--- a/src/HOL/IsaMakefile Sun Apr 11 17:40:43 2010 +0200
+++ b/src/HOL/IsaMakefile Sun Apr 11 17:46:42 2010 +0200
@@ -415,7 +415,7 @@
Library/Boolean_Algebra.thy Library/Countable.thy \
Library/Diagonalize.thy Library/RBT.thy Library/Univ_Poly.thy \
Library/Poly_Deriv.thy Library/Polynomial.thy Library/Preorder.thy \
- Library/Product_plus.thy Library/Product_Vector.thy Library/Tree.thy \
+ Library/Product_plus.thy Library/Product_Vector.thy \
Library/Enum.thy Library/Float.thy Library/Quotient_List.thy \
Library/Quotient_Option.thy Library/Quotient_Product.thy \
Library/Quotient_Sum.thy Library/Quotient_Syntax.thy \
--- a/src/HOL/Library/Tree.thy Sun Apr 11 17:40:43 2010 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,152 +0,0 @@
-(* Author: Florian Haftmann, TU Muenchen *)
-
-header {* Trees implementing mappings. *}
-
-theory Tree
-imports Mapping
-begin
-
-subsection {* Type definition and operations *}
-
-datatype ('a, 'b) tree = Empty
- | Branch 'b 'a "('a, 'b) tree" "('a, 'b) tree"
-
-primrec lookup :: "('a\<Colon>linorder, 'b) tree \<Rightarrow> 'a \<rightharpoonup> 'b" where
- "lookup Empty = (\<lambda>_. None)"
- | "lookup (Branch v k l r) = (\<lambda>k'. if k' = k then Some v
- else if k' \<le> k then lookup l k' else lookup r k')"
-
-primrec update :: "'a\<Colon>linorder \<Rightarrow> 'b \<Rightarrow> ('a, 'b) tree \<Rightarrow> ('a, 'b) tree" where
- "update k v Empty = Branch v k Empty Empty"
- | "update k' v' (Branch v k l r) = (if k' = k then
- Branch v' k l r else if k' \<le> k
- then Branch v k (update k' v' l) r
- else Branch v k l (update k' v' r))"
-
-primrec keys :: "('a\<Colon>linorder, 'b) tree \<Rightarrow> 'a list" where
- "keys Empty = []"
- | "keys (Branch _ k l r) = k # keys l @ keys r"
-
-definition size :: "('a\<Colon>linorder, 'b) tree \<Rightarrow> nat" where
- "size t = length (filter (\<lambda>x. x \<noteq> None) (map (lookup t) (remdups (keys t))))"
-
-fun bulkload :: "'a list \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) tree" where
- [simp del]: "bulkload ks f = (case ks of [] \<Rightarrow> Empty | _ \<Rightarrow> let
- mid = length ks div 2;
- ys = take mid ks;
- x = ks ! mid;
- zs = drop (Suc mid) ks
- in Branch (f x) x (bulkload ys f) (bulkload zs f))"
-
-
-subsection {* Properties *}
-
-lemma dom_lookup:
- "dom (Tree.lookup t) = set (filter (\<lambda>k. lookup t k \<noteq> None) (remdups (keys t)))"
-proof -
- have "dom (Tree.lookup t) = set (filter (\<lambda>k. lookup t k \<noteq> None) (keys t))"
- by (induct t) (auto simp add: dom_if)
- also have "\<dots> = set (filter (\<lambda>k. lookup t k \<noteq> None) (remdups (keys t)))"
- by simp
- finally show ?thesis .
-qed
-
-lemma lookup_finite:
- "finite (dom (lookup t))"
- unfolding dom_lookup by simp
-
-lemma lookup_update:
- "lookup (update k v t) = (lookup t)(k \<mapsto> v)"
- by (induct t) (simp_all add: expand_fun_eq)
-
-lemma lookup_bulkload:
- "sorted ks \<Longrightarrow> lookup (bulkload ks f) = (Some o f) |` set ks"
-proof (induct ks f rule: bulkload.induct)
- case (1 ks f) show ?case proof (cases ks)
- case Nil then show ?thesis by (simp add: bulkload.simps)
- next
- case (Cons w ws)
- then have case_simp: "\<And>w v::('a, 'b) tree. (case ks of [] \<Rightarrow> v | _ \<Rightarrow> w) = w"
- by (cases ks) auto
- from Cons have "ks \<noteq> []" by simp
- then have "0 < length ks" by simp
- let ?mid = "length ks div 2"
- let ?ys = "take ?mid ks"
- let ?x = "ks ! ?mid"
- let ?zs = "drop (Suc ?mid) ks"
- from `ks \<noteq> []` have ks_split: "ks = ?ys @ [?x] @ ?zs"
- by (simp add: id_take_nth_drop)
- then have in_ks: "\<And>x. x \<in> set ks \<longleftrightarrow> x \<in> set (?ys @ [?x] @ ?zs)"
- by simp
- with ks_split have ys_x: "\<And>y. y \<in> set ?ys \<Longrightarrow> y \<le> ?x"
- and x_zs: "\<And>z. z \<in> set ?zs \<Longrightarrow> ?x \<le> z"
- using `sorted ks` sorted_append [of "?ys" "[?x] @ ?zs"] sorted_append [of "[?x]" "?zs"]
- by simp_all
- have ys: "lookup (bulkload ?ys f) = (Some o f) |` set ?ys"
- by (rule "1.hyps"(1)) (auto intro: Cons sorted_take `sorted ks`)
- have zs: "lookup (bulkload ?zs f) = (Some o f) |` set ?zs"
- by (rule "1.hyps"(2)) (auto intro: Cons sorted_drop `sorted ks`)
- show ?thesis using `0 < length ks`
- by (simp add: bulkload.simps)
- (auto simp add: restrict_map_def in_ks case_simp Let_def ys zs expand_fun_eq
- dest: in_set_takeD in_set_dropD ys_x x_zs)
- qed
-qed
-
-
-subsection {* Trees as mappings *}
-
-definition Tree :: "('a\<Colon>linorder, 'b) tree \<Rightarrow> ('a, 'b) mapping" where
- "Tree t = Mapping (Tree.lookup t)"
-
-lemma [code, code del]:
- "(eq_class.eq :: (_, _) mapping \<Rightarrow> _) = eq_class.eq" ..
-
-lemma [code, code del]:
- "Mapping.delete k m = Mapping.delete k m" ..
-
-code_datatype Tree
-
-lemma empty_Tree [code]:
- "Mapping.empty = Tree Empty"
- by (simp add: Tree_def Mapping.empty_def)
-
-lemma lookup_Tree [code]:
- "Mapping.lookup (Tree t) = lookup t"
- by (simp add: Tree_def)
-
-lemma is_empty_Tree [code]:
- "Mapping.is_empty (Tree Empty) \<longleftrightarrow> True"
- "Mapping.is_empty (Tree (Branch v k l r)) \<longleftrightarrow> False"
- by (simp_all only: is_empty_def lookup_Tree dom_lookup) auto
-
-lemma update_Tree [code]:
- "Mapping.update k v (Tree t) = Tree (update k v t)"
- by (simp add: Tree_def lookup_update)
-
-lemma [code, code del]:
- "Mapping.ordered_keys = Mapping.ordered_keys " ..
-
-lemma keys_Tree [code]:
- "Mapping.keys (Tree t) = set (filter (\<lambda>k. lookup t k \<noteq> None) (remdups (keys t)))"
- by (simp add: Mapping.keys_def lookup_Tree dom_lookup)
-
-lemma size_Tree [code]:
- "Mapping.size (Tree t) = size t"
-proof -
- have "card (dom (Tree.lookup t)) = length (filter (\<lambda>x. x \<noteq> None) (map (lookup t) (remdups (keys t))))"
- unfolding dom_lookup by (subst distinct_card) (auto simp add: comp_def)
- then show ?thesis by (auto simp add: Tree_def Mapping.size_def size_def)
-qed
-
-lemma tabulate_Tree [code]:
- "Mapping.tabulate ks f = Tree (bulkload (sort ks) f)"
-proof -
- have "Mapping.lookup (Mapping.tabulate ks f) = Mapping.lookup (Tree (bulkload (sort ks) f))"
- by (simp add: lookup_bulkload lookup_Tree)
- then show ?thesis by (simp only: lookup_inject)
-qed
-
-hide (open) const Empty Branch lookup update keys size bulkload Tree
-
-end
--- a/src/HOL/ex/Codegenerator_Candidates.thy Sun Apr 11 17:40:43 2010 +0200
+++ b/src/HOL/ex/Codegenerator_Candidates.thy Sun Apr 11 17:46:42 2010 +0200
@@ -22,7 +22,6 @@
"~~/src/HOL/ex/Records"
SetsAndFunctions
Table
- Tree
While_Combinator
Word
begin