src/HOL/UNITY/Lift.thy
author paulson
Thu Aug 06 15:47:26 1998 +0200 (1998-08-06)
changeset 5277 e4297d03e5d2
child 5320 79b326bceafb
permissions -rw-r--r--
A higher-level treatment of LeadsTo, minimizing use of "reachable"
     1 (*  Title:      HOL/UNITY/Lift.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1998  University of Cambridge
     5 
     6 The Lift-Control Example
     7 *)
     8 
     9 Lift = SubstAx +
    10 
    11 record state =
    12   floor :: nat		(*current position of the lift*)
    13   open  :: bool		(*whether the door is open at floor*)
    14   stop  :: bool		(*whether the lift is stopped at floor*)
    15   req   :: nat set	(*for each floor, whether the lift is requested*)
    16   up    :: bool		(*current direction of movement*)
    17   move  :: bool		(*whether moving takes precedence over opening*)
    18 
    19 consts
    20   min, max :: nat	(*least and greatest floors*)
    21 
    22 rules
    23   min_le_max  "min <= max"
    24   
    25 
    26 constdefs
    27   
    28   (** Abbreviations: the "always" part **)
    29   
    30   above :: "state set"
    31     "above == {s. EX i. floor s < i & i <= max & i : req s}"
    32 
    33   below :: "state set"
    34     "below == {s. EX i. min <= i & i < floor s & i : req s}"
    35 
    36   queueing :: "state set"
    37     "queueing == above Un below"
    38 
    39   goingup :: "state set"
    40     "goingup == above Int ({s. up s} Un Compl below)"
    41 
    42   goingdown :: "state set"
    43     "goingdown == below Int ({s. ~ up s} Un Compl above)"
    44 
    45   ready :: "state set"
    46     "ready == {s. stop s & ~ open s & move s}"
    47 
    48 
    49   (** The program **)
    50   
    51   request_act :: "(state*state) set"
    52     "request_act == {(s,s'). s' = s (|stop:=True, move:=False|)
    53 		                  & ~ stop s & floor s : req s}"
    54 
    55   open_act :: "(state*state) set"
    56     "open_act ==
    57          {(s,s'). s' = s (|open :=True,
    58 			   req  := req s - {floor s},
    59 			   move := True|)
    60 		       & stop s & ~ open s & floor s : req s
    61 	               & ~(move s & s: queueing)}"
    62 
    63   close_act :: "(state*state) set"
    64     "close_act == {(s,s'). s' = s (|open := False|) & open s}"
    65 
    66   req_up_act :: "(state*state) set"
    67     "req_up_act ==
    68          {(s,s'). s' = s (|stop  :=False,
    69 			   floor := Suc (floor s),
    70 			   up    := True|)
    71 		       & s : (ready Int goingup)}"
    72 
    73   req_down_act :: "(state*state) set"
    74     "req_down_act ==
    75          {(s,s'). s' = s (|stop  :=False,
    76 			   floor := floor s - 1,
    77 			   up    := False|)
    78 		       & s : (ready Int goingdown)}"
    79 
    80   move_up :: "(state*state) set"
    81     "move_up ==
    82          {(s,s'). s' = s (|floor := Suc (floor s)|)
    83 		       & ~ stop s & up s & floor s ~: req s}"
    84 
    85   move_down :: "(state*state) set"
    86     "move_down ==
    87          {(s,s'). s' = s (|floor := floor s - 1|)
    88 		       & ~ stop s & ~ up s & floor s ~: req s}"
    89 
    90   Lprg :: state program
    91     "Lprg == (|Init = {s. floor s = min & ~ up s & move s & stop s &
    92 		          ~ open s & req s = {}},
    93 	       Acts = {id, request_act, open_act, close_act,
    94 		       req_up_act, req_down_act, move_up, move_down}|)"
    95 
    96 
    97   (** Invariants **)
    98 
    99   bounded :: state set
   100     "bounded == {s. min <= floor s & floor s <= max}"
   101 
   102   (** ???
   103 		    (~ stop s & up s --> floor s < max) &
   104 		    (~ stop s & ~ up s --> min < floor s)}"
   105   **)
   106 
   107   open_stop :: state set
   108     "open_stop == {s. open s --> stop s}"
   109   
   110   open_move :: state set
   111     "open_move == {s. open s --> move s}"
   112   
   113   stop_floor :: state set
   114     "stop_floor == {s. open s & ~ move s --> floor s : req s}"
   115   
   116   moving_up :: state set
   117     "moving_up == {s. ~ stop s & up s -->
   118                    (EX f. floor s <= f & f <= max & f : req s)}"
   119   
   120   moving_down :: state set
   121     "moving_down == {s. ~ stop s & ~ up s -->
   122                      (EX f. min <= f & f <= floor s & f : req s)}"
   123   
   124   valid :: "state set"
   125     "valid == bounded Int open_stop Int open_move"
   126 
   127 end