diff options
| author | aarne <aarne@cs.chalmers.se> | 2008-06-25 16:54:35 +0000 |
|---|---|---|
| committer | aarne <aarne@cs.chalmers.se> | 2008-06-25 16:54:35 +0000 |
| commit | e9e80fc389365e24d4300d7d5390c7d833a96c50 (patch) | |
| tree | f0b58473adaa670bd8fc52ada419d8cad470ee03 /examples/logic/Arithm.gf | |
| parent | b96b36f43de3e2f8b58d5f539daa6f6d47f25870 (diff) | |
changed names of resource-1.3; added a note on homepage on release
Diffstat (limited to 'examples/logic/Arithm.gf')
| -rw-r--r-- | examples/logic/Arithm.gf | 64 |
1 files changed, 0 insertions, 64 deletions
diff --git a/examples/logic/Arithm.gf b/examples/logic/Arithm.gf deleted file mode 100644 index 331a0d7c6..000000000 --- a/examples/logic/Arithm.gf +++ /dev/null @@ -1,64 +0,0 @@ -abstract Arithm = Logic ** { - --- arithmetic -fun - Nat : Dom ; -data - Zero : Elem Nat ; - Succ : Elem Nat -> Elem Nat ; -fun - EqNat : (m,n : Elem Nat) -> Prop ; - LtNat : (m,n : Elem Nat) -> Prop ; - Div : (m,n : Elem Nat) -> Prop ; - Even : Elem Nat -> Prop ; - Odd : Elem Nat -> Prop ; - Prime : Elem Nat -> Prop ; - - one : Elem Nat ; - two : Elem Nat ; - sum : (m,n : Elem Nat) -> Elem Nat ; - prod : (m,n : Elem Nat) -> Elem Nat ; -data - evax1 : Proof (Even Zero) ; - evax2 : (n : Elem Nat) -> Proof (Even n) -> Proof (Odd (Succ n)) ; - evax3 : (n : Elem Nat) -> Proof (Odd n) -> Proof (Even (Succ n)) ; - - eqax1 : Proof (EqNat Zero Zero) ; - eqax2 : (m,n : Elem Nat) -> Proof (EqNat m n) -> - Proof (EqNat (Succ m) (Succ n)) ; -fun - IndNat : (C : Elem Nat -> Prop) -> - Proof (C Zero) -> - ((x : Elem Nat) -> Hypo (C x) -> Proof (C (Succ x))) -> - Proof (Univ Nat C) ; - -def - one = Succ Zero ; - two = Succ one ; - sum m (Succ n) = Succ (sum m n) ; - sum m Zero = m ; - prod m (Succ n) = sum (prod m n) m ; - prod m Zero = Zero ; - LtNat m n = Exist Nat (\x -> EqNat n (sum m (Succ x))) ; - Div m n = Exist Nat (\x -> EqNat m (prod x n)) ; - Prime n = - Conj (LtNat one n) - (Univ Nat (\x -> Impl (Conj (LtNat one x) (Div n x)) (EqNat x n))) ; - -fun ex1 : Text ; -def ex1 = - ThmWithProof - (Univ Nat (\x -> Disj (Even x) (Odd x))) - (IndNat - (\x -> Disj (Even x) (Odd x)) - (DisjIl (Even Zero) (Odd Zero) evax1) - (\x -> \h -> DisjE (Even x) (Odd x) (Disj (Even (Succ x)) (Odd (Succ x))) - (Hypoth (Disj (Even x) (Odd x)) h) - (\a -> DisjIr (Even (Succ x)) (Odd (Succ x)) - (evax2 x (Hypoth (Even x) a))) - (\b -> DisjIl (Even (Succ x)) (Odd (Succ x)) - (evax3 x (Hypoth (Odd x) b)) - ) - ) - ) ; -} ; |
