<h2>Full example</h2>
<pre><code>(* source: https://github.com/HarrisonGrodin/ml-numbers/blob/ba35c763092052e391871edf224f17474c6231b1/src/Rational.sml *)
structure Rational :> RATIONAL =
struct
type t = int * int (* (a,b) invariant: a,b coprime; b nonnegative *)
local
val rec gcd = fn
(m,0) => m
| (m,n) => gcd (n, m mod n)
in
infix 8 //
val op // = fn (x,y) => (
let
val gcd = gcd (x,y)
in
(x div gcd, y div gcd)
end
)
end
val show = Fn.id
val zero = (0,1)
val one = (1,1)
val eq : t * t -> bool = (op =)
val compare = fn ((a,b),(x,y)) => Int.compare (a * y, b * x)
val toString = fn (x,y) => Int.toString x ^ " // " ^ Int.toString y
val percent =
Fn.curry (Fn.flip (op ^)) "%"
o Int.toString
o (fn (a,b) => (100 * a) div b)
val op + = fn ((a,b),(x,y)) => (a * y + b * x) // (b * y)
val ~ = fn (a,b) => (~a,b)
val op - = fn (r1,r2) => r1 + ~r2
val op * = fn ((a,b),(x,y)) => (a * x) // (b * y)
val inv = Fn.flip (op //)
val op / = fn (r1,r2) => r1 * inv r2
end</code></pre>
