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POCovering all the cases of a promoted datatype
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copied!<p>So I recently came up with this neat idea, in the hope of sharing code between the strict and lazy <code>State</code> transformer modules:</p> <pre><code>{-# LANGUAGE FlexibleInstances, DataKinds, KindSignatures #-} module State where data Strictness = Strict | Lazy newtype State (t :: Strictness) s a = State (s -> (s, a)) returnState :: a -> State t s a returnState x = State $ \s -> (s, x) instance Monad (State Lazy s) where return = returnState State ma >>= amb = State $ \s -> case ma s of ~(s', x) -> runState (amb x) s' instance Monad (State Strict s) where return = returnState State ma >>= amb = State $ \s -> case ma s of (s', x) -> runState (amb x) s' get :: State t s s get = State $ \s -> (s, s) put :: s -> State t s () put s = State $ \_ -> (s, ()) </code></pre> <p>You can see that <code>get</code> and <code>put</code> both work without any duplication – no type class instances, no anything – on both the strict and lazy types. However, even though I cover both possible cases for <code>Strictness</code>, I don't have a Monad instance for <code>State t s a</code> in general:</p> <pre><code>-- from http://blog.melding-monads.com/2009/12/30/fun-with-the-lazy-state-monad/ pro :: State t [Bool] () pro = do pro s <- get put (True : s) -- No instance for (Monad (State t [Bool])) arising from a do statement </code></pre> <p>The following works fine, albeit requiring <code>FlexibleContexts</code>:</p> <pre><code>pro :: (Monad (State t [Bool])) => State t [Bool] () -- otherwise as before </code></pre> <p>Then I can instantiate <code>t</code> at <code>Lazy</code> or <code>Strict</code> and run the result and get what I expect. But why do I have to give that context? Is this a conceptual limitation, or a practical one? Is there some reason I'm missing why <code>Monad (State t s a)</code> actually doesn't hold, or is there just no way to convince GHC of it yet?</p> <p>(Aside: using the context <code>Monad (State t s)</code> <em>doesn't</em> work:</p> <blockquote> <p><code>Could not deduce (Monad (State t [Bool])) arising from a do statement</code> <code>from the context (Monad (State t s))</code></p> </blockquote> <p>which just confuses me even more. Surely the former is deducible from the latter?)</p>

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