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authoraarne <aarne@cs.chalmers.se>2008-06-25 16:54:35 +0000
committeraarne <aarne@cs.chalmers.se>2008-06-25 16:54:35 +0000
commite9e80fc389365e24d4300d7d5390c7d833a96c50 (patch)
treef0b58473adaa670bd8fc52ada419d8cad470ee03 /examples/logic/Arithm.gf
parentb96b36f43de3e2f8b58d5f539daa6f6d47f25870 (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.gf64
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))
- )
- )
- ) ;
-} ;