Down Shoe ∪
Monadic Down Shoe means Unique
∪ 'ab' 'ba' 'ab' 1 1 2
┌──┬──┬─┬─┐
│ab│ba│1│2│
└──┴──┴─┴─┘
mat
flywheel
shyster
flywheel
∪mat
flywheel
shyster
Dyadic Down Shoe means Union
'ab' 'cde' 'fg' ∪ 'a' 'ab'
┌──┬───┬──┬─┐
│ab│cde│fg│a│
└──┴───┴──┴─┘