; ---------- SORTS ------------------------------------------

TYPE
  relation = tuple-set;
  tuple = atribute -> value;
ENDTYPE


; ---------- FUNCTIONS -------------------------------------


FUNC proj ( r:relation, ats:artibute-set ): relation
RETURN  {x / ats | x <- r};

FUNC agree(x:tuple ,condi:tuple) : Bool
PRE  subset(dom(condi),dom(x))
RETURN 
 if (condi == []) then true
                  else
                      let ( y=choice(dom(condi)))
                      in  x[y] == condi[y] && agree(x,condi\{y});

FUNC sel(r:relation ,condi:tuple):relation
RETURN { x | x <- r :agree(x,condi)};

FUNC join(r1:relation,r2:relation):relation 
RETURN {t1+t2 | t1<-r1, t2<-r2: let (d = dom(t2) * dom(t1))
                                in  agree(t1,t2/d)};

; ----------  TEST --------------------------------------------

r <- { ["name" -> "Paul Smith","sig" -> "ps"],
       ["name" -> "David West","sig" -> "dw"],
       ["name" -> "Anna Rose","sig" -> "ar"]};

r1 <- {["sig" -> "ps", "tel" -> 379],
       ["sig" -> "ps", "tel" -> 675866],
       ["sig" -> "dw", "tel" -> 375],
       ["sig" -> "dw", "tel" -> "At home does not have"]};

r2 <- proj (r,{"sig"});

r3 <- sel( r, ["sig" -> "dw"]);

r5 <- sel(r1,["sig"->"ps"]);

r6 <- join(r,r1);