Documentation

split x y == (m,(b,d)) means that b == (x<=y), m == min x y, d == max x y - min x y, that is d == abs(x-y).

We have chosen this function as base function, since it provides comparison and subtraction in one go, which is important for replacing common structures like

if x<=y
  then f(x-y)
  else g(y-x)

that lead to a memory leak for peano numbers. We have choosen the simple check x<=y instead of a full-blown compare, since we want Zero <= undefined for peano numbers. Because of undefined values split is in general not commutative in the sense

let (m0,(b0,d0)) = split x y
    (m1,(b1,d1)) = split y x
in  m0==m1 && d0==d1

The result values are in the order in which they are generated for Peano numbers. We have chosen the nested pair instead of a triple in order to prevent a memory leak that occurs if you only use b and d and ignore m. This is demonstrated by test cases Chunky.splitSpaceLeak3 and Chunky.splitSpaceLeak4.