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(* Title: HOL/Hoare/HeapSyntaxAbort.thy
Author: Tobias Nipkow
Copyright 2002 TUM
*)
section \<open>Heap syntax (abort)\<close>
theory HeapSyntaxAbort
imports Hoare_Logic_Abort Heap
begin
subsection "Field access and update"
text\<open>Heap update \<open>p^.h := e\<close> is now guarded against \<^term>\<open>p\<close>
being Null. However, \<^term>\<open>p\<close> may still be illegal,
e.g. uninitialized or dangling. To guard against that, one needs a
more detailed model of the heap where allocated and free addresses are
distinguished, e.g. by making the heap a map, or by carrying the set
of free addresses around. This is needed anyway as soon as we want to
reason about storage allocation/deallocation.\<close>
syntax
"_refupdate" :: "('a \ 'b) \ 'a ref \ 'b \ ('a \ 'b)"
("_/'((_ \ _)')" [1000,0] 900)
"_fassign" :: "'a ref => id => 'v => 's com"
("(2_^._ :=/ _)" [70,1000,65] 61)
"_faccess" :: "'a ref => ('a ref \ 'v) => 'v"
("_^._" [65,1000] 65)
translations
"_refupdate f r v" == "f(CONST addr r := v)"
"p^.f := e" => "(p \ CONST Null) \ (f := _refupdate f p e)"
"p^.f" => "f(CONST addr p)"
declare fun_upd_apply[simp del] fun_upd_same[simp] fun_upd_other[simp]
text "An example due to Suzuki:"
lemma "VARS v n
{w = Ref w0 & x = Ref x0 & y = Ref y0 & z = Ref z0 &
distinct[w0,x0,y0,z0]}
w^.v := (1::int); w^.n := x;
x^.v := 2; x^.n := y;
y^.v := 3; y^.n := z;
z^.v := 4; x^.n := z
{w^.n^.n^.v = 4}"
by vcg_simp
end
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