Theory HeapSyntax (Isabelle2005: October 2005)

(*  Title:      HOL/Hoare/HeapSyntax.thy
    ID:         $Id: HeapSyntax.thy,v 1.2 2005/06/17 14:13:07 haftmann Exp $
    Author:     Tobias Nipkow
    Copyright   2002 TUM
*)

theory HeapSyntax imports Hoare Heap begin

subsection "Field access and update"

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
  "f(r -> v)"  ==  "f(addr r := v)"
  "p^.f := e"  =>  "f := f(p -> e)"
  "p^.f"       =>  "f(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

Field access and update

lemma

  {w = Ref w0.0 ∧
   x = Ref x0.0 ∧
   y = Ref y0.0 ∧ z = Ref z0.0 ∧ distinct [w0.0, x0.0, y0.0, z0.0]} 
   v := v(w -> 1);
   n := n(w -> x);
   v := v(x -> 2);
   n := n(x -> y); v := v(y -> 3); n := n(y -> z); v := v(z -> 4); n := n(x -> z) 
   {v (addr (n (addr (n (addr w))))) = 4}