--- a/src/HOL/Library/RBT.thy Thu Apr 12 13:47:21 2012 +0200
+++ b/src/HOL/Library/RBT.thy Fri Apr 13 11:45:30 2012 +0200
@@ -35,7 +35,7 @@
subsection {* Primitive operations *}
definition lookup :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> 'a \<rightharpoonup> 'b" where
- [code]: "lookup t = RBT_Impl.lookup (impl_of t)"
+ [code]: "lookup t = rbt_lookup (impl_of t)"
definition empty :: "('a\<Colon>linorder, 'b) rbt" where
"empty = RBT RBT_Impl.Empty"
@@ -45,17 +45,17 @@
by (simp add: empty_def RBT_inverse)
definition insert :: "'a\<Colon>linorder \<Rightarrow> 'b \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" where
- "insert k v t = RBT (RBT_Impl.insert k v (impl_of t))"
+ "insert k v t = RBT (rbt_insert k v (impl_of t))"
lemma impl_of_insert [code abstract]:
- "impl_of (insert k v t) = RBT_Impl.insert k v (impl_of t)"
+ "impl_of (insert k v t) = rbt_insert k v (impl_of t)"
by (simp add: insert_def RBT_inverse)
definition delete :: "'a\<Colon>linorder \<Rightarrow> ('a, 'b) rbt \<Rightarrow> ('a, 'b) rbt" where
- "delete k t = RBT (RBT_Impl.delete k (impl_of t))"
+ "delete k t = RBT (rbt_delete k (impl_of t))"
lemma impl_of_delete [code abstract]:
- "impl_of (delete k t) = RBT_Impl.delete k (impl_of t)"
+ "impl_of (delete k t) = rbt_delete k (impl_of t)"
by (simp add: delete_def RBT_inverse)
definition entries :: "('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a \<times> 'b) list" where
@@ -65,17 +65,17 @@
[code]: "keys t = RBT_Impl.keys (impl_of t)"
definition bulkload :: "('a\<Colon>linorder \<times> 'b) list \<Rightarrow> ('a, 'b) rbt" where
- "bulkload xs = RBT (RBT_Impl.bulkload xs)"
+ "bulkload xs = RBT (rbt_bulkload xs)"
lemma impl_of_bulkload [code abstract]:
- "impl_of (bulkload xs) = RBT_Impl.bulkload xs"
+ "impl_of (bulkload xs) = rbt_bulkload xs"
by (simp add: bulkload_def RBT_inverse)
definition map_entry :: "'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a, 'b) rbt" where
- "map_entry k f t = RBT (RBT_Impl.map_entry k f (impl_of t))"
+ "map_entry k f t = RBT (rbt_map_entry k f (impl_of t))"
lemma impl_of_map_entry [code abstract]:
- "impl_of (map_entry k f t) = RBT_Impl.map_entry k f (impl_of t)"
+ "impl_of (map_entry k f t) = rbt_map_entry k f (impl_of t)"
by (simp add: map_entry_def RBT_inverse)
definition map :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) rbt \<Rightarrow> ('a, 'b) rbt" where
@@ -98,11 +98,11 @@
subsection {* Abstract lookup properties *}
lemma lookup_RBT:
- "is_rbt t \<Longrightarrow> lookup (RBT t) = RBT_Impl.lookup t"
+ "is_rbt t \<Longrightarrow> lookup (RBT t) = rbt_lookup t"
by (simp add: lookup_def RBT_inverse)
lemma lookup_impl_of:
- "RBT_Impl.lookup (impl_of t) = lookup t"
+ "rbt_lookup (impl_of t) = lookup t"
by (simp add: lookup_def)
lemma entries_impl_of:
@@ -119,11 +119,11 @@
lemma lookup_insert [simp]:
"lookup (insert k v t) = (lookup t)(k \<mapsto> v)"
- by (simp add: insert_def lookup_RBT lookup_insert lookup_impl_of)
+ by (simp add: insert_def lookup_RBT rbt_lookup_rbt_insert lookup_impl_of)
lemma lookup_delete [simp]:
"lookup (delete k t) = (lookup t)(k := None)"
- by (simp add: delete_def lookup_RBT RBT_Impl.lookup_delete lookup_impl_of restrict_complement_singleton_eq)
+ by (simp add: delete_def lookup_RBT rbt_lookup_rbt_delete lookup_impl_of restrict_complement_singleton_eq)
lemma map_of_entries [simp]:
"map_of (entries t) = lookup t"
@@ -131,19 +131,19 @@
lemma entries_lookup:
"entries t1 = entries t2 \<longleftrightarrow> lookup t1 = lookup t2"
- by (simp add: entries_def lookup_def entries_lookup)
+ by (simp add: entries_def lookup_def entries_rbt_lookup)
lemma lookup_bulkload [simp]:
"lookup (bulkload xs) = map_of xs"
- by (simp add: bulkload_def lookup_RBT RBT_Impl.lookup_bulkload)
+ by (simp add: bulkload_def lookup_RBT rbt_lookup_rbt_bulkload)
lemma lookup_map_entry [simp]:
"lookup (map_entry k f t) = (lookup t)(k := Option.map f (lookup t k))"
- by (simp add: map_entry_def lookup_RBT RBT_Impl.lookup_map_entry lookup_impl_of)
+ by (simp add: map_entry_def lookup_RBT rbt_lookup_rbt_map_entry lookup_impl_of)
lemma lookup_map [simp]:
"lookup (map f t) k = Option.map (f k) (lookup t k)"
- by (simp add: map_def lookup_RBT RBT_Impl.lookup_map lookup_impl_of)
+ by (simp add: map_def lookup_RBT rbt_lookup_map lookup_impl_of)
lemma fold_fold:
"fold f t = List.fold (prod_case f) (entries t)"
@@ -154,7 +154,7 @@
by (simp add: rbt_eq_iff is_empty_def impl_of_empty split: rbt.split)
lemma RBT_lookup_empty [simp]: (*FIXME*)
- "RBT_Impl.lookup t = Map.empty \<longleftrightarrow> t = RBT_Impl.Empty"
+ "rbt_lookup t = Map.empty \<longleftrightarrow> t = RBT_Impl.Empty"
by (cases t) (auto simp add: fun_eq_iff)
lemma lookup_empty_empty [simp]:
@@ -163,7 +163,7 @@
lemma sorted_keys [iff]:
"sorted (keys t)"
- by (simp add: keys_def RBT_Impl.keys_def sorted_entries)
+ by (simp add: keys_def RBT_Impl.keys_def rbt_sorted_entries)
lemma distinct_keys [iff]:
"distinct (keys t)"