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Examples

•  split-add: N => (N => N)

  {

  (0, { (0,0), (1,1), (2,2), ...}),

  (1, { (0,1), (1,2), (2,3), ...}),

  (2, { (0,2), (1,3), (2,4), ...}),

  ...,

  (n, { (0,n), (1,n+1), (2,n+2), ...}),

  ...}

•  make-succ: (N => N) => (N => N)

  {

  ...,

  ({(0,1),(1,1),(2,1),(3,6),...},

  {(0,2),(1,2),(2,2),(3,7),...}), ...}

•  apply: (((N => N)) ×N) => N

  {

  ...,

  (({(0,1),(1,1),(2,1),(3,6),...}, 0), 1),

  (({(0,1),(1,1),(2,1),(3,6),...}, 1), 1),

  (({(0,1),(1,1),(2,1),(3,6),...}, 2), 1),

  (({(0,1),(1,1),(2,1),(3,6),...}, 3), 6),

  ...}