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│
└──┴───┴──┴─┘