# HG changeset patch
# User krauss
# Date 1278688503 -7200
# Node ID 8380686be5cd6a85ab2357e38ea9b7ee9b152ec8
# Parent  00ff97087ab54925821f8ceb5f0c81c578a5ff4d
moved example to its own file in HOL/ex

diff -r 00ff97087ab5 -r 8380686be5cd src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Fri Jul 09 17:00:42 2010 +0200
+++ b/src/HOL/IsaMakefile	Fri Jul 09 17:15:03 2010 +0200
@@ -1006,7 +1006,8 @@
   ex/Refute_Examples.thy ex/SAT_Examples.thy ex/SVC_Oracle.thy		\
   ex/Serbian.thy ex/Sqrt.thy ex/Sqrt_Script.thy ex/Sudoku.thy		\
   ex/Tarski.thy ex/Termination.thy ex/Transfer_Ex.thy ex/Tree23.thy	\
-  ex/Unification.thy ex/document/root.bib ex/document/root.tex		\
+  ex/Unification.thy ex/While_Combinator_Example.thy ex/document/root.bib \
+	ex/document/root.tex		\
   ex/set.thy ex/svc_funcs.ML ex/svc_test.thy
 	@$(ISABELLE_TOOL) usedir $(OUT)/HOL ex
 
diff -r 00ff97087ab5 -r 8380686be5cd src/HOL/Library/While_Combinator.thy
--- a/src/HOL/Library/While_Combinator.thy	Fri Jul 09 17:00:42 2010 +0200
+++ b/src/HOL/Library/While_Combinator.thy	Fri Jul 09 17:15:03 2010 +0200
@@ -10,7 +10,7 @@
 imports Main
 begin
 
-subsection {* Option result *}
+subsection {* Partial version *}
 
 definition while_option :: "('a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a option" where
 "while_option b c s = (if (\<exists>k. ~ b ((c ^^ k) s))
@@ -81,7 +81,7 @@
 qed
 
 
-subsection {* Totalized version *}
+subsection {* Total version *}
 
 definition while :: "('a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> 'a) \<Rightarrow> 'a \<Rightarrow> 'a"
 where "while b c s = the (while_option b c s)"
@@ -127,54 +127,5 @@
   apply blast
   done
 
-text {*
- \medskip An application: computation of the @{term lfp} on finite
- sets via iteration.
-*}
-
-theorem lfp_conv_while:
-  "[| mono f; finite U; f U = U |] ==>
-    lfp f = fst (while (\<lambda>(A, fA). A \<noteq> fA) (\<lambda>(A, fA). (fA, f fA)) ({}, f {}))"
-apply (rule_tac P = "\<lambda>(A, B). (A \<subseteq> U \<and> B = f A \<and> A \<subseteq> B \<and> B \<subseteq> lfp f)" and
-                r = "((Pow U \<times> UNIV) \<times> (Pow U \<times> UNIV)) \<inter>
-                     inv_image finite_psubset (op - U o fst)" in while_rule)
-   apply (subst lfp_unfold)
-    apply assumption
-   apply (simp add: monoD)
-  apply (subst lfp_unfold)
-   apply assumption
-  apply clarsimp
-  apply (blast dest: monoD)
- apply (fastsimp intro!: lfp_lowerbound)
- apply (blast intro: wf_finite_psubset Int_lower2 [THEN [2] wf_subset])
-apply (clarsimp simp add: finite_psubset_def order_less_le)
-apply (blast intro!: finite_Diff dest: monoD)
-done
-
-
-subsection {* Example *}
-
-text{* Cannot use @{thm[source]set_eq_subset} because it leads to
-looping because the antisymmetry simproc turns the subset relationship
-back into equality. *}
-
-theorem "P (lfp (\<lambda>N::int set. {0} \<union> {(n + 2) mod 6 | n. n \<in> N})) =
-  P {0, 4, 2}"
-proof -
-  have seteq: "!!A B. (A = B) = ((!a : A. a:B) & (!b:B. b:A))"
-    by blast
-  have aux: "!!f A B. {f n | n. A n \<or> B n} = {f n | n. A n} \<union> {f n | n. B n}"
-    apply blast
-    done
-  show ?thesis
-    apply (subst lfp_conv_while [where ?U = "{0, 1, 2, 3, 4, 5}"])
-       apply (rule monoI)
-      apply blast
-     apply simp
-    apply (simp add: aux set_eq_subset)
-    txt {* The fixpoint computation is performed purely by rewriting: *}
-    apply (simp add: while_unfold aux seteq del: subset_empty)
-    done
-qed
 
 end
diff -r 00ff97087ab5 -r 8380686be5cd src/HOL/ex/ROOT.ML
--- a/src/HOL/ex/ROOT.ML	Fri Jul 09 17:00:42 2010 +0200
+++ b/src/HOL/ex/ROOT.ML	Fri Jul 09 17:15:03 2010 +0200
@@ -23,6 +23,7 @@
   "InductiveInvariant_examples",
   "LocaleTest2",
   "Records",
+  "While_Combinator_Example",
   "MonoidGroup",
   "BinEx",
   "Hex_Bin_Examples",
diff -r 00ff97087ab5 -r 8380686be5cd src/HOL/ex/While_Combinator_Example.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/ex/While_Combinator_Example.thy	Fri Jul 09 17:15:03 2010 +0200
@@ -0,0 +1,60 @@
+(*  Title:      HOL/Library/While_Combinator.thy
+    Author:     Tobias Nipkow
+    Copyright   2000 TU Muenchen
+*)
+
+header {* An application of the While combinator *}
+
+theory While_Combinator_Example
+imports While_Combinator
+begin
+
+text {* Computation of the @{term lfp} on finite sets via 
+  iteration. *}
+
+theorem lfp_conv_while:
+  "[| mono f; finite U; f U = U |] ==>
+    lfp f = fst (while (\<lambda>(A, fA). A \<noteq> fA) (\<lambda>(A, fA). (fA, f fA)) ({}, f {}))"
+apply (rule_tac P = "\<lambda>(A, B). (A \<subseteq> U \<and> B = f A \<and> A \<subseteq> B \<and> B \<subseteq> lfp f)" and
+                r = "((Pow U \<times> UNIV) \<times> (Pow U \<times> UNIV)) \<inter>
+                     inv_image finite_psubset (op - U o fst)" in while_rule)
+   apply (subst lfp_unfold)
+    apply assumption
+   apply (simp add: monoD)
+  apply (subst lfp_unfold)
+   apply assumption
+  apply clarsimp
+  apply (blast dest: monoD)
+ apply (fastsimp intro!: lfp_lowerbound)
+ apply (blast intro: wf_finite_psubset Int_lower2 [THEN [2] wf_subset])
+apply (clarsimp simp add: finite_psubset_def order_less_le)
+apply (blast intro!: finite_Diff dest: monoD)
+done
+
+
+subsection {* Example *}
+
+text{* Cannot use @{thm[source]set_eq_subset} because it leads to
+looping because the antisymmetry simproc turns the subset relationship
+back into equality. *}
+
+theorem "P (lfp (\<lambda>N::int set. {0} \<union> {(n + 2) mod 6 | n. n \<in> N})) =
+  P {0, 4, 2}"
+proof -
+  have seteq: "!!A B. (A = B) = ((!a : A. a:B) & (!b:B. b:A))"
+    by blast
+  have aux: "!!f A B. {f n | n. A n \<or> B n} = {f n | n. A n} \<union> {f n | n. B n}"
+    apply blast
+    done
+  show ?thesis
+    apply (subst lfp_conv_while [where ?U = "{0, 1, 2, 3, 4, 5}"])
+       apply (rule monoI)
+      apply blast
+     apply simp
+    apply (simp add: aux set_eq_subset)
+    txt {* The fixpoint computation is performed purely by rewriting: *}
+    apply (simp add: while_unfold aux seteq del: subset_empty)
+    done
+qed
+
+end
\ No newline at end of file