--- a/src/HOL/Imperative_HOL/Ref.thy Mon Jul 05 15:36:37 2010 +0200
+++ b/src/HOL/Imperative_HOL/Ref.thy Mon Jul 05 16:46:23 2010 +0200
@@ -5,7 +5,7 @@
header {* Monadic references *}
theory Ref
-imports Heap_Monad
+imports Array
begin
text {*
@@ -14,11 +14,111 @@
and http://www.smlnj.org/doc/Conversion/top-level-comparison.html
*}
+subsection {* Primitive layer *}
+
+definition
+ ref_present :: "'a\<Colon>heap ref \<Rightarrow> heap \<Rightarrow> bool" where
+ "ref_present r h \<longleftrightarrow> addr_of_ref r < lim h"
+
+definition
+ get_ref :: "'a\<Colon>heap ref \<Rightarrow> heap \<Rightarrow> 'a" where
+ "get_ref r h = from_nat (refs h (TYPEREP('a)) (addr_of_ref r))"
+
+definition
+ set_ref :: "'a\<Colon>heap ref \<Rightarrow> 'a \<Rightarrow> heap \<Rightarrow> heap" where
+ "set_ref r x =
+ refs_update (\<lambda>h. h(TYPEREP('a) := ((h (TYPEREP('a))) (addr_of_ref r:=to_nat x))))"
+
+definition ref :: "'a \<Rightarrow> heap \<Rightarrow> 'a\<Colon>heap ref \<times> heap" where
+ "ref x h = (let
+ l = lim h;
+ r = Ref l;
+ h'' = set_ref r x (h\<lparr>lim := l + 1\<rparr>)
+ in (r, h''))"
+
+definition noteq_refs :: "('a\<Colon>heap) ref \<Rightarrow> ('b\<Colon>heap) ref \<Rightarrow> bool" (infix "=!=" 70) where
+ "r =!= s \<longleftrightarrow> TYPEREP('a) \<noteq> TYPEREP('b) \<or> addr_of_ref r \<noteq> addr_of_ref s"
+
+lemma noteq_refs_sym: "r =!= s \<Longrightarrow> s =!= r"
+ and unequal_refs [simp]: "r \<noteq> r' \<longleftrightarrow> r =!= r'" -- "same types!"
+ unfolding noteq_refs_def by auto
+
+lemma noteq_refs_irrefl: "r =!= r \<Longrightarrow> False"
+ unfolding noteq_refs_def by auto
+
+lemma present_new_ref: "ref_present r h \<Longrightarrow> r =!= fst (ref v h)"
+ by (simp add: ref_present_def ref_def Let_def noteq_refs_def)
+
+lemma next_ref_fresh [simp]:
+ assumes "(r, h') = ref x h"
+ shows "\<not> ref_present r h"
+ using assms by (cases h) (auto simp add: ref_def ref_present_def Let_def)
+
+lemma next_ref_present [simp]:
+ assumes "(r, h') = ref x h"
+ shows "ref_present r h'"
+ using assms by (cases h) (auto simp add: ref_def set_ref_def ref_present_def Let_def)
+
+lemma ref_get_set_eq [simp]: "get_ref r (set_ref r x h) = x"
+ by (simp add: get_ref_def set_ref_def)
+
+lemma ref_get_set_neq [simp]: "r =!= s \<Longrightarrow> get_ref r (set_ref s x h) = get_ref r h"
+ by (simp add: noteq_refs_def get_ref_def set_ref_def)
+
+(* FIXME: We need some infrastructure to infer that locally generated
+ new refs (by new_ref(_no_init), new_array(')) are distinct
+ from all existing refs.
+*)
+
+lemma ref_set_get: "set_ref r (get_ref r h) h = h"
+apply (simp add: set_ref_def get_ref_def)
+oops
+
+lemma set_ref_same[simp]:
+ "set_ref r x (set_ref r y h) = set_ref r x h"
+ by (simp add: set_ref_def)
+
+lemma ref_set_set_swap:
+ "r =!= r' \<Longrightarrow> set_ref r x (set_ref r' x' h) = set_ref r' x' (set_ref r x h)"
+ by (simp add: Let_def expand_fun_eq noteq_refs_def set_ref_def)
+
+lemma ref_new_set: "fst (ref v (set_ref r v' h)) = fst (ref v h)"
+ by (simp add: ref_def set_ref_def Let_def)
+
+lemma ref_get_new [simp]:
+ "get_ref (fst (ref v h)) (snd (ref v' h)) = v'"
+ by (simp add: ref_def Let_def split_def)
+
+lemma ref_set_new [simp]:
+ "set_ref (fst (ref v h)) new_v (snd (ref v h)) = snd (ref new_v h)"
+ by (simp add: ref_def Let_def split_def)
+
+lemma ref_get_new_neq: "r =!= (fst (ref v h)) \<Longrightarrow>
+ get_ref r (snd (ref v h)) = get_ref r h"
+ by (simp add: get_ref_def set_ref_def ref_def Let_def noteq_refs_def)
+
+lemma lim_set_ref [simp]:
+ "lim (set_ref r v h) = lim h"
+ by (simp add: set_ref_def)
+
+lemma ref_present_new_ref [simp]:
+ "ref_present r h \<Longrightarrow> ref_present r (snd (ref v h))"
+ by (simp add: ref_present_def ref_def Let_def)
+
+lemma ref_present_set_ref [simp]:
+ "ref_present r (set_ref r' v h) = ref_present r h"
+ by (simp add: set_ref_def ref_present_def)
+
+lemma noteq_refsI: "\<lbrakk> ref_present r h; \<not>ref_present r' h \<rbrakk> \<Longrightarrow> r =!= r'"
+ unfolding noteq_refs_def ref_present_def
+ by auto
+
+
subsection {* Primitives *}
definition
new :: "'a\<Colon>heap \<Rightarrow> 'a ref Heap" where
- [code del]: "new v = Heap_Monad.heap (Heap.ref v)"
+ [code del]: "new v = Heap_Monad.heap (Ref.ref v)"
definition
lookup :: "'a\<Colon>heap ref \<Rightarrow> 'a Heap" ("!_" 61) where
@@ -55,6 +155,48 @@
by (auto simp add: change_def lookup_chain)
+text {* Non-interaction between imperative array and imperative references *}
+
+lemma get_array_set_ref [simp]: "get_array a (set_ref r v h) = get_array a h"
+ by (simp add: get_array_def set_ref_def)
+
+lemma nth_set_ref [simp]: "get_array a (set_ref r v h) ! i = get_array a h ! i"
+ by simp
+
+lemma get_ref_upd [simp]: "get_ref r (Array.change a i v h) = get_ref r h"
+ by (simp add: get_ref_def set_array_def Array.change_def)
+
+lemma new_ref_upd: "fst (ref v (Array.change a i v' h)) = fst (ref v h)"
+ by (simp add: set_array_def get_array_def Let_def ref_new_set Array.change_def ref_def)
+
+lemma upd_set_ref_swap: "Array.change a i v (set_ref r v' h) = set_ref r v' (Array.change a i v h)"
+ by (simp add: set_ref_def Array.change_def get_array_def set_array_def)
+
+lemma length_new_ref[simp]:
+ "length a (snd (ref v h)) = length a h"
+ by (simp add: get_array_def set_ref_def length_def ref_def Let_def)
+
+lemma get_array_new_ref [simp]:
+ "get_array a (snd (ref v h)) = get_array a h"
+ by (simp add: ref_def set_ref_def get_array_def Let_def)
+
+lemma ref_present_upd [simp]:
+ "ref_present r (Array.change a i v h) = ref_present r h"
+ by (simp add: Array.change_def ref_present_def set_array_def get_array_def)
+
+lemma array_present_set_ref [simp]:
+ "array_present a (set_ref r v h) = array_present a h"
+ by (simp add: array_present_def set_ref_def)
+
+lemma array_present_new_ref [simp]:
+ "array_present a h \<Longrightarrow> array_present a (snd (ref v h))"
+ by (simp add: array_present_def ref_def Let_def)
+
+lemma array_ref_set_set_swap:
+ "set_array r x (set_ref r' x' h) = set_ref r' x' (set_array r x h)"
+ by (simp add: Let_def expand_fun_eq set_array_def set_ref_def)
+
+
subsection {* Code generator setup *}
subsubsection {* SML *}