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