--- a/src/HOL/Library/Array.thy Thu Jan 08 17:25:06 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,209 +0,0 @@
-(* Title: HOL/Library/Array.thy
- ID: $Id$
- Author: John Matthews, Galois Connections; Alexander Krauss, Lukas Bulwahn & Florian Haftmann, TU Muenchen
-*)
-
-header {* Monadic arrays *}
-
-theory Array
-imports Heap_Monad Code_Index
-begin
-
-subsection {* Primitives *}
-
-definition
- new :: "nat \<Rightarrow> 'a\<Colon>heap \<Rightarrow> 'a array Heap" where
- [code del]: "new n x = Heap_Monad.heap (Heap.array n x)"
-
-definition
- of_list :: "'a\<Colon>heap list \<Rightarrow> 'a array Heap" where
- [code del]: "of_list xs = Heap_Monad.heap (Heap.array_of_list xs)"
-
-definition
- length :: "'a\<Colon>heap array \<Rightarrow> nat Heap" where
- [code del]: "length arr = Heap_Monad.heap (\<lambda>h. (Heap.length arr h, h))"
-
-definition
- nth :: "'a\<Colon>heap array \<Rightarrow> nat \<Rightarrow> 'a Heap"
-where
- [code del]: "nth a i = (do len \<leftarrow> length a;
- (if i < len
- then Heap_Monad.heap (\<lambda>h. (get_array a h ! i, h))
- else raise (''array lookup: index out of range''))
- done)"
-
--- {* FIXME adjustion for List theory *}
-no_syntax
- nth :: "'a list \<Rightarrow> nat \<Rightarrow> 'a" (infixl "!" 100)
-
-abbreviation
- nth_list :: "'a list \<Rightarrow> nat \<Rightarrow> 'a" (infixl "!" 100)
-where
- "nth_list \<equiv> List.nth"
-
-definition
- upd :: "nat \<Rightarrow> 'a \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> 'a\<Colon>heap array Heap"
-where
- [code del]: "upd i x a = (do len \<leftarrow> length a;
- (if i < len
- then Heap_Monad.heap (\<lambda>h. (a, Heap.upd a i x h))
- else raise (''array update: index out of range''))
- done)"
-
-lemma upd_return:
- "upd i x a \<guillemotright> return a = upd i x a"
-proof (rule Heap_eqI)
- fix h
- obtain len h' where "Heap_Monad.execute (Array.length a) h = (len, h')"
- by (cases "Heap_Monad.execute (Array.length a) h")
- then show "Heap_Monad.execute (upd i x a \<guillemotright> return a) h = Heap_Monad.execute (upd i x a) h"
- by (auto simp add: upd_def bindM_def split: sum.split)
-qed
-
-
-subsection {* Derivates *}
-
-definition
- map_entry :: "nat \<Rightarrow> ('a\<Colon>heap \<Rightarrow> 'a) \<Rightarrow> 'a array \<Rightarrow> 'a array Heap"
-where
- "map_entry i f a = (do
- x \<leftarrow> nth a i;
- upd i (f x) a
- done)"
-
-definition
- swap :: "nat \<Rightarrow> 'a \<Rightarrow> 'a\<Colon>heap array \<Rightarrow> 'a Heap"
-where
- "swap i x a = (do
- y \<leftarrow> nth a i;
- upd i x a;
- return y
- done)"
-
-definition
- make :: "nat \<Rightarrow> (nat \<Rightarrow> 'a\<Colon>heap) \<Rightarrow> 'a array Heap"
-where
- "make n f = of_list (map f [0 ..< n])"
-
-definition
- freeze :: "'a\<Colon>heap array \<Rightarrow> 'a list Heap"
-where
- "freeze a = (do
- n \<leftarrow> length a;
- mapM (nth a) [0..<n]
- done)"
-
-definition
- map :: "('a\<Colon>heap \<Rightarrow> 'a) \<Rightarrow> 'a array \<Rightarrow> 'a array Heap"
-where
- "map f a = (do
- n \<leftarrow> length a;
- mapM (\<lambda>n. map_entry n f a) [0..<n];
- return a
- done)"
-
-hide (open) const new map -- {* avoid clashed with some popular names *}
-
-
-subsection {* Properties *}
-
-lemma array_make [code]:
- "Array.new n x = make n (\<lambda>_. x)"
- by (induct n) (simp_all add: make_def new_def Heap_Monad.heap_def
- monad_simp array_of_list_replicate [symmetric]
- map_replicate_trivial replicate_append_same
- of_list_def)
-
-lemma array_of_list_make [code]:
- "of_list xs = make (List.length xs) (\<lambda>n. xs ! n)"
- unfolding make_def map_nth ..
-
-
-subsection {* Code generator setup *}
-
-subsubsection {* Logical intermediate layer *}
-
-definition new' where
- [code del]: "new' = Array.new o nat_of_index"
-hide (open) const new'
-lemma [code]:
- "Array.new = Array.new' o index_of_nat"
- by (simp add: new'_def o_def)
-
-definition of_list' where
- [code del]: "of_list' i xs = Array.of_list (take (nat_of_index i) xs)"
-hide (open) const of_list'
-lemma [code]:
- "Array.of_list xs = Array.of_list' (index_of_nat (List.length xs)) xs"
- by (simp add: of_list'_def)
-
-definition make' where
- [code del]: "make' i f = Array.make (nat_of_index i) (f o index_of_nat)"
-hide (open) const make'
-lemma [code]:
- "Array.make n f = Array.make' (index_of_nat n) (f o nat_of_index)"
- by (simp add: make'_def o_def)
-
-definition length' where
- [code del]: "length' = Array.length \<guillemotright>== liftM index_of_nat"
-hide (open) const length'
-lemma [code]:
- "Array.length = Array.length' \<guillemotright>== liftM nat_of_index"
- by (simp add: length'_def monad_simp',
- simp add: liftM_def comp_def monad_simp,
- simp add: monad_simp')
-
-definition nth' where
- [code del]: "nth' a = Array.nth a o nat_of_index"
-hide (open) const nth'
-lemma [code]:
- "Array.nth a n = Array.nth' a (index_of_nat n)"
- by (simp add: nth'_def)
-
-definition upd' where
- [code del]: "upd' a i x = Array.upd (nat_of_index i) x a \<guillemotright> return ()"
-hide (open) const upd'
-lemma [code]:
- "Array.upd i x a = Array.upd' a (index_of_nat i) x \<guillemotright> return a"
- by (simp add: upd'_def monad_simp upd_return)
-
-
-subsubsection {* SML *}
-
-code_type array (SML "_/ array")
-code_const Array (SML "raise/ (Fail/ \"bare Array\")")
-code_const Array.new' (SML "(fn/ ()/ =>/ Array.array/ ((_),/ (_)))")
-code_const Array.of_list (SML "(fn/ ()/ =>/ Array.fromList/ _)")
-code_const Array.make' (SML "(fn/ ()/ =>/ Array.tabulate/ ((_),/ (_)))")
-code_const Array.length' (SML "(fn/ ()/ =>/ Array.length/ _)")
-code_const Array.nth' (SML "(fn/ ()/ =>/ Array.sub/ ((_),/ (_)))")
-code_const Array.upd' (SML "(fn/ ()/ =>/ Array.update/ ((_),/ (_),/ (_)))")
-
-code_reserved SML Array
-
-
-subsubsection {* OCaml *}
-
-code_type array (OCaml "_/ array")
-code_const Array (OCaml "failwith/ \"bare Array\"")
-code_const Array.new' (OCaml "(fun/ ()/ ->/ Array.make/ _/ _)")
-code_const Array.of_list (OCaml "(fun/ ()/ ->/ Array.of'_list/ _)")
-code_const Array.make' (OCaml "(fun/ ()/ ->/ Array.init/ _/ _)")
-code_const Array.length' (OCaml "(fun/ ()/ ->/ Array.length/ _)")
-code_const Array.nth' (OCaml "(fun/ ()/ ->/ Array.get/ _/ _)")
-code_const Array.upd' (OCaml "(fun/ ()/ ->/ Array.set/ _/ _/ _)")
-
-code_reserved OCaml Array
-
-
-subsubsection {* Haskell *}
-
-code_type array (Haskell "STArray/ RealWorld/ _")
-code_const Array (Haskell "error/ \"bare Array\"")
-code_const Array.new' (Haskell "newArray/ (0,/ _)")
-code_const Array.of_list' (Haskell "newListArray/ (0,/ _)")
-code_const Array.length' (Haskell "lengthArray")
-code_const Array.nth' (Haskell "readArray")
-code_const Array.upd' (Haskell "writeArray")
-
-end