/ finds the non-duplicated union of two lists
union:{[x;y]; ?x,y}

/finds intersection of two lists with duplicate removal
intersect:{[x;y]; z: x ?/: y; ii: & z < #x; ?x[z[ii]]}

/ finds intersection of two lists with duplicate removal
/ Much faster.
/ intersect: {[x;y] i:  x ?/: y; j: & i < #x; :?y[j] }

/finds set difference of two lists x - y
/ differ:{[x;y]; ?x[&~ x _in\: y]}

/ A faster difference
differ:{[x;y] i: y ?/: x; j: & i = #y; ?x[j] }

/ Single attribute equi-join where T1.att1 is a key
/ index1 are the rows of T1 that are still available coming into the join.
/ Similarly for index2.
/ Give indexes of T1 and T2
/ cardinality is as big as T2.att2[index2]
/ the jth element says where in T1.att1[index1]
/ there is a match for the jth element of T2.att2[index2].
/ if i[j] = size1 then there is no match.
/ T1.a: `c`d`e`f`a`b
/ T2.b: `d`b`h`e`c`b`e`f`e
/ index1: !#T1.a
/ index2: !#T2.b
/ att1: `a
/ att2: `b 
/ ((T1[att1][index1[i[goods]]]) ; T2[att2][index2[goods]])



fkjoin:{[T1; att1; index1; T2; att2; index2] i: T1[att1][index1] ?/: T2[att2][index2]; goods: & i < #index1; ((index1[i[goods]]) ; index2[goods]) }

findindex:{[myvals; othervals; i] x: & myvals[i] = othervals; ((#x) # i) ,' x}

/ This means: find index pairs in tab1 and tab2
/ such that tab1.attsin1 matches via equality tab2.attsin2.
/ Here we  assume the join is on one attribute.
/ Result is a pair of lists whose ith members match.


eqjoinone:{[T1; attsin1; index1;  T2; attsin2; index2] att1: *attsin1; att2: *attsin2; size: # ? T1[att1][index1]; if[size = #index1; out:fkjoin[T1;att1;index1; T2;att2;index2]];size: # ? T2[att2][index2]; if[size = #index2; out:| fkjoin[T2;att2;index2; T1;att1;index1] ]; myind: !#T1[att1][index1]; x: findindex[T1[att1][index1];  T2[att2][index2]]'myind; y: ,/ x; (y[;0]; y[;1])}

eqjoinone:{[T1; attsin1; index1;  T2; attsin2; index2] flag: 0; att1: *attsin1; att2: *attsin2; size: # ? T1[att1][index1]; if[size = #index1; flag: 1; out:fkjoin[T1;att1;index1; T2;att2;index2]];size: # ? T2[att2][index2]; if[size = #index2; flag: 1; out:| fkjoin[T2;att2;index2; T1;att1;index1] ]; if[flag = 0; myind: !#T1[att1][index1]; x: findindex[T1[att1][index1];  T2[att2][index2]]'myind; y: ,/ x; out: (y[;0]; y[;1])]; out}


T1.a: `c`d`e`f`a`b`c
T2.b: `d`b`h`e`c`b`e`f`e
index1: !#T1.a
index2: !#T2.b
att1: `a
att2: `b 
attsin1: ,att1
attsin2: ,att2
eqjoinone[T1; attsin1;index1; T2; attsin2; index2]