%
% Understanding Relational Database Query Languages, S. W. Dietrich, Prentice Hall, 2001.
%
%---------------------------------------------------------------------------------------------------------------------------
%        RELATIONAL ALGEBRA
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%  Abstract Division Example
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%  abTable(a,b)
%       primary key (a, b)
%  bTable(b)
%       primary key (b)
%
%  Query: Find the a's that are related to all of the b's in the bTable
%---------------------------------------------------------------------------------------------------------------------------

% Division in one step

divisionOneStep :=
    (project a (abTable)) difference 
	(project a ( ( (project a (abTable)) product bTable) difference abTable));

% Division broken down into multiple steps

aTable := project a (abTable);

allaWithAllb := aTable product bTable;

aNotRelatedToSomeb := project a (allaWithAllb difference abTable);

aRelatedToAllb := aTable difference aNotRelatedToSomeb;