Theory HeapSyntaxAbort

(*  Title:      HOL/Hoare/HeapSyntaxAbort.thy
    Author:     Tobias Nipkow
    Copyright   2002 TUM
*)

section ‹Heap syntax (abort)›

theory HeapSyntaxAbort
  imports Hoare_Logic_Abort Heap
begin

subsection "Field access and update"

text‹Heap update ‹p^.h := e› is now guarded against \<^term>‹p›
being Null. However, \<^term>‹p› 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.›

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