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PORecursive Type Families
 

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    <p>I am experimenting with an <code>mtl</code>-style class that allows me to lift <code>Pipe</code> composition over an outer monad. To do so, I must define which two variables of the type are the domain and codomain of <code>Pipe</code> composition.</p> <p>I tried using an associated type family approach, but to no avail:</p> <pre><code>{-# LANGUAGE TypeFamilies #-} import Control.Monad.Trans.Free import Control.Monad.Trans.State import Control.Pipe hiding (Pipe) data Pipe a b m r = Pipe { unPipe :: FreeT (PipeF a b) m r } class MonadPipe m where type C a b (m :: * -&gt; *) :: * -&gt; * idT :: C a a m r (&lt;-&lt;) :: C b c m r -&gt; C a b m r -&gt; C a c m r instance (Monad m) =&gt; MonadPipe (Pipe i o m) where type C a b (Pipe i o m) = Pipe a b m idT = Pipe idP (Pipe p1) &lt;-&lt; (Pipe p2) = Pipe (p1 &lt;+&lt; p2) instance (MonadPipe m) =&gt; MonadPipe (StateT s m) where type C a b (StateT s m) = StateT s (C a b m) idT = StateT $ \s -&gt; idT (StateT f1) &lt;-&lt; (StateT f2) = StateT $ \s -&gt; f1 s &lt;-&lt; f2 s </code></pre> <p>However, the above code does not type-check. GHC gives the following errors:</p> <pre><code>family.hs:23:15: Could not deduce (C a a m ~ C a0 a0 m0) from the context (MonadPipe m) bound by the instance declaration at family.hs:21:14-52 NB: `C' is a type function, and may not be injective Expected type: C a a (StateT s m) r Actual type: StateT s (C a0 a0 m0) r In the expression: StateT $ \ s -&gt; idT In an equation for `idT': idT = StateT $ \ s -&gt; idT In the instance declaration for `MonadPipe (StateT s m)' family.hs:24:10: Could not deduce (C b c m ~ C b0 c0 m1) from the context (MonadPipe m) bound by the instance declaration at family.hs:21:14-52 NB: `C' is a type function, and may not be injective Expected type: C b c (StateT s m) r Actual type: StateT s (C b0 c0 m1) r In the pattern: StateT f1 In an equation for `&lt;-&lt;': (StateT f1) &lt;-&lt; (StateT f2) = StateT $ \ s -&gt; f1 s &lt;-&lt; f2 s In the instance declaration for `MonadPipe (StateT s m)' &lt;&lt;Two other errors for 'C a b m' and 'C a c m'&gt;&gt; </code></pre> <p>It's hard for me to understand why the types won't unify, especially for the <code>idT</code> definition, since I'd expect the inner <code>idT</code> to be universally quantified over <code>a</code> so it would match the outer one.</p> <p>So my question is whether this is implementable with type families, and if not possible with type families, how could it be implemented?</p>
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    1. COThe last part of my answer using data families comes quite close to your desired code. How does that solution miss what you need?
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      1. USChris Kuklewicz
 

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