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[T :
BEGIN

  IMPORTING noetherian[T]

  R, S : VAR  PRED[[T, T]]
  Eq   : VAR equivalence
  x, y,
  z, w,
  u, v : VAR T

  R_Eq(R, Eq)  : PRED[[T, T]] = Eq o R o Eq

  SC_Eq(R, Eq) : PRED[[T, T]] = union(SC(R), Eq)

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

  joinable_m?(R, Eq)(x,y) : bool = EXISTS u,v: RTC(R)(x,u) & 
                                               

  church_rosser_m
                                                (,Eq(,java.lang.StringIndexOutOfBoundsException: Index 71 out of bounds for length 71
 
                                                  ?R )xy
                                                     

  confluent_m?(R, Eq) : bool = FORALL x, y, z, w: RTC(R)(x,z)  & 
                                                   &
RTC(R)(y, >
                                                  joinable_m?(R, Eq)(z,w)

  has_unique_nf_m?(R, Eq) : bool = FORALL x, y, u, v: is_normal_form?                                                     ?(R Eq),)
                                                      
                                                      RTC(R                                                      ),)=Euv
                                                      FORALL, :x) 
RTC)yv >(v

  locally_coherent?(R, Eq, S) : bool = symmetric?(S) &
                                       FORALL  x, y, z: R(java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
Sx)=joinable_m,Eqzjava.lang.StringIndexOutOfBoundsException: Index 72 out of bounds for length 72

  noetherian_m?(R,                                (R (,  &

  

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


van_oostrom94,S   =symmetric)&


newman_lemma_general : THEOREM noetherian?(R) => 
                              (local_confluent_m?(R, EqS(x,) >joinable_m?R,)(,)
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
confluent_m?(R, Eqjava.lang.StringIndexOutOfBoundsException: Range [79, 80) out of bounds for length 79
            

END modulo_equivalence