export {
    import "int.lt";
    import "euclidean.lt";

	/* Implementation of Rational Numbers
	 */
    let ratio-sign = λ{
        p: machine.Int64 ~ machine.Word;
        q: machine.Int64 ~ machine.Word;
    }
    ↦ bool-xor (int-sign p) (int-sign q);

    let ratio-scale = λ{
        {
            p: machine.Int64~machine.Word;
            q: machine.Int64~machine.Word;
        } : ℚ ~ <Ratio machine.Int64~machine.Word>;
        n : machine.Int64 ~machine.Word;
    } ↦ {
        i* q n;
        i* p n;
    };

    let ratio-normalize = λ{
        p: machine.Int64 ~ machine.Word;
        q: machine.Int64 ~ machine.Word;
    } : ℚ ~ <Ratio machine.Int64 ~ machine.Word>
    ↦ {
        let s = gcd p q;
        i/ q s;
        i/ p s;
    };

    let ratio-add = λ{
        {
            ap:machine.Int64~machine.Word;
            aq:machine.Int64~machine.Word;
        }: ℚ ~ <Ratio machine.Int64 ~ machine.Word> ;
        {
            bp:machine.Int64~machine.Word;
            bq:machine.Int64~machine.Word;
        }: ℚ ~ <Ratio machine.Int64 ~ machine.Word> ;
    } ↦ {
        let l = lcm aq bq;
        let a = i/ l aq;
        let b = i/ l bq;

        i* aq a;
        i+ (i* ap a) (i* bp b);
    };

    let ratio-mul = λ{
        {
            ap:machine.Int64~machine.Word;
            aq:machine.Int64~machine.Word;
        }: ℚ ~ <Ratio machine.Int64 ~ machine.Word> ;
        {
            bp:machine.Int64~machine.Word;
            bq:machine.Int64~machine.Word;
        }: ℚ ~ <Ratio machine.Int64 ~ machine.Word> ;
    } ↦ ratio-normalize (i* ap bp) (i* aq bq);

/*
    let fmt-ratio = λ{ p:ℤ; q:ℤ; }: ℚ~<Ratio ℤ> ↦ {
        fmt-int q;':';fmt-int p;
    };
*/
}