(* Title: HOL/IMP/Denotation.thy
ID: $Id$
Author: Heiko Loetzbeyer & Robert Sandner, TUM
Copyright 1994 TUM
Denotational semantics of commands
*)
Denotation = Natural +
types com_den = "(state*state)set"
constdefs
Gamma :: [bexp,com_den] => (com_den => com_den)
"Gamma b cd == (%phi.{(s,t). (s,t) : (phi O cd) & b(s)} Un
{(s,t). s=t & ~b(s)})"
consts
C :: com => com_den
primrec
C_skip "C(SKIP) = Id"
C_assign "C(x :== a) = {(s,t). t = s[x::=a(s)]}"
C_comp "C(c0 ; c1) = C(c1) O C(c0)"
C_if "C(IF b THEN c1 ELSE c2) = {(s,t). (s,t) : C(c1) & b(s)} Un
{(s,t). (s,t) : C(c2) & ~ b(s)}"
C_while "C(WHILE b DO c) = lfp (Gamma b (C c))"
end