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POFunctor/Applicative-like typeclass for composing (a->a) functions instead of (a->b)?
 

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  1. POFunctor/Applicative-like typeclass for composing (a->a) functions instead of (a->b)?
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    <p>I have a type that looks like this:</p> <pre><code>newtype Canonical Int = Canonical Int </code></pre> <p>and a function</p> <pre><code>canonicalize :: Int -&gt; Canonical Int canonicalize = Canonical . (`mod` 10) -- or whatever </code></pre> <p>(The Canonical type may not be important, it just serves to distinguish "raw" values from "canonicalized" values.)</p> <p>I'd like to create some machinery so that I can canonicalize the results of function applications.</p> <p>For example: <strong>(Edit: fixed bogus definitions)</strong></p> <pre><code>cmap :: (b-&gt;Int) -&gt; (Canonical b) -&gt; (Canonical Int) cmap f (Canonical x) = canonicalize $ f x cmap2 :: (b-&gt;c-&gt;Int) -&gt; (Canonical b) -&gt; (Canonical c) -&gt; (Canonical Int) cmap2 f (Canonical x) (Canonical y) = canonicalize $ f x y </code></pre> <p>That's superficially similar to Functor and Applicative, but it isn't quite, because it's too specialized: I can't actually compose functions (as required by the homomorphism laws for Functor/Applicative) unless 'b' is Int.</p> <p>My goal is to use existing library functions/combinators, instead of writing my own variants like <code>cmap</code>, <code>cmap2</code>. Is that possible? Is there a different typeclass, or a different way to structure Canonical type, to enable my goal?</p> <p>I've tried other structures, like </p> <pre><code>newtype Canonical a = Canonical { value :: a, canonicalizer :: a -&gt; a } </code></pre> <p>but that hits the same non-composability problem, because I can't translate one canonicalizer to another (I just want to use the canonicalizer of the result type, which is always <code>Int</code> (or <code>Integral a</code>)</p> <p>And I can't force "specialization-only" like so, this isn't valid Haskell:</p> <pre><code>instance (Functor Int) (Canonical Int) </code></pre> <p>(and similar variations)</p> <p>I also tried</p> <pre><code>newtype (Integral a) =&gt; Canonical a = Canonical a -- -XDatatypeContexts instance (Integral a) =&gt; Functor Canonical where fmap f (Canonical x) = canonicalize $ f x </code></pre> <p>but GHC says that <code>DatatypeContexts</code> is deprecated, and a bad idea, and more severely, I get:</p> <pre><code> `Could not deduce (Integral a1) arising from a use of 'C' from the context (Integral a) bound by the instance declaration [...] fmap :: (a1 -&gt; b) -&gt; (C a1 -&gt; C b) </code></pre> <p>which I think is saying that the constraint <code>Integral a</code> can't actually be used to constrain <code>fmap</code> to <code>(Integral -&gt; Integral)</code> the way I wish, which is sort of obvious (since <code>fmap</code> has two type variables) :-(</p> <p>And of course this isn't valid Haskell either</p> <pre><code>instance (Integer a) =&gt; Functor Canonical where </code></pre> <p><strong>Is there a similar typeclass I could use, or am I wrong to try to use a typeclass at all for this functionality of "implicitly canonicalize the results of function calls"?</strong></p>
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    1. USmisterbee
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    1. COLet's step back a bit. Are you sure the type signature `cmap2 :: (b->c->Int) -> (Canonical Int) -> (Canonical Int)` describes what you want? Because it looks pretty senseless. It also has nothing to do with `Functor`. Here's an example of a valid functor signature: `(Int -> Int) -> Canonical Int -> Canonical Int`.
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      1. USNikita Volkov
    2. COMy mistake, I made errors when simplifiying my more complicated type down to something to ask on SO. I've (tried to) improve the definitions, made an edit.
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