1.1 --- a/src/HOL/IsaMakefile Sat Mar 06 11:21:09 2010 +0100
1.2 +++ b/src/HOL/IsaMakefile Sat Mar 06 15:31:30 2010 +0100
1.3 @@ -401,7 +401,7 @@
1.4 Library/Ramsey.thy Library/Zorn.thy Library/Library/ROOT.ML \
1.5 Library/Library/document/root.tex Library/Library/document/root.bib \
1.6 Library/Transitive_Closure_Table.thy Library/While_Combinator.thy \
1.7 - Library/Product_ord.thy Library/Char_nat.thy \
1.8 + Library/Product_ord.thy Library/Char_nat.thy Library/Table.thy \
1.9 Library/Sublist_Order.thy Library/List_lexord.thy \
1.10 Library/Coinductive_List.thy Library/AssocList.thy \
1.11 Library/Formal_Power_Series.thy Library/Binomial.thy \
2.1 --- a/src/HOL/Library/Library.thy Sat Mar 06 11:21:09 2010 +0100
2.2 +++ b/src/HOL/Library/Library.thy Sat Mar 06 15:31:30 2010 +0100
2.3 @@ -58,6 +58,7 @@
2.4 SML_Quickcheck
2.5 State_Monad
2.6 Sum_Of_Squares
2.7 + Table
2.8 Transitive_Closure_Table
2.9 Univ_Poly
2.10 While_Combinator
3.1 --- /dev/null Thu Jan 01 00:00:00 1970 +0000
3.2 +++ b/src/HOL/Library/Table.thy Sat Mar 06 15:31:30 2010 +0100
3.3 @@ -0,0 +1,139 @@
3.4 +(* Author: Florian Haftmann, TU Muenchen *)
3.5 +
3.6 +header {* Tables: finite mappings implemented by red-black trees *}
3.7 +
3.8 +theory Table
3.9 +imports Main RBT
3.10 +begin
3.11 +
3.12 +subsection {* Type definition *}
3.13 +
3.14 +typedef (open) ('a, 'b) table = "{t :: ('a\<Colon>linorder, 'b) rbt. is_rbt t}"
3.15 + morphisms tree_of Table
3.16 +proof -
3.17 + have "RBT.Empty \<in> ?table" by simp
3.18 + then show ?thesis ..
3.19 +qed
3.20 +
3.21 +lemma is_rbt_tree_of [simp, intro]:
3.22 + "is_rbt (tree_of t)"
3.23 + using tree_of [of t] by simp
3.24 +
3.25 +lemma table_eq:
3.26 + "t1 = t2 \<longleftrightarrow> tree_of t1 = tree_of t2"
3.27 + by (simp add: tree_of_inject)
3.28 +
3.29 +code_abstype Table tree_of
3.30 + by (simp add: tree_of_inverse)
3.31 +
3.32 +
3.33 +subsection {* Primitive operations *}
3.34 +
3.35 +definition lookup :: "('a\<Colon>linorder, 'b) table \<Rightarrow> 'a \<rightharpoonup> 'b" where
3.36 + [code]: "lookup t = RBT.lookup (tree_of t)"
3.37 +
3.38 +definition empty :: "('a\<Colon>linorder, 'b) table" where
3.39 + "empty = Table RBT.Empty"
3.40 +
3.41 +lemma tree_of_empty [code abstract]:
3.42 + "tree_of empty = RBT.Empty"
3.43 + by (simp add: empty_def Table_inverse)
3.44 +
3.45 +definition update :: "'a\<Colon>linorder \<Rightarrow> 'b \<Rightarrow> ('a, 'b) table \<Rightarrow> ('a, 'b) table" where
3.46 + "update k v t = Table (RBT.insert k v (tree_of t))"
3.47 +
3.48 +lemma tree_of_update [code abstract]:
3.49 + "tree_of (update k v t) = RBT.insert k v (tree_of t)"
3.50 + by (simp add: update_def Table_inverse)
3.51 +
3.52 +definition delete :: "'a\<Colon>linorder \<Rightarrow> ('a, 'b) table \<Rightarrow> ('a, 'b) table" where
3.53 + "delete k t = Table (RBT.delete k (tree_of t))"
3.54 +
3.55 +lemma tree_of_delete [code abstract]:
3.56 + "tree_of (delete k t) = RBT.delete k (tree_of t)"
3.57 + by (simp add: delete_def Table_inverse)
3.58 +
3.59 +definition entries :: "('a\<Colon>linorder, 'b) table \<Rightarrow> ('a \<times> 'b) list" where
3.60 + [code]: "entries t = RBT.entries (tree_of t)"
3.61 +
3.62 +definition bulkload :: "('a\<Colon>linorder \<times> 'b) list \<Rightarrow> ('a, 'b) table" where
3.63 + "bulkload xs = Table (RBT.bulkload xs)"
3.64 +
3.65 +lemma tree_of_bulkload [code abstract]:
3.66 + "tree_of (bulkload xs) = RBT.bulkload xs"
3.67 + by (simp add: bulkload_def Table_inverse)
3.68 +
3.69 +definition map_entry :: "'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) table \<Rightarrow> ('a, 'b) table" where
3.70 + "map_entry k f t = Table (RBT.map_entry k f (tree_of t))"
3.71 +
3.72 +lemma tree_of_map_entry [code abstract]:
3.73 + "tree_of (map_entry k f t) = RBT.map_entry k f (tree_of t)"
3.74 + by (simp add: map_entry_def Table_inverse)
3.75 +
3.76 +definition map :: "('a \<Rightarrow> 'b \<Rightarrow> 'b) \<Rightarrow> ('a\<Colon>linorder, 'b) table \<Rightarrow> ('a, 'b) table" where
3.77 + "map f t = Table (RBT.map f (tree_of t))"
3.78 +
3.79 +lemma tree_of_map [code abstract]:
3.80 + "tree_of (map f t) = RBT.map f (tree_of t)"
3.81 + by (simp add: map_def Table_inverse)
3.82 +
3.83 +definition fold :: "('a \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> 'c) \<Rightarrow> ('a\<Colon>linorder, 'b) table \<Rightarrow> 'c \<Rightarrow> 'c" where
3.84 + [code]: "fold f t = RBT.fold f (tree_of t)"
3.85 +
3.86 +
3.87 +subsection {* Derived operations *}
3.88 +
3.89 +definition is_empty :: "('a\<Colon>linorder, 'b) table \<Rightarrow> bool" where
3.90 + [code]: "is_empty t = (case tree_of t of RBT.Empty \<Rightarrow> True | _ \<Rightarrow> False)"
3.91 +
3.92 +
3.93 +subsection {* Abstract lookup properties *}
3.94 +
3.95 +lemma lookup_Table:
3.96 + "is_rbt t \<Longrightarrow> lookup (Table t) = RBT.lookup t"
3.97 + by (simp add: lookup_def Table_inverse)
3.98 +
3.99 +lemma lookup_tree_of:
3.100 + "RBT.lookup (tree_of t) = lookup t"
3.101 + by (simp add: lookup_def)
3.102 +
3.103 +lemma entries_tree_of:
3.104 + "RBT.entries (tree_of t) = entries t"
3.105 + by (simp add: entries_def)
3.106 +
3.107 +lemma lookup_empty [simp]:
3.108 + "lookup empty = Map.empty"
3.109 + by (simp add: empty_def lookup_Table expand_fun_eq)
3.110 +
3.111 +lemma lookup_update [simp]:
3.112 + "lookup (update k v t) = (lookup t)(k \<mapsto> v)"
3.113 + by (simp add: update_def lookup_Table lookup_insert lookup_tree_of)
3.114 +
3.115 +lemma lookup_delete [simp]:
3.116 + "lookup (delete k t) = (lookup t)(k := None)"
3.117 + by (simp add: delete_def lookup_Table lookup_delete lookup_tree_of restrict_complement_singleton_eq)
3.118 +
3.119 +lemma map_of_entries [simp]:
3.120 + "map_of (entries t) = lookup t"
3.121 + by (simp add: entries_def map_of_entries lookup_tree_of)
3.122 +
3.123 +lemma lookup_bulkload [simp]:
3.124 + "lookup (bulkload xs) = map_of xs"
3.125 + by (simp add: bulkload_def lookup_Table lookup_bulkload)
3.126 +
3.127 +lemma lookup_map_entry [simp]:
3.128 + "lookup (map_entry k f t) = (lookup t)(k := Option.map f (lookup t k))"
3.129 + by (simp add: map_entry_def lookup_Table lookup_map_entry lookup_tree_of)
3.130 +
3.131 +lemma lookup_map [simp]:
3.132 + "lookup (map f t) k = Option.map (f k) (lookup t k)"
3.133 + by (simp add: map_def lookup_Table lookup_map lookup_tree_of)
3.134 +
3.135 +lemma fold_fold:
3.136 + "fold f t = (\<lambda>s. foldl (\<lambda>s (k, v). f k v s) s (entries t))"
3.137 + by (simp add: fold_def expand_fun_eq RBT.fold_def entries_tree_of)
3.138 +
3.139 +hide (open) const tree_of lookup empty update delete
3.140 + entries bulkload map_entry map fold
3.141 +
3.142 +end
4.1 --- a/src/HOL/ex/Codegenerator_Candidates.thy Sat Mar 06 11:21:09 2010 +0100
4.2 +++ b/src/HOL/ex/Codegenerator_Candidates.thy Sat Mar 06 15:31:30 2010 +0100
4.3 @@ -21,6 +21,7 @@
4.4 Product_ord
4.5 "~~/src/HOL/ex/Records"
4.6 SetsAndFunctions
4.7 + Table
4.8 Tree
4.9 While_Combinator
4.10 Word