/Prelude-v20.2.0/Integer/subtract.dhall

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subtract m n computes n - m.

Examples

subtract +3 +5 ≡ +2
subtract +4 +4 ≡ +0
subtract +5 +3 ≡ -2
subtract -3 -5 ≡ -2
subtract -4 -4 ≡ +0
subtract -5 -3 ≡ +2
subtract -3 +5 ≡ +8
subtract +3 -5 ≡ -8
subtract +0 -3 ≡ -3

Source

--| `subtract m n` computes `n - m`.
let nonPositive =
./nonPositive.dhall sha256:e00a852eed5b84ff60487097d8aadce53c9e5301f53ff4954044bd68949fac3b
? ./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