231_destruct.mlw 1.71 KB
Newer Older
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

module T
  predicate p1
  predicate p2
  predicate p3

  axiom H: p1 -> p2 -> p3
  axiom H1: p1 /\ p2 /\ p3
  axiom H2: p1 \/ p2 \/ p3

  goal G : (p1 \/ p2 \/ p3) -> 1 = 1
end

module T2
  use int.Int

  predicate p1 int
  predicate p2 int
  predicate p3 int

  axiom H: forall x. p1 x -> p2 x-> p3 x
  axiom H1: exists x y z. p1 x /\ p2 y /\ p3 z
  axiom H2: exists x. p1 x \/ exists y. p2 y \/ exists z. p3 z

  goal G : (forall x. p1 x \/ p2 x \/ p3 x) -> 1 = 1
end

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
module Unsoundness

  predicate a
  predicate b
  predicate c
  (* Here if we do things badly we could use a on the right to prove the new 
     hypothesis a on the left (and vice versa with b) 
     This should not be provable.
  *)
  axiom H: (a -> (c /\ b)) /\ (b -> a)
  goal t1: c

end

module Incompleteness

  predicate a
  predicate b
  predicate c

  axiom H: (a -> (c /\ b)) /\ (b -> a) /\ a
  goal t1: c

end

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67
module Imbrication
  predicate p1
  predicate p2
  predicate p3  
  predicate p4
  predicate p5
  predicate p6
  predicate p7

  axiom H: (p1 /\ p2) \/ (p3 /\ p4 /\ (p5 \/ p6 \/ p7)) 
  
  goal G: True

end

68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110

(* TODO add more complex examples *)


module Injection

  (* To avoid warning on axioms not containing local abstract symbol *)
  predicate p int
  constant z: int

  type t = 
    | C int
    | D
    | E bool
    | F int

  axiom H: exists x. C x = D /\ p z
  axiom H1: C 1 = C 4 /\ p z
  axiom H2: E true = F 4 /\ p z
  
  goal G: True

end

module Injection2

  (* To avoid warning on axioms not containing local abstract symbol *)
  predicate p int
  constant z: int

  type t = 
    | C int
    | D
    | E bool
    | F int

  axiom H: exists x. C x <> D /\ p z
  axiom H1: C 1 <> C 4 /\ p z
  axiom H2: E true <> F 4 /\ p z
  
  goal G: True

end