use> !create ra:RelationalAlgebra

use> \
     !let Country=Set{Sequence{'Germany',    'Berlin',   '80'},
                      Sequence{'France',     'Paris',    '60'},
                      Sequence{'Netherlands','Amsterdam','25'}}
.

use> ?ra.isRelation(Country)
     true : Boolean

use> \
     !let Town=Set{Sequence{'Berlin',   '4'},
                   Sequence{'Hamburg',  '2'},
                   Sequence{'Koeln',    '1'},
                   Sequence{'Paris',    '9'},
                   Sequence{'Marseille','2'},
                   Sequence{'Amsterdam','2'}}
.

use> ?ra.isRelation(Town)
     true : Boolean

use> ?ra.selectV(3,#LE,'60',Country)
     Set{Sequence{'France',     'Paris',    '60'},
         Sequence{'Netherlands','Amsterdam','25'}} : Set(Sequence(String))

use> ?ra.selectC(1,#GT,2,Country)
     Set{Sequence{'Germany',    'Berlin',   '80'},
         Sequence{'Netherlands','Amsterdam','25'}} : Set(Sequence(String))

use> ?ra.project(Sequence{3,1},Country)
     Set{Sequence{'25','Netherlands'},
         Sequence{'60','France'     },
         Sequence{'80','Germany'}   } : Set(Sequence(String))

use> ?ra.product(Country,Town)
     Set{Sequence{'France',      'Paris',     '60', 'Amsterdam', '2'},
         Sequence{'France',      'Paris',     '60', 'Berlin',    '4'},
         Sequence{'France',      'Paris',     '60', 'Hamburg',   '2'},
         Sequence{'France',      'Paris',     '60', 'Koeln',     '1'},
         Sequence{'France',      'Paris',     '60', 'Marseille', '2'},
         Sequence{'France',      'Paris',     '60', 'Paris',     '9'},
         Sequence{'Germany',     'Berlin',    '80', 'Amsterdam', '2'},
         Sequence{'Germany',     'Berlin',    '80', 'Berlin',    '4'},
         Sequence{'Germany',     'Berlin',    '80', 'Hamburg',   '2'},
         Sequence{'Germany',     'Berlin',    '80', 'Koeln',     '1'},
         Sequence{'Germany',     'Berlin',    '80', 'Marseille', '2'},
         Sequence{'Germany',     'Berlin',    '80', 'Paris',     '9'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Amsterdam', '2'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Berlin',    '4'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Hamburg',   '2'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Koeln',     '1'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Marseille', '2'},
         Sequence{'Netherlands', 'Amsterdam', '25', 'Paris',     '9'}} :
         Set(Sequence(String)) 

use> ?ra.project(Sequence{1,2,5},
        ra.selectC(2,#EQ,4,
          ra.product(Country,Town)))
     Set{Sequence{'France',      'Paris',     '9'},
         Sequence{'Germany',     'Berlin',    '4'},
         Sequence{'Netherlands', 'Amsterdam', '2'}} : Set(Sequence(String))

use> \
     ?ra.minus(ra.project(Sequence{1},Town),
        ra.project(Sequence{2},Country))
.
     Set{Sequence{'Hamburg'  },
         Sequence{'Koeln'    },
         Sequence{'Marseille'}} : Set(Sequence(String))

use> ?ra.union(Town,ra.project(Sequence{1,3},Country)) 
     Set{Sequence{'Amsterdam',    '2'},
         Sequence{'Berlin',       '4'},
         Sequence{'France',      '60'},
         Sequence{'Germany',     '80'},
         Sequence{'Hamburg',      '2'},
         Sequence{'Koeln',        '1'},
         Sequence{'Marseille',    '2'},
         Sequence{'Netherlands', '25'},
         Sequence{'Paris',        '9'}} : Set(Sequence(String))

use> -- project[1](Country) - project[1](select[3 gt 6](Country,Country))

use> \
     ?ra.minus(ra.project(Sequence{1},Country),
        ra.project(Sequence{1},
          ra.selectC(3,#LT,6,ra.product(Country,Country))))
.
     Set{Sequence{'Germany'}} : Set(Sequence(String))

use> \
     !let Job=Set{Sequence{'Ada','Analysis'},
                  Sequence{'Ada','Design'  },
                  Sequence{'Bea','Analysis'},
                  Sequence{'Bea','Design'  },
                  Sequence{'Bea','Coding'  },
                  Sequence{'Cyd','Design'  },
                  Sequence{'Cyd','Coding'  }}
.

use> -- R(A,B), S(B): project[A](R)-project[A](product(project[A](R),S)-R)

use> \
     ?ra.minus(ra.project(Sequence{1},Job),
        ra.project(Sequence{1},
          ra.minus(ra.product(ra.project(Sequence{1},Job),
                              ra.project(Sequence{2},Job)),
                   Job)))
.
     Set{Sequence{'Bea'}} : Set(Sequence(String))

use> ?ra.join(Country,2,#EQ,1,Town)
     Set{Sequence{'France',      'Paris',    '60', 'Paris',     '9'},
         Sequence{'Germany',     'Berlin',   '80', 'Berlin',    '4'},
         Sequence{'Netherlands', 'Amsterdam','25', 'Amsterdam', '2'}} :
     Set(Sequence(String))

use> ?ra.project(Sequence{1,2,3,5},ra.join(Country,2,#EQ,1,Town))
     Set{Sequence{'France',      'Paris',     '60', '9'},
         Sequence{'Germany',     'Berlin',    '80', '4'},
         Sequence{'Netherlands', 'Amsterdam', '25', '2'}} : Set(Sequence(String))

use> ?ra.natjoin(Country,Sequence{2},Sequence{1},Town)
     Set{Sequence{'France',      'Paris',     '60', '9'},
         Sequence{'Germany',     'Berlin',    '80', '4'},
         Sequence{'Netherlands', 'Amsterdam', '25', '2'}} : Set(Sequence(String))

use> ?let Age=Set{Sequence{'Ada', 'Apple',  '42'},
                  Sequence{'Bea', 'Banana', '36'},
                  Sequence{'Cyd', 'Cherry', '42'},
                  Sequence{'Dan', 'Cherry', '10'}} in
      let Hair=Set{Sequence{'Almond', 'Ada', 'Blonde'},
                   Sequence{'Banana', 'Bea', 'Black' },
                   Sequence{'Cherry', 'Can', 'Black' },
                   Sequence{'Cherry', 'Dan', 'Brown' }} in
      ra.natjoin(Age,Sequence{2,1},Sequence{1,2},Hair)

      Set{Sequence{'Bea','Banana','36','Black'},
          Sequence{'Dan','Cherry','10','Brown'}} : Set(Sequence(String))

use> ?let Rainy=Set{Sequence{'Oslo'},Sequence{'London'},Sequence{'Berlin'}} in
      let Sunny=Set{Sequence{'Berlin'},Sequence{'Rome'},Sequence{'Madrid'}} in
      ra.intersect(Rainy,Sunny)
      Set{Sequence{'Berlin'}} : Set(Sequence(String))

use> ?ra.max(3,Country)
     Set{Sequence{'Germany','Berlin','80'}} : Set(Sequence(String))

use> ?ra.min(3,Country)
     Set{Sequence{'Netherlands','Amsterdam','25'}} : Set(Sequence(String))

use> ?ra.max(2,Town)
     Set{Sequence{'Paris','9'}} : Set(Sequence(String))

use> ?ra.min(2,Town)
     Set{Sequence{'Koeln','1'}} : Set(Sequence(String))

use> ?ra.allValues(Country)
     Set{Sequence{'25'},
         Sequence{'60'},
         Sequence{'80'},
         Sequence{'Amsterdam'},
         Sequence{'Berlin'},
         Sequence{'France'},
         Sequence{'Germany'},
         Sequence{'Netherlands'},
         Sequence{'Paris'}} : Set(Sequence(String))

use> ?ra.allValues(Town)
     Set{Sequence{'1'},
         Sequence{'2'},
         Sequence{'4'},
         Sequence{'9'},
         Sequence{'Amsterdam'},
         Sequence{'Berlin'},
         Sequence{'Hamburg'},
         Sequence{'Koeln'},
         Sequence{'Marseille'},
         Sequence{'Paris'}} : Set(Sequence(String))

use> ?ra.union(ra.allValues(Country),ra.allValues(Town))->flatten()
     Set{'1','2','25','4','60','80','9','Amsterdam','Berlin','France',
         'Germany','Hamburg','Koeln','Marseille','Netherlands','Paris'} :
     Set(String)

use> ?ra.divide(1,Job,ra.project(Sequence{2},Job))
     Set{Sequence{'Bea'}} : Set(Sequence(String))

use> !let Job=Set{Sequence{'Ada','Apple', 'UML', 'Analysis'},
                  Sequence{'Ada','Apple', 'UML', 'Design'},
                  Sequence{'Bea','Banana','UML', 'Analysis'},
                  Sequence{'Bea','Banana','UML', 'Design'},
                  Sequence{'Bea','Banana','Ruby','Coding'},
                  Sequence{'Cyd','Cherry','UML', 'Design'},
                  Sequence{'Cyd','Cherry','Ruby','Coding'}}

use> ?ra.divide(2,Job,ra.project(Sequence{3,4},Job))
     Set{Sequence{'Bea','Banana'}} : Set(Sequence(String))

use> ?ra.product(ra.divide(2,Job,ra.project(Sequence{3,4},Job)),
     ra.project(Sequence{3,4},Job))
     Set{Sequence{'Bea','Banana','Ruby','Coding'},
         Sequence{'Bea','Banana','UML', 'Analysis'},
         Sequence{'Bea','Banana','UML', 'Design'}} : Set(Sequence(String))

use> ?ra.modulo(2,Job,ra.project(Sequence{3,4},Job))
     Set{Sequence{'Ada','Apple','UML','Analysis'},
         Sequence{'Ada','Apple','UML','Design'},
         Sequence{'Cyd','Cherry','Ruby','Coding'},
         Sequence{'Cyd','Cherry','UML','Design'}} : Set(Sequence(String))

use> ?ra.divide(3,Job,ra.project(Sequence{4},Job))
     Set{} : Set(Sequence(String))

use> ?ra.divide(2,ra.project(Sequence{1,2,4},Job),ra.project(Sequence{4},Job))
     Set{Sequence{'Bea','Banana'}} : Set(Sequence(String))