%
% Understanding Relational Database Query Languages, S. W. Dietrich, Prentice Hall, 2001.
%
%---------------------------------------------------------------------------------------------------------------------------
%        TUPLE RELATIONAL CALCULUS (TRC)
%---------------------------------------------------------------------------------------------------------------------------
%  Abstract Division Example
%
%  abTable(a,b)
%       primary key (a, b)
%  bTable(b)
%       primary key (b)
%---------------------------------------------------------------------------------------------------------------------------

universalDivision :=
    { T.a | abTable(T) and (forall B) (not bTable(B) or  
	(exists AB) (abTable(AB) and AB.a=T.a and AB.b=B.b)) };

forallExistsEquivalence :=
  { T.a | abTable(T) and not (exists B)( not (not bTable(B) or  
            (exists AB) (abTable(AB) and AB.a=T.a and AB.b=B.b) ) )};

existentialDivision :=
    { T.a | abTable(T) and not (exists B) (bTable(B) and  
	not (exists AB) (abTable(AB) and AB.a=T.a and AB.b=B.b) ) };