Theory EvalProof

(*  Title:       BDD

    Author:      Veronika Ortner and Norbert Schirmer, 2004
    Maintainer:  Norbert Schirmer,  norbert.schirmer at web de
    License:     LPGL
*)

(*  
EvalProof.thy

Copyright (C) 2004-2008 Veronika Ortner and Norbert Schirmer 
Some rights reserved, TU Muenchen

This library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as
published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.

This library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public
License along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
USA
*)

section ‹Proof of Procedure Eval›
theory EvalProof imports ProcedureSpecs begin

lemma (in Eval_impl) Eval_modifies:
  shows "σ. Γ{σ}  PROC Eval (´p, ´varval, ´R) 
                {t. t may_not_modify_globals σ}"
  apply (hoare_rule HoarePartial.ProcRec1)
  apply (vcg spec=modifies)
  done 


lemma (in Eval_impl) Eval_spec:
  shows "σ t bdt1. Γ
  σ. Dag ´p ´low ´high t  bdt t ´var = Some bdt1 
   ´R :== PROC Eval(´p, ´varval) 
  ´R = eval bdt1 σvarval "
apply (hoare_rule HoarePartial.ProcRec1)
apply vcg
apply clarsimp
apply safe
apply    (case_tac bdt1)
apply      simp
apply     fastforce
apply    fastforce
apply   simp
apply   (case_tac bdt1)
apply     fastforce
apply    fastforce
apply   fastforce
apply  (case_tac bdt1)
apply    fastforce
apply   fastforce
apply  fastforce
apply (case_tac bdt1)
apply   fastforce
apply  fastforce
apply fastforce
done



end