{-
`subtract m n` computes `n - m`.
-}
let nonPositive =
        ./nonPositive sha256:e00a852eed5b84ff60487097d8aadce53c9e5301f53ff4954044bd68949fac3b
      ? ./nonPositive

let subtractNonNegative =
        λ(xi : Integer)
      → λ(yi : Integer)
      → let xn = Integer/clamp xi

        let yn = Integer/clamp yi

        let dn = Natural/subtract xn yn

        in        if Natural/isZero dn

            then  Integer/negate (Natural/toInteger (Natural/subtract yn xn))

            else  Natural/toInteger dn

let subtract
    : Integer → Integer → Integer
    =   λ(m : Integer)
      → λ(n : Integer)
      →       if nonPositive m

        then        if nonPositive n

              then  subtractNonNegative (Integer/negate n) (Integer/negate m)

              else  Natural/toInteger
                      (Integer/clamp (Integer/negate m) + Integer/clamp n)

        else  if nonPositive n

        then  Integer/negate
                ( Natural/toInteger
                    (Integer/clamp m + Integer/clamp (Integer/negate n))
                )

        else  subtractNonNegative m n

let example0 = assert : subtract +3 +5 ≡ +2

let example1 = assert : subtract +4 +4 ≡ +0

let example2 = assert : subtract +5 +3 ≡ -2

let example3 = assert : subtract -3 -5 ≡ -2

let example4 = assert : subtract -4 -4 ≡ +0

let example5 = assert : subtract -5 -3 ≡ +2

let example6 = assert : subtract -3 +5 ≡ +8

let example7 = assert : subtract +3 -5 ≡ -8

let example8 = assert : subtract +0 -3 ≡ -3

in  subtract