dhall-nix-lib/Integer/subtract.dhall

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--| `subtract m n` computes `n - m`.
let nonPositive = ./nonPositive.dhall
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