--- a/src/HOL/IsaMakefile Wed Jun 01 23:08:04 2011 +0200
+++ b/src/HOL/IsaMakefile Thu Jun 02 08:55:08 2011 +0200
@@ -443,6 +443,7 @@
Library/Code_Prolog.thy Tools/Predicate_Compile/code_prolog.ML \
Library/ContNotDenum.thy Library/Continuity.thy Library/Convex.thy \
Library/Countable.thy Library/Diagonalize.thy Library/Dlist.thy \
+ Library/Dlist_Cset.thy \
Library/Efficient_Nat.thy Library/Eval_Witness.thy \
Library/Executable_Set.thy Library/Extended_Reals.thy \
Library/Float.thy Library/Formal_Power_Series.thy \
--- a/src/HOL/Library/Dlist.thy Wed Jun 01 23:08:04 2011 +0200
+++ b/src/HOL/Library/Dlist.thy Thu Jun 02 08:55:08 2011 +0200
@@ -3,10 +3,10 @@
header {* Lists with elements distinct as canonical example for datatype invariants *}
theory Dlist
-imports Main Cset
+imports Main More_List
begin
-section {* The type of distinct lists *}
+subsection {* The type of distinct lists *}
typedef (open) 'a dlist = "{xs::'a list. distinct xs}"
morphisms list_of_dlist Abs_dlist
@@ -80,7 +80,7 @@
"foldr f dxs = List.foldr f (list_of_dlist dxs)"
-section {* Executable version obeying invariant *}
+subsection {* Executable version obeying invariant *}
lemma list_of_dlist_empty [simp, code abstract]:
"list_of_dlist empty = []"
@@ -130,7 +130,7 @@
by (fact equal_refl)
-section {* Induction principle and case distinction *}
+subsection {* Induction principle and case distinction *}
lemma dlist_induct [case_names empty insert, induct type: dlist]:
assumes empty: "P empty"
@@ -173,146 +173,12 @@
qed
-section {* Functorial structure *}
+subsection {* Functorial structure *}
enriched_type map: map
by (simp_all add: List.map.id remdups_map_remdups fun_eq_iff dlist_eq_iff)
-section {* Implementation of sets by distinct lists -- canonical! *}
-
-definition Set :: "'a dlist \<Rightarrow> 'a Cset.set" where
- "Set dxs = Cset.set (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 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]
-declare Infimum_inf [code del]
-declare Supremum_sup [code del]
-
-lemma Set_Dlist [simp]:
- "Set (Dlist xs) = Cset.Set (set xs)"
- by (rule Cset.set_eqI) (simp add: Set_def)
-
-lemma Coset_Dlist [simp]:
- "Coset (Dlist xs) = Cset.Set (- set xs)"
- by (rule Cset.set_eqI) (simp add: Coset_def)
-
-lemma member_Set [simp]:
- "Cset.member (Set dxs) = List.member (list_of_dlist dxs)"
- by (simp add: Set_def member_set)
-
-lemma member_Coset [simp]:
- "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]:
- "Cset.set xs = Set (dlist_of_list xs)"
- by (rule Cset.set_eqI) simp
-
-lemma Coset_dlist_of_list [code]:
- "Cset.coset xs = Coset (dlist_of_list xs)"
- by (rule Cset.set_eqI) simp
-
-lemma is_empty_Set [code]:
- "Cset.is_empty (Set dxs) \<longleftrightarrow> null dxs"
- by (simp add: null_def List.null_def member_set)
-
-lemma bot_code [code]:
- "bot = Set empty"
- by (simp add: empty_def)
-
-lemma top_code [code]:
- "top = Coset empty"
- by (simp add: empty_def)
-
-lemma insert_code [code]:
- "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]:
- "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]:
- "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 Cset.set_eqI, simp add: member_set not_set_compl)+
-
-lemma map_code [code]:
- "Cset.map f (Set dxs) = Set (map f dxs)"
- by (rule Cset.set_eqI) (simp add: member_set)
-
-lemma filter_code [code]:
- "Cset.filter f (Set dxs) = Set (filter f dxs)"
- by (rule Cset.set_eqI) (simp add: member_set)
-
-lemma forall_Set [code]:
- "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]:
- "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]:
- "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 (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 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 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
-begin
-
-lemma Infimum_code [code]:
- "Infimum (Set As) = foldr inf As top"
- by (simp only: Set_def Infimum_inf foldr_def inf.commute)
-
-lemma Supremum_code [code]:
- "Supremum (Set As) = foldr sup As bot"
- by (simp only: Set_def Supremum_sup foldr_def sup.commute)
-
-end
-
-
hide_const (open) member fold foldr empty insert remove map filter null member length fold
end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Library/Dlist_Cset.thy Thu Jun 02 08:55:08 2011 +0200
@@ -0,0 +1,140 @@
+(* Author: Florian Haftmann, TU Muenchen *)
+
+header {* Canonical implementation of sets by distinct lists *}
+
+theory Dlist_Cset
+imports Dlist Cset
+begin
+
+definition Set :: "'a dlist \<Rightarrow> 'a Cset.set" where
+ "Set dxs = Cset.set (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 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]
+declare Infimum_inf [code del]
+declare Supremum_sup [code del]
+
+lemma Set_Dlist [simp]:
+ "Set (Dlist xs) = Cset.Set (set xs)"
+ by (rule Cset.set_eqI) (simp add: Set_def)
+
+lemma Coset_Dlist [simp]:
+ "Coset (Dlist xs) = Cset.Set (- set xs)"
+ by (rule Cset.set_eqI) (simp add: Coset_def)
+
+lemma member_Set [simp]:
+ "Cset.member (Set dxs) = List.member (list_of_dlist dxs)"
+ by (simp add: Set_def member_set)
+
+lemma member_Coset [simp]:
+ "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]:
+ "Cset.set xs = Set (dlist_of_list xs)"
+ by (rule Cset.set_eqI) simp
+
+lemma Coset_dlist_of_list [code]:
+ "Cset.coset xs = Coset (dlist_of_list xs)"
+ by (rule Cset.set_eqI) simp
+
+lemma is_empty_Set [code]:
+ "Cset.is_empty (Set dxs) \<longleftrightarrow> Dlist.null dxs"
+ by (simp add: Dlist.null_def List.null_def member_set)
+
+lemma bot_code [code]:
+ "bot = Set Dlist.empty"
+ by (simp add: empty_def)
+
+lemma top_code [code]:
+ "top = Coset Dlist.empty"
+ by (simp add: empty_def)
+
+lemma insert_code [code]:
+ "Cset.insert x (Set dxs) = Set (Dlist.insert x dxs)"
+ "Cset.insert x (Coset dxs) = Coset (Dlist.remove x dxs)"
+ by (simp_all add: Dlist.insert_def Dlist.remove_def member_set not_set_compl)
+
+lemma remove_code [code]:
+ "Cset.remove x (Set dxs) = Set (Dlist.remove x dxs)"
+ "Cset.remove x (Coset dxs) = Coset (Dlist.insert x dxs)"
+ by (auto simp add: Dlist.insert_def Dlist.remove_def member_set not_set_compl)
+
+lemma member_code [code]:
+ "Cset.member (Set dxs) = Dlist.member dxs"
+ "Cset.member (Coset dxs) = Not \<circ> Dlist.member dxs"
+ by (simp_all add: member_def)
+
+lemma compl_code [code]:
+ "- Set dxs = Coset dxs"
+ "- Coset dxs = Set dxs"
+ by (rule Cset.set_eqI, simp add: member_set not_set_compl)+
+
+lemma map_code [code]:
+ "Cset.map f (Set dxs) = Set (Dlist.map f dxs)"
+ by (rule Cset.set_eqI) (simp add: member_set)
+
+lemma filter_code [code]:
+ "Cset.filter f (Set dxs) = Set (Dlist.filter f dxs)"
+ by (rule Cset.set_eqI) (simp add: member_set)
+
+lemma forall_Set [code]:
+ "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]:
+ "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]:
+ "Cset.card (Set dxs) = Dlist.length dxs"
+ by (simp add: length_def member_set distinct_card)
+
+lemma inter_code [code]:
+ "inf A (Set xs) = Set (Dlist.filter (Cset.member A) xs)"
+ "inf A (Coset xs) = Dlist.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 = Dlist.foldr Cset.remove xs A"
+ "A - Coset xs = Set (Dlist.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 = Dlist.foldr Cset.insert xs A"
+ "sup (Coset xs) A = Coset (Dlist.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
+begin
+
+lemma Infimum_code [code]:
+ "Infimum (Set As) = Dlist.foldr inf As top"
+ by (simp only: Set_def Infimum_inf foldr_def inf.commute)
+
+lemma Supremum_code [code]:
+ "Supremum (Set As) = Dlist.foldr sup As bot"
+ by (simp only: Set_def Supremum_sup foldr_def sup.commute)
+
+end
+
+end
--- a/src/HOL/Library/Library.thy Wed Jun 01 23:08:04 2011 +0200
+++ b/src/HOL/Library/Library.thy Thu Jun 02 08:55:08 2011 +0200
@@ -13,7 +13,7 @@
Convex
Countable
Diagonalize
- Dlist
+ Dlist_Cset
Eval_Witness
Float
Formal_Power_Series