<div dir="ltr"><div class="markdown-here-wrapper" style=""><p style="margin:0px 0px 1.2em!important">What about taking a mathematical approach to numbers?</p>
<pre style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;font-size:1em;line-height:1.2em;margin:1.2em 0px"><code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:pre-wrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline;white-space:pre;overflow:auto;border-radius:3px;border:1px solid rgb(204,204,204);padding:0.5em 0.7em;display:block!important">protocol Group : Equatable {
    static var zero: Self { get }
    static func + (Self, Self) -&gt; Self
    static func += (inout Self, Self)
    static func - (Self, Self) -&gt; Self
    static func -= (inout Self, Self)
    static prefix func - (Self) -&gt; Self
}

protocol Ring : Group {
    static var one: Self { get }
    static func * (Self, Self) -&gt; Self
    static func *= (inout Self, Self)
    func tryDivide(by: Self) -&gt; Self?
    func tryInvert() -&gt; Self?
}

protocol Field : Ring {
    static func / (Self, Self) -&gt; Self
    static func /= (inout Self, Self)
    var inverted: Self { get }
}

protocol VectorSpace : Group {
    associatedtype Scalar : Field
    static func * (Self, Scalar) -&gt; Self
    static func *= (inout Self, Scalar) -&gt; Self
    static func / (Self, Scalar) -&gt; Self
    static func /= (inout Self, Scalar) -&gt; Self
    static func * (Scalar, Self) -&gt; Self
}
</code></pre><p style="margin:0px 0px 1.2em!important">Detalization of mathematical terminology will be determined by what kind of types we have in the standard library. Integer types are rings (except for overflow), floating-point types are fields (except for precision), point types are linear spaces, so I thought the abstractions above are the bare minimum.</p>
<p style="margin:0px 0px 1.2em!important">Unfortunately, Swift doesn’t have rename operations for protocol requirements, so we can’t express groups that use operations other than <code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:pre-wrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline">+</code> and <code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:pre-wrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline">-</code>. What we can do is to include an adapter to wrap current instance in an additive group interface:</p>
<pre style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;font-size:1em;line-height:1.2em;margin:1.2em 0px"><code style="font-size:0.85em;font-family:Consolas,Inconsolata,Courier,monospace;margin:0px 0.15em;padding:0px 0.3em;white-space:pre-wrap;border:1px solid rgb(234,234,234);background-color:rgb(248,248,248);border-radius:3px;display:inline;white-space:pre;overflow:auto;border-radius:3px;border:1px solid rgb(204,204,204);padding:0.5em 0.7em;display:block!important">struct MultiplicativeGroupAdapter&lt;T: Field&gt; : Group {
    // ...
}

extension Field {
    var multiplicativeGroup: MultiplicativeGroupAdapter&lt;Self&gt;
}
</code></pre><div title="MDH:V2hhdCBhYm91dCB0YWtpbmcgYSBtYXRoZW1hdGljYWwgYXBwcm9hY2ggdG8gbnVtYmVycz88ZGl2
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