--- a/src/HOL/ex/LexOrds.thy Sat Dec 27 17:09:27 2008 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,182 +0,0 @@
-(* Title: HOL/ex/LexOrds.thy
- ID: $Id$
- Author: Lukas Bulwahn, TU Muenchen
-*)
-
-header {* Examples and regression tests for method lexicographic order. *}
-
-theory LexOrds
-imports Main
-begin
-
-subsection {* Trivial examples *}
-
-fun identity :: "nat \<Rightarrow> nat"
-where
- "identity n = n"
-
-fun yaSuc :: "nat \<Rightarrow> nat"
-where
- "yaSuc 0 = 0"
-| "yaSuc (Suc n) = Suc (yaSuc n)"
-
-
-subsection {* Examples on natural numbers *}
-
-fun bin :: "(nat * nat) \<Rightarrow> nat"
-where
- "bin (0, 0) = 1"
-| "bin (Suc n, 0) = 0"
-| "bin (0, Suc m) = 0"
-| "bin (Suc n, Suc m) = bin (n, m) + bin (Suc n, m)"
-
-
-fun t :: "(nat * nat) \<Rightarrow> nat"
-where
- "t (0,n) = 0"
-| "t (n,0) = 0"
-| "t (Suc n, Suc m) = (if (n mod 2 = 0) then (t (Suc n, m)) else (t (n, Suc m)))"
-
-
-fun k :: "(nat * nat) * (nat * nat) \<Rightarrow> nat"
-where
- "k ((0,0),(0,0)) = 0"
-| "k ((Suc z, y), (u,v)) = k((z, y), (u, v))" (* z is descending *)
-| "k ((0, Suc y), (u,v)) = k((1, y), (u, v))" (* y is descending *)
-| "k ((0,0), (Suc u, v)) = k((1, 1), (u, v))" (* u is descending *)
-| "k ((0,0), (0, Suc v)) = k((1,1), (1,v))" (* v is descending *)
-
-
-fun gcd2 :: "nat \<Rightarrow> nat \<Rightarrow> nat"
-where
- "gcd2 x 0 = x"
-| "gcd2 0 y = y"
-| "gcd2 (Suc x) (Suc y) = (if x < y then gcd2 (Suc x) (y - x)
- else gcd2 (x - y) (Suc y))"
-
-fun ack :: "(nat * nat) \<Rightarrow> nat"
-where
- "ack (0, m) = Suc m"
-| "ack (Suc n, 0) = ack(n, 1)"
-| "ack (Suc n, Suc m) = ack (n, ack (Suc n, m))"
-
-
-fun greedy :: "nat * nat * nat * nat * nat => nat"
-where
- "greedy (Suc a, Suc b, Suc c, Suc d, Suc e) =
- (if (a < 10) then greedy (Suc a, Suc b, c, d + 2, Suc e) else
- (if (a < 20) then greedy (Suc a, b, Suc c, d, Suc e) else
- (if (a < 30) then greedy (Suc a, b, Suc c, d, Suc e) else
- (if (a < 40) then greedy (Suc a, b, Suc c, d, Suc e) else
- (if (a < 50) then greedy (Suc a, b, Suc c, d, Suc e) else
- (if (a < 60) then greedy (a, Suc b, Suc c, d, Suc e) else
- (if (a < 70) then greedy (a, Suc b, Suc c, d, Suc e) else
- (if (a < 80) then greedy (a, Suc b, Suc c, d, Suc e) else
- (if (a < 90) then greedy (Suc a, Suc b, Suc c, d, e) else
- greedy (Suc a, Suc b, Suc c, d, e))))))))))"
-| "greedy (a, b, c, d, e) = 0"
-
-
-fun blowup :: "nat => nat => nat => nat => nat => nat => nat => nat => nat => nat"
-where
- "blowup 0 0 0 0 0 0 0 0 0 = 0"
-| "blowup 0 0 0 0 0 0 0 0 (Suc i) = Suc (blowup i i i i i i i i i)"
-| "blowup 0 0 0 0 0 0 0 (Suc h) i = Suc (blowup h h h h h h h h i)"
-| "blowup 0 0 0 0 0 0 (Suc g) h i = Suc (blowup g g g g g g g h i)"
-| "blowup 0 0 0 0 0 (Suc f) g h i = Suc (blowup f f f f f f g h i)"
-| "blowup 0 0 0 0 (Suc e) f g h i = Suc (blowup e e e e e f g h i)"
-| "blowup 0 0 0 (Suc d) e f g h i = Suc (blowup d d d d e f g h i)"
-| "blowup 0 0 (Suc c) d e f g h i = Suc (blowup c c c d e f g h i)"
-| "blowup 0 (Suc b) c d e f g h i = Suc (blowup b b c d e f g h i)"
-| "blowup (Suc a) b c d e f g h i = Suc (blowup a b c d e f g h i)"
-
-
-subsection {* Simple examples with other datatypes than nat, e.g. trees and lists *}
-
-datatype tree = Node | Branch tree tree
-
-fun g_tree :: "tree * tree \<Rightarrow> tree"
-where
- "g_tree (Node, Node) = Node"
-| "g_tree (Node, Branch a b) = Branch Node (g_tree (a,b))"
-| "g_tree (Branch a b, Node) = Branch (g_tree (a,Node)) b"
-| "g_tree (Branch a b, Branch c d) = Branch (g_tree (a,c)) (g_tree (b,d))"
-
-
-fun acklist :: "'a list * 'a list \<Rightarrow> 'a list"
-where
- "acklist ([], m) = ((hd m)#m)"
-| "acklist (n#ns, []) = acklist (ns, [n])"
-| "acklist ((n#ns), (m#ms)) = acklist (ns, acklist ((n#ns), ms))"
-
-
-subsection {* Examples with mutual recursion *}
-
-fun evn od :: "nat \<Rightarrow> bool"
-where
- "evn 0 = True"
-| "od 0 = False"
-| "evn (Suc n) = od (Suc n)"
-| "od (Suc n) = evn n"
-
-
-fun sizechange_f :: "'a list => 'a list => 'a list" and
-sizechange_g :: "'a list => 'a list => 'a list => 'a list"
-where
- "sizechange_f i x = (if i=[] then x else sizechange_g (tl i) x i)"
-| "sizechange_g a b c = sizechange_f a (b @ c)"
-
-
-fun
- prod :: "nat => nat => nat => nat" and
- eprod :: "nat => nat => nat => nat" and
- oprod :: "nat => nat => nat => nat"
-where
- "prod x y z = (if y mod 2 = 0 then eprod x y z else oprod x y z)"
-| "oprod x y z = eprod x (y - 1) (z+x)"
-| "eprod x y z = (if y=0 then z else prod (2*x) (y div 2) z)"
-
-
-fun
- pedal :: "nat => nat => nat => nat"
-and
- coast :: "nat => nat => nat => nat"
-where
- "pedal 0 m c = c"
-| "pedal n 0 c = c"
-| "pedal n m c =
- (if n < m then coast (n - 1) (m - 1) (c + m)
- else pedal (n - 1) m (c + m))"
-
-| "coast n m c =
- (if n < m then coast n (m - 1) (c + n)
- else pedal n m (c + n))"
-
-
-subsection {*Examples for an unprovable termination *}
-
-text {* If termination cannot be proven, the tactic gives further information about unprovable subgoals on the arguments *}
-
-function noterm :: "(nat * nat) \<Rightarrow> nat"
-where
- "noterm (a,b) = noterm(b,a)"
-by pat_completeness auto
-(* termination by apply lexicographic_order*)
-
-function term_but_no_prove :: "nat * nat \<Rightarrow> nat"
-where
- "term_but_no_prove (0,0) = 1"
-| "term_but_no_prove (0, Suc b) = 0"
-| "term_but_no_prove (Suc a, 0) = 0"
-| "term_but_no_prove (Suc a, Suc b) = term_but_no_prove (b, a)"
-by pat_completeness auto
-(* termination by lexicographic_order *)
-
-text{* The tactic distinguishes between N = not provable AND F = False *}
-function no_proof :: "nat \<Rightarrow> nat"
-where
- "no_proof m = no_proof (Suc m)"
-by pat_completeness auto
-(* termination by lexicographic_order *)
-
-end
\ No newline at end of file