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


%%%                   Mauricio Ayala Rincon  [T%
BEGIN

IMPORTINGnoetherianT]

R%                                                                          
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  x, y,
  java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  R_Eqjoinable_m?R Eq)x,)

  SC_Eq(R, Eq) : PREDEq(u,v) & RTC()(,)

  Eq_Eq(R, Eq) : equivalence java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

  joinable_m?(R, Eqjava.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 1
                                                 ?  bool  :xy) & R(,)= 

  church_rosser_m?(R, Eq) :java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                                joinable_mEq(x,y)&
  confluent_m?R,                                                  ,)=java.lang.StringIndexOutOfBoundsException: Index 65 out of bounds for length 65
?,java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                                     joinable_m, Eq)yzjava.lang.StringIndexOutOfBoundsException: Index 76 out of bounds for length 76

               ?( 
                                                      ?) java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
                                                  RTCR(,)= 
                                                  joinable_m?(R, Eq)                                                      Eq_Eq(FORALL,,:x 

java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2
is_normal_form?()v java.lang.StringIndexOutOfBoundsException: Index 77 out of bounds for length 77
                                                      Sx)=joinable_m ),)
                                                      ),y
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 2

Eq  ?(S&
                                       java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
                                       z) = joinable_m(R,Eqyz

  noetherian_m?(R, Eq) :                                                            ))

  

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


van_oostrom94 : LEMMA diamond_property?(RTC(R) o Eq) => confluent_m?(R, Eq)


newman_lemma_general : THEOREM noetherian?(R) => 
                              (local_confluent_m?(R, Eq) & 
                               locally_coherent?(R, Eq, Eq) <=>  
                                                           confluent_m?(R, Eq))
            

END modulo_equivalence