(* Title: HOL/NanoJava/State.thy
Author: David von Oheimb
Copyright 2001 Technische Universitaet Muenchen
*)
section "Program State"
theory State imports TypeRel begin
definition body :: "cname \<times> mname => stmt" where
"body \<equiv> \<lambda>(C,m). bdy (the (method C m))"
text \<open>Locations, i.e.\ abstract references to objects\<close>
typedecl loc
datatype val
= Null \<comment> \<open>null reference\<close>
| Addr loc \<comment> \<open>address, i.e. location of object\<close>
type_synonym fields
= "(fname \<rightharpoonup> val)"
type_synonym
obj = "cname \<times> fields"
translations
(type) "fields" \<leftharpoondown> (type) "fname => val option"
(type) "obj" \<leftharpoondown> (type) "cname \<times> fields"
definition init_vars :: "('a \<rightharpoonup> 'b) => ('a \<rightharpoonup> val)" where
"init_vars m == map_option (\<lambda>T. Null) o m"
text \<open>private:\<close>
type_synonym heap = "loc \<rightharpoonup> obj"
type_synonym locals = "vname \<rightharpoonup> val"
text \<open>private:\<close>
record state
= heap :: heap
locals :: locals
translations
(type) "heap" \<leftharpoondown> (type) "loc => obj option"
(type) "locals" \<leftharpoondown> (type) "vname => val option"
(type) "state" \<leftharpoondown> (type) "(|heap :: heap, locals :: locals|)"
definition del_locs :: "state => state" where
"del_locs s \<equiv> s (| locals := empty |)"
definition init_locs :: "cname => mname => state => state" where
"init_locs C m s \<equiv> s (| locals := locals s ++
init_vars (map_of (lcl (the (method C m)))) |)"
text \<open>The first parameter of @{term set_locs} is of type @{typ state}
rather than @{typ locals} in order to keep @{typ locals} private.\<close>
definition set_locs :: "state => state => state" where
"set_locs s s' \<equiv> s' (| locals := locals s |)"
definition get_local :: "state => vname => val" ("_<_>" [99,0] 99) where
"get_local s x \<equiv> the (locals s x)"
\<comment> \<open>local function:\<close>
definition get_obj :: "state => loc => obj" where
"get_obj s a \<equiv> the (heap s a)"
definition obj_class :: "state => loc => cname" where
"obj_class s a \<equiv> fst (get_obj s a)"
definition get_field :: "state => loc => fname => val" where
"get_field s a f \<equiv> the (snd (get_obj s a) f)"
\<comment> \<open>local function:\<close>
definition hupd :: "loc => obj => state => state" ("hupd'(_\<mapsto>_')" [10,10] 1000) where
"hupd a obj s \<equiv> s (| heap := ((heap s)(a\<mapsto>obj))|)"
definition lupd :: "vname => val => state => state" ("lupd'(_\<mapsto>_')" [10,10] 1000) where
"lupd x v s \<equiv> s (| locals := ((locals s)(x\<mapsto>v ))|)"
definition new_obj :: "loc => cname => state => state" where
"new_obj a C \<equiv> hupd(a\<mapsto>(C,init_vars (field C)))"
definition upd_obj :: "loc => fname => val => state => state" where
"upd_obj a f v s \<equiv> let (C,fs) = the (heap s a) in hupd(a\<mapsto>(C,fs(f\<mapsto>v))) s"
definition new_Addr :: "state => val" where
"new_Addr s == SOME v. (\<exists>a. v = Addr a \<and> (heap s) a = None) | v = Null"
subsection "Properties not used in the meta theory"
lemma locals_upd_id [simp]: "s\<lparr>locals := locals s\<rparr> = s"
by simp
lemma lupd_get_local_same [simp]: "lupd(x\<mapsto>v) s<x> = v"
by (simp add: lupd_def get_local_def)
lemma lupd_get_local_other [simp]: "x \<noteq> y \<Longrightarrow> lupd(x\<mapsto>v) s<y> = s<y>"
apply (drule not_sym)
by (simp add: lupd_def get_local_def)
lemma get_field_lupd [simp]:
"get_field (lupd(x\<mapsto>y) s) a f = get_field s a f"
by (simp add: lupd_def get_field_def get_obj_def)
lemma get_field_set_locs [simp]:
"get_field (set_locs l s) a f = get_field s a f"
by (simp add: lupd_def get_field_def set_locs_def get_obj_def)
lemma get_field_del_locs [simp]:
"get_field (del_locs s) a f = get_field s a f"
by (simp add: lupd_def get_field_def del_locs_def get_obj_def)
lemma new_obj_get_local [simp]: "new_obj a C s <x> = s<x>"
by (simp add: new_obj_def hupd_def get_local_def)
lemma heap_lupd [simp]: "heap (lupd(x\<mapsto>y) s) = heap s"
by (simp add: lupd_def)
lemma heap_hupd_same [simp]: "heap (hupd(a\<mapsto>obj) s) a = Some obj"
by (simp add: hupd_def)
lemma heap_hupd_other [simp]: "aa \<noteq> a \<Longrightarrow> heap (hupd(aa\<mapsto>obj) s) a = heap s a"
apply (drule not_sym)
by (simp add: hupd_def)
lemma hupd_hupd [simp]: "hupd(a\<mapsto>obj) (hupd(a\<mapsto>obj') s) = hupd(a\<mapsto>obj) s"
by (simp add: hupd_def)
lemma heap_del_locs [simp]: "heap (del_locs s) = heap s"
by (simp add: del_locs_def)
lemma heap_set_locs [simp]: "heap (set_locs l s) = heap s"
by (simp add: set_locs_def)
lemma hupd_lupd [simp]:
"hupd(a\<mapsto>obj) (lupd(x\<mapsto>y) s) = lupd(x\<mapsto>y) (hupd(a\<mapsto>obj) s)"
by (simp add: hupd_def lupd_def)
lemma hupd_del_locs [simp]:
"hupd(a\<mapsto>obj) (del_locs s) = del_locs (hupd(a\<mapsto>obj) s)"
by (simp add: hupd_def del_locs_def)
lemma new_obj_lupd [simp]:
"new_obj a C (lupd(x\<mapsto>y) s) = lupd(x\<mapsto>y) (new_obj a C s)"
by (simp add: new_obj_def)
lemma new_obj_del_locs [simp]:
"new_obj a C (del_locs s) = del_locs (new_obj a C s)"
by (simp add: new_obj_def)
lemma upd_obj_lupd [simp]:
"upd_obj a f v (lupd(x\<mapsto>y) s) = lupd(x\<mapsto>y) (upd_obj a f v s)"
by (simp add: upd_obj_def Let_def split_beta)
lemma upd_obj_del_locs [simp]:
"upd_obj a f v (del_locs s) = del_locs (upd_obj a f v s)"
by (simp add: upd_obj_def Let_def split_beta)
lemma get_field_hupd_same [simp]:
"get_field (hupd(a\<mapsto>(C, fs)) s) a = the \<circ> fs"
apply (rule ext)
by (simp add: get_field_def get_obj_def)
lemma get_field_hupd_other [simp]:
"aa \<noteq> a \<Longrightarrow> get_field (hupd(aa\<mapsto>obj) s) a = get_field s a"
apply (rule ext)
by (simp add: get_field_def get_obj_def)
lemma new_AddrD:
"new_Addr s = v \<Longrightarrow> (\<exists>a. v = Addr a \<and> heap s a = None) | v = Null"
apply (unfold new_Addr_def)
apply (erule subst)
apply (rule someI)
apply (rule disjI2)
apply (rule HOL.refl)
done
end