alt-ergo-models.why 2.11 KB
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theory T
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  use import int.Int

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  goal g_no_lab : forall x:int. x >= 42 -> x + 3 <= 50

  goal g_lab0 : forall x "model:0":int. ("model:cond" x >= 42) -> 
    ("model:concl" x + 3 <= 50)

  goal g_lab1 : forall x "model:1":int. ("model:cond" x >= 42) -> 
    ("model:concl" x + 3 <= 50)

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  constant g : int
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  goal g2_lab : forall x "model:0":int. ("model:concl" g >= x)
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end

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theory ModelInt
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use import int.Int
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goal test0 : forall x "model:0":int. not (0 < x < 1)

goal test1 : forall x "model:0":int. not (0 <= x <= 1)

use import int.EuclideanDivision

goal test2 : forall x "model:0":int. div x x = 1

goal test_overflow:
  forall x "model:0" y "model:0" :  int.
     0 <= x <= 65535 /\ 0 <= y <= 65535 -> 0 <= x + y <= 65535

goal test_overflow2:
  forall x "model:0" y "model:0" :  int.
     -2 <= x <= 65535 /\ -2 <= y <= 65535 -> -2 <= x + y <= 65535

predicate is_int16 (x:int) = -65536 <= x <= 65535

goal test_overflow_int16:
  forall x "model:0" y "model:0" :  int.
     is_int16 x /\ is_int16 y -> is_int16 (x + y)

goal test_overflow_int16_alt:
  forall x "model:0" y "model:0" :  int.
      -65536 <= x <= 65535 /\ -65536 <= y <= 65535 -> -65536 <= x+y <= 65535 
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goal test_overflow_int16_bis:
  forall x "model:0" y "model:0" :  int.
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     is_int16 x /\ is_int16 y /\ 
     ("model:cond1" 0 <= x) /\ (x <= y) -> is_int16 (x + y)
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predicate is_int32 (x:int) = -2147483648 <= x <= 2147483647

goal test_overflow_int32:
  forall x "model:0" y "model:0" :  int.
     is_int32 x /\ is_int32 y -> is_int32 (x + y)

goal test_overflow_int32_bis:
  forall x "model:0" y "model:0" :  int.
     is_int32 x /\ is_int32 y /\ 0 <= x <= y -> is_int32 (x + y)

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goal test_overflow_int32_bis_inline:
  forall x "model:0" y "model:0" :  int.
     -2147483648 <= x <= 2147483647 /\ -2147483648 <= y <= 2147483647 /\ 0 <= x <= y -> -2147483648 <= x + y <= 2147483647

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end

theory ModelReal

use import real.Real

goal test1 : forall x "model:0":real. not (0.0 < x < 1.0)

goal test2 : forall x "model:0":real. x/x=1.0

end

theory ModelArray

use import map.Map

goal t1 : forall t "model:0" :map int int, i "model:0" : int. 
   get (set t 0 42) i = get t i
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end
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