--- a/src/HOL/Library/Dlist.thy Mon Nov 22 09:37:39 2010 +0100
+++ b/src/HOL/Library/Dlist.thy Mon Nov 22 17:46:51 2010 +0100
@@ -3,7 +3,7 @@
header {* Lists with elements distinct as canonical example for datatype invariants *}
theory Dlist
-imports Main Fset
+imports Main Cset
begin
section {* The type of distinct lists *}
@@ -181,27 +181,27 @@
section {* Implementation of sets by distinct lists -- canonical! *}
-definition Set :: "'a dlist \<Rightarrow> 'a fset" where
- "Set dxs = Fset.Set (list_of_dlist dxs)"
+definition Set :: "'a dlist \<Rightarrow> 'a Cset.set" where
+ "Set dxs = Cset.set (list_of_dlist dxs)"
-definition Coset :: "'a dlist \<Rightarrow> 'a fset" where
- "Coset dxs = Fset.Coset (list_of_dlist dxs)"
+definition Coset :: "'a dlist \<Rightarrow> 'a Cset.set" where
+ "Coset dxs = Cset.coset (list_of_dlist dxs)"
code_datatype Set Coset
declare member_code [code del]
-declare is_empty_Set [code del]
-declare empty_Set [code del]
-declare UNIV_Set [code del]
-declare insert_Set [code del]
-declare remove_Set [code del]
-declare compl_Set [code del]
-declare compl_Coset [code del]
-declare map_Set [code del]
-declare filter_Set [code del]
-declare forall_Set [code del]
-declare exists_Set [code del]
-declare card_Set [code del]
+declare Cset.is_empty_set [code del]
+declare Cset.empty_set [code del]
+declare Cset.UNIV_set [code del]
+declare insert_set [code del]
+declare remove_set [code del]
+declare compl_set [code del]
+declare compl_coset [code del]
+declare map_set [code del]
+declare filter_set [code del]
+declare forall_set [code del]
+declare exists_set [code del]
+declare card_set [code del]
declare inter_project [code del]
declare subtract_remove [code del]
declare union_insert [code del]
@@ -209,31 +209,31 @@
declare Supremum_sup [code del]
lemma Set_Dlist [simp]:
- "Set (Dlist xs) = Fset (set xs)"
- by (rule fset_eqI) (simp add: Set_def)
+ "Set (Dlist xs) = Cset.Set (set xs)"
+ by (rule Cset.set_eqI) (simp add: Set_def)
lemma Coset_Dlist [simp]:
- "Coset (Dlist xs) = Fset (- set xs)"
- by (rule fset_eqI) (simp add: Coset_def)
+ "Coset (Dlist xs) = Cset.Set (- set xs)"
+ by (rule Cset.set_eqI) (simp add: Coset_def)
lemma member_Set [simp]:
- "Fset.member (Set dxs) = List.member (list_of_dlist dxs)"
+ "Cset.member (Set dxs) = List.member (list_of_dlist dxs)"
by (simp add: Set_def member_set)
lemma member_Coset [simp]:
- "Fset.member (Coset dxs) = Not \<circ> List.member (list_of_dlist dxs)"
+ "Cset.member (Coset dxs) = Not \<circ> List.member (list_of_dlist dxs)"
by (simp add: Coset_def member_set not_set_compl)
lemma Set_dlist_of_list [code]:
- "Fset.Set xs = Set (dlist_of_list xs)"
- by (rule fset_eqI) simp
+ "Cset.set xs = Set (dlist_of_list xs)"
+ by (rule Cset.set_eqI) simp
lemma Coset_dlist_of_list [code]:
- "Fset.Coset xs = Coset (dlist_of_list xs)"
- by (rule fset_eqI) simp
+ "Cset.coset xs = Coset (dlist_of_list xs)"
+ by (rule Cset.set_eqI) simp
lemma is_empty_Set [code]:
- "Fset.is_empty (Set dxs) \<longleftrightarrow> null dxs"
+ "Cset.is_empty (Set dxs) \<longleftrightarrow> null dxs"
by (simp add: null_def List.null_def member_set)
lemma bot_code [code]:
@@ -245,58 +245,58 @@
by (simp add: empty_def)
lemma insert_code [code]:
- "Fset.insert x (Set dxs) = Set (insert x dxs)"
- "Fset.insert x (Coset dxs) = Coset (remove x dxs)"
+ "Cset.insert x (Set dxs) = Set (insert x dxs)"
+ "Cset.insert x (Coset dxs) = Coset (remove x dxs)"
by (simp_all add: insert_def remove_def member_set not_set_compl)
lemma remove_code [code]:
- "Fset.remove x (Set dxs) = Set (remove x dxs)"
- "Fset.remove x (Coset dxs) = Coset (insert x dxs)"
+ "Cset.remove x (Set dxs) = Set (remove x dxs)"
+ "Cset.remove x (Coset dxs) = Coset (insert x dxs)"
by (auto simp add: insert_def remove_def member_set not_set_compl)
lemma member_code [code]:
- "Fset.member (Set dxs) = member dxs"
- "Fset.member (Coset dxs) = Not \<circ> member dxs"
+ "Cset.member (Set dxs) = member dxs"
+ "Cset.member (Coset dxs) = Not \<circ> member dxs"
by (simp_all add: member_def)
lemma compl_code [code]:
"- Set dxs = Coset dxs"
"- Coset dxs = Set dxs"
- by (rule fset_eqI, simp add: member_set not_set_compl)+
+ by (rule Cset.set_eqI, simp add: member_set not_set_compl)+
lemma map_code [code]:
- "Fset.map f (Set dxs) = Set (map f dxs)"
- by (rule fset_eqI) (simp add: member_set)
+ "Cset.map f (Set dxs) = Set (map f dxs)"
+ by (rule Cset.set_eqI) (simp add: member_set)
lemma filter_code [code]:
- "Fset.filter f (Set dxs) = Set (filter f dxs)"
- by (rule fset_eqI) (simp add: member_set)
+ "Cset.filter f (Set dxs) = Set (filter f dxs)"
+ by (rule Cset.set_eqI) (simp add: member_set)
lemma forall_Set [code]:
- "Fset.forall P (Set xs) \<longleftrightarrow> list_all P (list_of_dlist xs)"
+ "Cset.forall P (Set xs) \<longleftrightarrow> list_all P (list_of_dlist xs)"
by (simp add: member_set list_all_iff)
lemma exists_Set [code]:
- "Fset.exists P (Set xs) \<longleftrightarrow> list_ex P (list_of_dlist xs)"
+ "Cset.exists P (Set xs) \<longleftrightarrow> list_ex P (list_of_dlist xs)"
by (simp add: member_set list_ex_iff)
lemma card_code [code]:
- "Fset.card (Set dxs) = length dxs"
+ "Cset.card (Set dxs) = length dxs"
by (simp add: length_def member_set distinct_card)
lemma inter_code [code]:
- "inf A (Set xs) = Set (filter (Fset.member A) xs)"
- "inf A (Coset xs) = foldr Fset.remove xs A"
+ "inf A (Set xs) = Set (filter (Cset.member A) xs)"
+ "inf A (Coset xs) = foldr Cset.remove xs A"
by (simp_all only: Set_def Coset_def foldr_def inter_project list_of_dlist_filter)
lemma subtract_code [code]:
- "A - Set xs = foldr Fset.remove xs A"
- "A - Coset xs = Set (filter (Fset.member A) xs)"
+ "A - Set xs = foldr Cset.remove xs A"
+ "A - Coset xs = Set (filter (Cset.member A) xs)"
by (simp_all only: Set_def Coset_def foldr_def subtract_remove list_of_dlist_filter)
lemma union_code [code]:
- "sup (Set xs) A = foldr Fset.insert xs A"
- "sup (Coset xs) A = Coset (filter (Not \<circ> Fset.member A) xs)"
+ "sup (Set xs) A = foldr Cset.insert xs A"
+ "sup (Coset xs) A = Coset (filter (Not \<circ> Cset.member A) xs)"
by (simp_all only: Set_def Coset_def foldr_def union_insert list_of_dlist_filter)
context complete_lattice