//! An 8-bit unsigned integer.

let { Semigroup, Monoid, Group, Eq, Ord, Ordering, Num, Show } = import! std.prelude

let additive =
    let semigroup : Semigroup Byte = {
        append = \x y -> x #Byte+ y,
    }

    let monoid : Monoid Byte = {
        semigroup = semigroup,
        empty = 0b,
    }

    let group : Group Byte = {
        monoid = monoid,
        inverse = \x -> 0b #Byte- x,
    }

    { semigroup, monoid, group }

let multiplicative =
    let semigroup : Semigroup Byte = {
        append = \x y -> x #Byte* y,
    }

    let monoid : Monoid Byte = {
        semigroup = semigroup,
        empty = 1b,
    }

    { semigroup, monoid }

let eq : Eq Byte = {
    (==) = \l r -> l #Byte== r,
}

let ord : Ord Byte = {
    eq = eq,
    compare = \l r -> if l #Byte< r then LT else if l #Byte== r then EQ else GT,
}

let num : Num Byte = {
    ord = ord,
    (+) = additive.semigroup.append,
    (-) = \l r -> l #Byte- r,
    (*) = multiplicative.semigroup.append,
    (/) = \l r -> l #Byte/ r,
    negate = additive.group.inverse,
}

let show : Show Byte = {
    show = (import! std.prim).show_byte,
}

{
    additive,
    multiplicative,
    eq,
    ord,
    num,
    show,
    ..
    import! std.byte.prim
}