--- a/src/HOL/Library/Dlist_Cset.thy Sat Aug 27 09:02:25 2011 +0200
+++ b/src/HOL/Library/Dlist_Cset.thy Sat Aug 27 09:44:45 2011 +0200
@@ -3,66 +3,44 @@
header {* Canonical implementation of sets by distinct lists *}
theory Dlist_Cset
-imports Dlist List_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 = List_Cset.coset (list_of_dlist dxs)"
+ "Coset dxs = Cset.coset (list_of_dlist dxs)"
code_datatype Set Coset
-declare member_code [code del]
-declare List_Cset.is_empty_set [code del]
-declare List_Cset.empty_set [code del]
-declare List_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 List_Cset.single_set [code del]
-declare List_Cset.bind_set [code del]
-declare List_Cset.pred_of_cset_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)"
+ "Set (Dlist xs) = Cset.set xs"
by (rule Cset.set_eqI) (simp add: Set_def)
lemma Coset_Dlist [simp]:
- "Coset (Dlist xs) = Cset.Set (- set xs)"
+ "Coset (Dlist xs) = Cset.coset 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)
+ by (simp add: Set_def fun_eq_iff List.member_def)
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)
+ by (simp add: Coset_def fun_eq_iff List.member_def)
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]:
- "List_Cset.coset xs = Coset (dlist_of_list xs)"
+ "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)
+ by (simp add: Dlist.null_def List.null_def Set_def)
lemma bot_code [code]:
"bot = Set Dlist.empty"
@@ -70,47 +48,47 @@
lemma top_code [code]:
"top = Coset Dlist.empty"
- by (simp add: empty_def)
+ by (simp add: empty_def Cset.coset_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)
+ by (simp_all add: Dlist.insert_def Dlist.remove_def Cset.set_def Cset.coset_def Set_def Coset_def)
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)
+ by (simp_all add: Dlist.insert_def Dlist.remove_def Cset.set_def Cset.coset_def Set_def Coset_def Compl_insert)
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)
+ by (simp_all add: List.member_def member_def fun_eq_iff Dlist.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)+
+ by (rule Cset.set_eqI, simp add: fun_eq_iff List.member_def Set_def Coset_def)+
lemma map_code [code]:
"Cset.map f (Set dxs) = Set (Dlist.map f dxs)"
- by (rule Cset.set_eqI) (simp add: member_set)
+ by (rule Cset.set_eqI) (simp add: fun_eq_iff List.member_def Set_def)
lemma filter_code [code]:
"Cset.filter f (Set dxs) = Set (Dlist.filter f dxs)"
- by (rule Cset.set_eqI) (simp add: member_set)
+ by (rule Cset.set_eqI) (simp add: fun_eq_iff List.member_def Set_def)
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)
+ by (simp add: Set_def 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)
+ by (simp add: Set_def list_ex_iff)
lemma card_code [code]:
"Cset.card (Set dxs) = Dlist.length dxs"
- by (simp add: length_def member_set distinct_card)
+ by (simp add: length_def Set_def distinct_card)
lemma inter_code [code]:
"inf A (Set xs) = Set (Dlist.filter (Cset.member A) xs)"
@@ -143,13 +121,15 @@
declare Cset.single_code[code]
lemma bind_set [code]:
- "Cset.bind (Dlist_Cset.Set xs) f = foldl (\<lambda>A x. sup A (f x)) Cset.empty (list_of_dlist xs)"
-by(simp add: List_Cset.bind_set Dlist_Cset.Set_def)
+ "Cset.bind (Dlist_Cset.Set xs) f = fold (sup \<circ> f) (list_of_dlist xs) Cset.empty"
+ by (simp add: Cset.bind_set Set_def)
hide_fact (open) bind_set
lemma pred_of_cset_set [code]:
"pred_of_cset (Dlist_Cset.Set xs) = foldr sup (map Predicate.single (list_of_dlist xs)) bot"
-by(simp add: List_Cset.pred_of_cset_set Dlist_Cset.Set_def)
+ by (simp add: Cset.pred_of_cset_set Dlist_Cset.Set_def)
hide_fact (open) pred_of_cset_set
+export_code "Cset._" in Haskell
+
end