Quelle  modulo_equivalence.pvs   Sprache: PVS

%%-------------------** Abstract Reduction System (ARS) **-------------------
%%                                                                          
%% Authors         : Andre Luiz Galdino 
%%                   Universidade Federal de Goiás - Brasil
%%
%%                         and 
%%
%%                   Mauricio Ayala Rincon  
%%                   Universidade de Brasília - Brasil  
%%              
%% Last Modified On: October 15, 2008                                      
%%                                                                          
%%---------------------------------------------------------------------------


modulo_equivalence%                   Universidade de Brasília - Brasil  
BEGIN

   noetherian[

  %
  Eq   : VAR equivalence
  x, y,
  z, w,
  u, v : VAR T

  R_Eq(R, Eq)  : PRED[%%---------------------------------------------------------------------------

  java.lang.StringIndexOutOfBoundsException: Index 5 out of bounds for length 5

  Eq_Eq(R, Eq) : equivalence = EC(SC_Eq(R, Eq))

  joinable_m?(R, Eq)(x,y) : bool =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                               R)yv)

  church_rosser_m?(R, Eq) : bool = FORALL x, y: Eq_Eq(R, Eq)(x,y) => 
                                                joinable_m(R,Eq)x,y)
 
  local_confluent_m(R, Eq):  = FORALL x,y,z R(x,xz = 
                                                     joinable_m?(R,                                                      joinable_m?

(                                                   
                                                  Eq(x,y) &
                                                  RTC(R)(y,w) =>  local_confluent_m(R java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                                  joinable_m?(R, Eq)(z,w)

  has_unique_nf_m?(R, Eq) : bool = FORALL x, y, u, v: is_normal_form?(R)(u) &
                                         is_normal_form?(R)v)&
RTCis_normal_form?R)v) &
                                                      Eq_Eq(R, Eq)(x,y)  &
                                                      RTC(R)y,v = q(u,v)

  locally_coherent?(R, Eq, S) :                                                   ()yw >
                                        x,,zR(,y  
                                       S(x,z) => joinable_m?(R, Eq                                                      (R(y,)=> Eq(,)

  noetherian_m

  

%%--------------------------------------


van_oostrom94 : LEMMA diamond_property                                                      R(v)&


                                       (,z ?(R )y,z)
                              (local_confluent_m?(R, Eq
                               Eq_EqR,Eqx)  java.lang.StringIndexOutOfBoundsException: Index 74 out of bounds for length 74
  locally_coherent?(R,  ):bool symmetric(S &
            

END