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    <p>Inspired by kvb's answer using NumericLiterals, I was driven to develop an approach which would allow us to force "sane" type signatures without having to add extensive type annotations.</p> <p>First we define some helper functions and wrapper type for language primitives:</p> <pre><code>let inline zero_of (target:'a) : 'a = LanguagePrimitives.GenericZero&lt;'a&gt; let inline one_of (target:'a) : 'a = LanguagePrimitives.GenericOne&lt;'a&gt; let inline two_of (target:'a) : 'a = one_of(target) + one_of(target) let inline three_of (target:'a) : 'a = two_of(target) + one_of(target) let inline negone_of (target:'a) : 'a = zero_of(target) - one_of(target) let inline any_of (target:'a) (x:int) : 'a = let one:'a = one_of target let zero:'a = zero_of target let xu = if x &gt; 0 then 1 else -1 let gu:'a = if x &gt; 0 then one else zero-one let rec get i g = if i = x then g else get (i+xu) (g+gu) get 0 zero type G&lt;'a&gt; = { negone:'a zero:'a one:'a two:'a three:'a any: int -&gt; 'a } let inline G_of (target:'a) : (G&lt;'a&gt;) = { zero = zero_of target one = one_of target two = two_of target three = three_of target negone = negone_of target any = any_of target } </code></pre> <p>Then we have:</p> <pre><code>let inline factorizeG n = let g = G_of n let rec factorize n j flist = if n = g.one then flist elif n % j = g.zero then factorize (n/j) j (j::flist) else factorize n (j + g.one) (flist) factorize n g.two [] </code></pre> <p>[<strong>Edit</strong>: due to an apparent bug with F# 2.0 / .NET 2.0, factorizen, factorizeL, and factorizeI below run significantly slower than factorizeG when compiled in Release-mode but otherwise run slightly faster as expected -- see <a href="https://stackoverflow.com/questions/2945880/f-performance-question-what-is-the-compiler-doing">F# performance question: what is the compiler doing?</a>]</p> <p>Or we can take it a few step further (inspired by Expert F#, p.110):</p> <pre><code>let inline factorize (g:G&lt;'a&gt;) n = //' let rec factorize n j flist = if n = g.one then flist elif n % j = g.zero then factorize (n/j) j (j::flist) else factorize n (j + g.one) (flist) factorize n g.two [] //identical to our earlier factorizeG let inline factorizeG n = factorize (G_of n) n let gn = G_of 1 //int32 let gL = G_of 1L //int64 let gI = G_of 1I //bigint //allow us to limit to only integral numeric types //and to reap performance gain by using pre-computed instances of G let factorizen = factorize gn let factorizeL = factorize gL let factorizeI = factorize gI </code></pre> <p>Also, here is an extended version of kvb's NumericLiteralG which allows us to use "2G", "-8G", etc. Though I couldn't figure out how to implement a memoization strategy (though that should be doable for G.any).</p> <pre><code>module NumericLiteralG = let inline FromZero() = LanguagePrimitives.GenericZero let inline FromOne() = LanguagePrimitives.GenericOne let inline FromInt32(n:int):'a = let one:'a = FromOne() let zero:'a = FromZero() let nu = if n &gt; 0 then 1 else -1 let gu:'a = if n &gt; 0 then one else zero-one let rec get i g = if i = n then g else get (i+nu) (g+gu) get 0 zero </code></pre>
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