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1
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2
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node Sofar( X : bool ) returns ( Sofar : bool );
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3
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let
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Sofar = X -> X and pre Sofar;
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5
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tel
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6
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7
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node excludes9( X1, X2, X3, X4, X5, X6, X7, X8, X9 : bool ) returns ( excludes : bool );
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8
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let
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9
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excludes = not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or
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10
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X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or
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11
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not X1 and X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or
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12
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not X1 and not X2 and X3 and not X4 and not X5 and not X6 and not X7 and not X8 and not X9 or
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13
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not X1 and not X2 and not X3 and X4 and not X5 and not X6 and not X7 and not X8 and not X9 or
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14
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not X1 and not X2 and not X3 and not X4 and X5 and not X6 and not X7 and not X8 and not X9 or
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15
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not X1 and not X2 and not X3 and not X4 and not X5 and X6 and not X7 and not X8 and not X9 or
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16
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not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and X7 and not X8 and not X9 or
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17
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not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and X8 and not X9 or
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not X1 and not X2 and not X3 and not X4 and not X5 and not X6 and not X7 and not X8 and X9;
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19
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tel
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node ticket3i(e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool;
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init_a1, init_a2, init_a3, init_t : int) returns (
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p1, p2, p3, t, s, a1, a2, a3 : int; erreur_ticket3i : bool);
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24
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var
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g1, g2, g3, g4, g5, g6, g7, g8, g9 : bool;
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26
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let
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27
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erreur_ticket3i = if((p1>=3) or (p2>=3) or (p3>=3)) then true else false;
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29
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g1 = pre p1 = 0;
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g2 = pre p1 = 1 and pre s >= a1;
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g3 = pre p1 = 2;
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33
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g4 = pre p2 = 0;
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34
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g5 = pre p2 = 1 and pre s >= a2;
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35
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g6 = pre p2 = 2;
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36
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g7 = pre p3 = 0;
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37
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g8 = pre p3 = 1 and pre s >= a3;
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38
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g9 = pre p3 = 2;
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39
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40
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p1 = 0 ->
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41
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if(e1) then if(g1) then 1 else pre p1 else
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42
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if(e2) then if(g2) then 2 else pre p1 else
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43
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if(e3) then if(g3) then 0 else pre p1 else
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44
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pre p1;
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45
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p2 = 0 ->
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47
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if(e4) then if(g4) then 1 else pre p2 else
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48
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if(e5) then if(g5) then 2 else pre p2 else
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49
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if(e6) then if(g6) then 0 else pre p2 else
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50
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pre p2;
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51
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52
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p3 = 0 ->
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53
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if(e7) then if(g7) then 1 else pre p3 else
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54
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if(e8) then if(g8) then 2 else pre p3 else
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55
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if(e9) then if(g9) then 0 else pre p3 else
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56
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pre p3;
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57
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58
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t = init_t ->
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59
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if(e1) then if(g1) then pre t+1 else pre t else
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60
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if(e4) then if(g4) then pre t+1 else pre t else
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61
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if(e7) then if(g7) then pre t+1 else pre t else
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62
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pre t;
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63
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64
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s = t ->
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65
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if(e3) then if(g3) then pre s+1 else pre s else
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66
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if(e6) then if(g6) then pre s+1 else pre s else
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67
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if(e9) then if(g9) then pre s+1 else pre s else
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68
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pre s;
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69
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70
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a1 = init_a1 ->
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71
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if(e1) then if(g1) then pre t else pre a1 else
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72
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pre a1;
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73
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74
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a2 = init_a2 ->
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75
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if(e4) then if(g4) then pre t else pre a2 else
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76
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pre a2;
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77
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78
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a3 = init_a3 ->
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79
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if(e7) then if(g7) then pre t else pre a3 else
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80
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pre a3;
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81
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82
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tel
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83
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84
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--@ ensures OK;
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85
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node top( e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool;
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86
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init_a1, init_a2, init_a3, init_t : int )
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87
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returns ( OK : bool );
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88
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var p1, p2, p3, t, s, a1, a2, a3 : int;
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89
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erreur_ticket3i : bool;
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90
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env : bool;
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91
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let
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92
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( p1, p2, p3, t, s, a1, a2, a3 , erreur_ticket3i ) =
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93
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ticket3i( e1, e2, e3, e4, e5, e6, e7, e8, e9,
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94
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init_a1, init_a2, init_a3, init_t );
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95
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env = Sofar( excludes9( e1, e2, e3, e4, e5, e6, e7, e8, e9 ) and
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96
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init_a1 >= 0 and
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97
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init_a2 >= 0 and
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98
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init_a3 >= 0 and
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99
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init_t >= 0 );
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100
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OK = env => 0 <= p1 and p1 <= 3 and
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101
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0 <= p2 and p2 <= 3 and
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102
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0 <= p3 and p3 <= 3 and
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103
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p1 + p2 + p3 <= 9;
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104
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--!k:2;
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105
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--!PROPERTY: OK=true;
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106
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--%MAIN;
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107
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tel
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