c1=: >:@]                     NB. if 0=x, 1+y
c2=: <:@[ ack 1:              NB. if 0=y, (x-1) ack 1
c3=: <:@[ ack [ ack <:@]      NB. else,   (x-1) ack x ack y-1
ack=: c1`c2`c3@.(,&* i. 0:)M.