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POType-level Map with DataKinds
 

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    <p>I have a common pattern where I have a type-level list of kind <code>[*]</code>, and I would like to apply a type constructor of kind <code>* -&gt; *</code> to each element in the list. For example, I would like to change the type <code>'[Int, Double, Integer]</code> to <code>'[Maybe Int, Maybe Double, Maybe Integer]</code>.</p> <p>Here's my attempt to implement a type-level <code>map</code>.</p> <pre><code>{-# LANGUAGE TypeFamilies, MultiParamTypeClasses, FlexibleInstances, FlexibleContexts, TypeOperators, DataKinds, ScopedTypeVariables, GADTs #-} -- turns a type list '[b1, b2, b3] -- into the type list '[a b1, a b2, a b3] class TypeMap (a :: * -&gt; *) (bs :: [*]) where type Map a bs :: [*] instance TypeMap a '[b] where type Map a '[b] = '[a b] instance TypeMap a (b1 ': b2 ': bs) where type Map a (b1 ': b2 ': bs) = ((a b1) ': (Map a (b2 ': bs))) data HList :: [*] -&gt; * where HNil :: HList '[] HCons :: a -&gt; HList as -&gt; HList (a ': as) class Foo as where toLists :: HList as -&gt; HList (Map [] as) instance Foo '[a] where toLists (HCons a HNil) = HCons [a] HNil instance (Foo (a2 ': as)) =&gt; Foo (a1 ': a2 ': as) where toLists (HCons a as) = let as' = case (toLists as) of (HCons a2 as'') -&gt; HCons [head a2] as'' -- ERROR in HCons [a] as' </code></pre> <p>This results in the error </p> <pre><code>Could not deduce (a3 ~ [t0]) from the context (Foo ((':) * a2 as)) bound by the instance declaration at Test.hs:35:10-50 or from ((':) * a1 ((':) * a2 as) ~ (':) * a as1) bound by a pattern with constructor HCons :: forall a (as :: [*]). a -&gt; HList as -&gt; HList ((':) * a as), in an equation for `toLists' at Test.hs:36:14-23 or from (Map [] as1 ~ (':) * a3 as2) bound by a pattern with constructor HCons :: forall a (as :: [*]). a -&gt; HList as -&gt; HList ((':) * a as), in a case alternative at Test.hs:38:22-34 `a3' is a rigid type variable bound by a pattern with constructor HCons :: forall a (as :: [*]). a -&gt; HList as -&gt; HList ((':) * a as), in a case alternative at Test.hs:38:22 Expected type: HList (Map [] ((':) * a2 as)) Actual type: HList ((':) * [t0] as2) In the return type of a call of `HCons' In the expression: HCons [head a2] as'' In a case alternative: (HCons a2 as'') -&gt; HCons [head a2] as'' </code></pre> <p>I've tried adding copious type annotations, but the error more or less comes out the same: GHC can't even infer that the first element of the HList is a (normal) list. Am I doing something silly here? Something illegal? Or is there any way around? </p>
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    1. UScrockeea
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    1. COWhy don't you have a `TypeMap a []` instance?
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      1. USDaniel Wagner
    2. CO@DanielWagner Agreed, those instances should probably be for '[] and (a ': as).
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