(* Title: HOL/MicroJava/J/State.thy ID: $Id: State.thy,v 1.18 2005/06/17 14:13:09 haftmann Exp $ Author: David von Oheimb Copyright 1999 Technische Universitaet Muenchen *) header {* \isaheader{Program State} *} theory State imports TypeRel Value begin types fields_ = "(vname × cname \<rightharpoonup> val)" -- "field name, defining class, value" obj = "cname × fields_" -- "class instance with class name and fields" constdefs obj_ty :: "obj => ty" "obj_ty obj == Class (fst obj)" init_vars :: "('a × ty) list => ('a \<rightharpoonup> val)" "init_vars == map_of o map (λ(n,T). (n,default_val T))" types aheap = "loc \<rightharpoonup> obj" -- {* "@{text heap}" used in a translation below *} locals = "vname \<rightharpoonup> val" -- "simple state, i.e. variable contents" state = "aheap × locals" -- "heap, local parameter including This" xstate = "val option × state" -- "state including exception information" syntax heap :: "state => aheap" locals :: "state => locals" Norm :: "state => xstate" abrupt :: "xstate => val option" store :: "xstate => state" lookup_obj :: "state => val => obj" translations "heap" => "fst" "locals" => "snd" "Norm s" == "(None,s)" "abrupt" => "fst" "store" => "snd" "lookup_obj s a'" == "the (heap s (the_Addr a'))" constdefs raise_if :: "bool => xcpt => val option => val option" "raise_if b x xo ≡ if b ∧ (xo = None) then Some (Addr (XcptRef x)) else xo" new_Addr :: "aheap => loc × val option" "new_Addr h ≡ SOME (a,x). (h a = None ∧ x = None) | x = Some (Addr (XcptRef OutOfMemory))" np :: "val => val option => val option" "np v == raise_if (v = Null) NullPointer" c_hupd :: "aheap => xstate => xstate" "c_hupd h'== λ(xo,(h,l)). if xo = None then (None,(h',l)) else (xo,(h,l))" cast_ok :: "'c prog => cname => aheap => val => bool" "cast_ok G C h v == v = Null ∨ G\<turnstile>obj_ty (the (h (the_Addr v)))\<preceq> Class C" lemma obj_ty_def2 [simp]: "obj_ty (C,fs) = Class C" apply (unfold obj_ty_def) apply (simp (no_asm)) done lemma new_AddrD: "new_Addr hp = (ref, xcp) ==> hp ref = None ∧ xcp = None ∨ xcp = Some (Addr (XcptRef OutOfMemory))" apply (drule sym) apply (unfold new_Addr_def) apply(simp add: Pair_fst_snd_eq Eps_split) apply(rule someI) apply(rule disjI2) apply(rule_tac r = "snd (?a,Some (Addr (XcptRef OutOfMemory)))" in trans) apply auto done lemma raise_if_True [simp]: "raise_if True x y ≠ None" apply (unfold raise_if_def) apply auto done lemma raise_if_False [simp]: "raise_if False x y = y" apply (unfold raise_if_def) apply auto done lemma raise_if_Some [simp]: "raise_if c x (Some y) ≠ None" apply (unfold raise_if_def) apply auto done lemma raise_if_Some2 [simp]: "raise_if c z (if x = None then Some y else x) ≠ None" apply (unfold raise_if_def) apply(induct_tac "x") apply auto done lemma raise_if_SomeD [rule_format (no_asm)]: "raise_if c x y = Some z --> c ∧ Some z = Some (Addr (XcptRef x)) | y = Some z" apply (unfold raise_if_def) apply auto done lemma raise_if_NoneD [rule_format (no_asm)]: "raise_if c x y = None --> ¬ c ∧ y = None" apply (unfold raise_if_def) apply auto done lemma np_NoneD [rule_format (no_asm)]: "np a' x' = None --> x' = None ∧ a' ≠ Null" apply (unfold np_def raise_if_def) apply auto done lemma np_None [rule_format (no_asm), simp]: "a' ≠ Null --> np a' x' = x'" apply (unfold np_def raise_if_def) apply auto done lemma np_Some [simp]: "np a' (Some xc) = Some xc" apply (unfold np_def raise_if_def) apply auto done lemma np_Null [simp]: "np Null None = Some (Addr (XcptRef NullPointer))" apply (unfold np_def raise_if_def) apply auto done lemma np_Addr [simp]: "np (Addr a) None = None" apply (unfold np_def raise_if_def) apply auto done lemma np_raise_if [simp]: "(np Null (raise_if c xc None)) = Some (Addr (XcptRef (if c then xc else NullPointer)))" apply (unfold raise_if_def) apply (simp (no_asm)) done lemma c_hupd_fst [simp]: "fst (c_hupd h (x, s)) = x" by (simp add: c_hupd_def split_beta) end
lemma obj_ty_def2:
obj_ty (C, fs) = Class C
lemma new_AddrD:
new_Addr hp = (ref, xcp) ==> hp ref = None ∧ xcp = None ∨ xcp = Some (Addr (XcptRef OutOfMemory))
lemma raise_if_True:
raise_if True x y ≠ None
lemma raise_if_False:
raise_if False x y = y
lemma raise_if_Some:
raise_if c x (Some y) ≠ None
lemma raise_if_Some2:
raise_if c z (if x = None then Some y else x) ≠ None
lemma raise_if_SomeD:
raise_if c x y = Some z ==> c ∧ Some z = Some (Addr (XcptRef x)) ∨ y = Some z
lemma raise_if_NoneD:
raise_if c x y = None ==> ¬ c ∧ y = None
lemma np_NoneD:
np a' x' = None ==> x' = None ∧ a' ≠ Null
lemma np_None:
a' ≠ Null ==> np a' x' = x'
lemma np_Some:
np a' (Some xc) = Some xc
lemma np_Null:
np Null None = Some (Addr (XcptRef NullPointer))
lemma np_Addr:
np (Addr a) None = None
lemma np_raise_if:
np Null (raise_if c xc None) = Some (Addr (XcptRef (if c then xc else NullPointer)))
lemma c_hupd_fst:
fst (c_hupd h (x, s)) = x