(* 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
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}