: vpov : Closed2Closed(uminus(Vmax),Rzero)
  inv5: asv : Closed2Closed(uminus(B),Amax)
  inv6: x_p = bind(bind(vsv,psv),ppov)
EVENTS
  INITIALISATION
  WITH
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: t := Rzero
    act2: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        solutionOf(
          RRealPlus,
          bind(bind(vsv',psv'),ppov'),
          ode(
            f_stable(vpov_init),
            (Rzero |-> Rzero |-> ppov_init),
            Rzero
          )
        )
    act3: x_s := waiting
    act4: vpov := vpov_init
    act5: asv := Rzero
  END

  Progress
  REFINES Progress
  THEN
    act1: t :| t' : RRealPlus & (t |-> t' : lt)
  END

  Behave
  REFINES Behave
  ANY
    e
    v
  WHERE
    grd1: e : DE(S)
    grd2: Solvable(Closed2Infinity(t),e)
    grd3: v : Closed2Closed(Rzero,Vmax)
  WITH
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          e,
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov')
        )
    act2: vpov := uminus(v)
  END

  Transition
  REFINES Transition
  ANY
    s
  WHERE
    grd1: s : POW1(STATES)
  THEN
    act1: x_s :: s
  END

  ctrl_transition_attempt_turn
  REFINES Transition
  WHERE
    grd1: x_s = waiting
    grd2: Tsv(Amin |-> vsv(t) |-> psv(t)) |-> Tpov(ppov(t)) : lt
  WITH
    s: s = {turning}
  THEN
    act1: x_s := turning
  END

  ctrl_sense_turn_end
  REFINES Sense
  WHERE
    grd1: psv(t) |-> q : geq
  WITH
    s: s = {passed}
    p: p = STATES*RReal*{ vsv_ |-> psv_ |-> ppov_ | vsv_ : RReal & psv_ |-> q : geq & ppov_ : RReal }
  THEN
    act1: x_s := passed
  END

  ctrl_actuate_waiting
  REFINES Actuate
  WHERE
    grd1: x_s = waiting
  WITH
    e: e = ode(f_stable(vpov),(vsv(t) |-> psv(t) |-> ppov(t)),t)
    s: s = {waiting}
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          ode(f_stable(vpov),(vsv(t) |-> psv(t) |-> ppov(t)),t),
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov') 
        )
  END

  ctrl_actuate_turning
  REFINES Actuate
  ANY
    a
  WHERE
    grd1: x_s = turning
    grd2: a : Closed2Closed(Amin,Amax)
  WITH
    e: e = ode(f_accelerate_min(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t)
    s: s = {turning}
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          ode(f_accelerate_min(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t),
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov') 
        )
    act2: asv := a
  END

  ctrl_actuate_passed_stable
  REFINES Actuate
  WHERE
    grd1: x_s = passed
  WITH
    e: e = ode(f_stable(vpov),(vsv(t) |-> psv(t) |-> ppov(t)),t)
    s: s = {passed}
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          ode(f_stable(vpov),(vsv(t) |-> psv(t) |-> ppov(t)),t),
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov') 
        )
    act2: asv := Rzero
  END

  ctrl_actuate_passed_accelerate
  REFINES Actuate
  ANY
    a
  WHERE
    grd1: x_s = passed
    grd2: a : Open2Closed(Rzero,Amax)
  WITH
    e: e = ode(f_accelerate(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t)
    s: s = {passed}
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          ode(f_accelerate(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t),
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov') 
        )
    act2: asv := a
  END

  ctrl_actuate_passed_decelerate
  REFINES Actuate
  ANY
    a
  WHERE
    grd1: x_s = passed
    grd2: a : Closed2Open(uminus(B),Rzero)
  WITH
    e: e = ode(f_decelerate(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t)
    s: s = {passed}
    x_p': x_p' = bind(bind(vsv',psv'),ppov')
  THEN
    act1: 
      vsv,psv,ppov :|
        vsv' : RRealPlus --> RReal & psv' : RRealPlus --> RReal & ppov' : RRealPlus --> RReal &
        AppendSolutionBAP(
          ode(f_decelerate(a |-> vpov |-> vsv(t)),(vsv(t) |-> psv(t) |-> ppov(t)),t),
          RRealPlus,
          Closed2Open(Rzero,t),
          Closed2Infinity(t),
          bind(bind(vsv,psv),ppov),
          bind(bind(vsv',psv'),ppov') 
        )
    act2: asv := a
  END

END