Elm extending `number` and `comparable` concept

Fraction.elm

module Fraction exposing (Fraction, create, toFloat_)


-- See https://discourse.elm-lang.org/t/proposal-extending-built-in-typeclasses/5510/2


type Fraction [ number, comparable ]
    = Fraction Int Int


create : Int -> Int -> Fraction
create a b =
    Fraction a b


toFloat_ : Fraction -> Float
toFloat_ ( Fraction a b ) =
    ( toFloat a ) / ( toFloat b )



-- ARITHMETIC


Fraction.(*) : Fraction -> Fraction -> Fraction
Fraction.(*) ( Fraction a1 b1 ) ( Fraction a2 b2 ) =
    Fraction ( a1 * a2 ) ( b1 * b2 )


Fraction.(/) : Fraction -> Fraction -> Fraction
Fraction.(/) ( Fraction a1 b1 ) ( Fraction a2 b2 ) =
    Fraction ( a1 * a2 ) ( b2 * b1 )


Fraction.(+) : Fraction -> Fraction -> Fraction
Fraction.(+) ( Fraction a1 b1 ) ( Fraction a2 b2 ) =
    -- todo


Fraction.(-) : Fraction -> Fraction -> Fraction
Fraction.(-) ( Fraction a1 b1 ) ( Fraction a2 b2 ) =
    -- todo



-- COMPARISON


Fraction.compare : Fraction -> Fraction -> Order
Fraction.compare f1 f2 =
    compare ( toFloat_ f1 ) ( toFloat_ f2 )

Usage.elm

import Fraction exposing (..)


-- Create fractions

f1 = create 3 1
f2 = create 1 2


-- Arithmetic operators can be used

f1 * f2 == create 3 2
f1 / f2 == create 6 1
-- ...


-- Comparison can be done

f1 > f2 == True
f1 < f2 == False
compare f1 f2 == GT


-- We can work with lists of fractions

List.maximum [ f1, f2 ] == Just f1