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1
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node First( X : int ) returns ( First : int );
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let
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First = X -> pre First;
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5
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tel
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node Sofar( X : bool ) returns ( Sofar : bool );
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7
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let
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Sofar = X -> X and pre Sofar;
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9
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tel
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10
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node excludes9( X1, X2, X3, X4, X5, X6, X7, X8, X9 : bool ) returns ( excludes : bool );
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11
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let
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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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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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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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15
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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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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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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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18
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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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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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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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22
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tel
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node illinois(e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool; init_invalid : int)
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24
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returns(invalid, dirty, exclusive, shared : int);
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var
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g1, g2, g3, g4, g5, g6, g7, g8, g9 : bool;
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let
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g1 = pre invalid>=1 and pre dirty=0 and pre shared=0 and pre exclusive=0;
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g2 = pre invalid>=1 and pre dirty>=1;
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g3 = pre invalid>=1 and pre shared+pre exclusive>=1;
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g4 = pre exclusive>=1;
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g5 = pre shared>=1;
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g6 = pre invalid>=1;
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g7 = pre dirty>=1;
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35
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g8 = pre shared>=1;
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g9 = pre exclusive>=1;
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invalid = (if(init_invalid>0) then init_invalid else 1-init_invalid) ->
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if(e1) then if(g1) then pre invalid-1 else pre invalid else
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if(e2) then if(g2) then pre invalid-1 else pre invalid else
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40
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if(e3) then if(g3) then pre invalid-1 else pre invalid else
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if(e5) then if(g5) then pre invalid+pre shared-1 else pre invalid else
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if(e6) then if(g6) then pre invalid+pre dirty+pre shared+pre exclusive-1 else pre invalid else
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if(e7) then if(g7) then pre invalid+1 else pre invalid else
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if(e8) then if(g8) then pre invalid+1 else pre invalid else
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if(e9) then if(g9) then pre invalid+1 else pre invalid else
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46
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pre invalid;
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dirty = 0 ->
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48
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if(e2) then if(g2) then pre dirty-1 else pre dirty else
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49
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if(e4) then if(g4) then pre dirty+1 else pre dirty else
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50
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if(e5) then if(g5) then pre dirty+1 else pre dirty else
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51
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if(e6) then if(g6) then 1 else pre dirty else
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52
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if(e7) then if(g7) then pre dirty-1 else pre dirty else
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53
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pre dirty;
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exclusive = 0 ->
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55
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if(e1) then if(g1) then pre exclusive+1 else pre exclusive else
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if(e3) then if(g3) then pre 0 else pre exclusive else
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if(e4) then if(g4) then pre exclusive-1 else pre exclusive else
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if(e6) then if(g6) then 0 else pre exclusive else
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if(e9) then if(g9) then pre exclusive-1 else pre exclusive else
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60
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pre exclusive;
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shared = 0 ->
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if(e2) then if(g2) then pre shared+2 else pre shared else
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if(e3) then if(g3) then pre shared+pre exclusive+1 else pre shared else
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if(e5) then if(g5) then 0 else pre shared else
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if(e6) then if(g6) then 0 else pre shared else
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if(e8) then if(g8) then pre shared-1 else pre shared else
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pre shared;
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68
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tel
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node top(e1, e2, e3, e4, e5, e6, e7, e8, e9 : bool; init_invalid : int)
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70
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returns( OK : bool);
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71
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--@ contract guarantees OK;
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72
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var invalid, dirty, exclusive, shared : int;
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73
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env : bool;
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74
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let
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( invalid, dirty, exclusive, shared ) =
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76
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illinois( e1, e2, e3, e4, e5, e6, e7, e8, e9, init_invalid );
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77
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env = Sofar( excludes9( e1, e2, e3, e4, e5, e6, e7, e8, e9 ) and
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78
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init_invalid > 0 );
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79
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OK = env => invalid -1- dirty + exclusive + shared = First( init_invalid );
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80
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--%MAIN;
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81
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--%PROPERTY OK=true;
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82
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tel
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