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18483658
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2013-08-28T09:07:23.790
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2013-08-28T09:07:23.790
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<code>>>=</code> aka bind has the signature: <code>m a -> (a -> m b) -> m b</code>. If we try to make this signature specific to Reader i.e replacing <code>m</code> with <code>Reader r</code> we will find that it becomes: <code>(Reader r) a -> (a -> (Reader r) b) -> (Reader r) b</code> Which is same as: <code>Reader r a -> (a -> Reader r b) -> Reader r b</code> Now we need to write such a function: <code>(>>=) m k = ...</code> where <code>m</code> is <code>Reader r a</code> and <code>k</code> is <code>(a -> Reader r b)</code> and we need to return <code>Reader r b</code> How can you create <code>Reader r b</code> as this is something that we have to return ? Well, <code>k</code> is a function that will allow you to create <code>Reader r b</code> but <code>k</code> need some value of type <code>a</code> to return <code>Reader r b</code>. How we can get a value of type <code>a</code> (so that we can use function <code>k</code>) ? Looks like <code>m</code> parameter which is of type <code>Reader r a</code> can help us to get a value of type <code>a</code>. How do we get value of <code>a</code> from <code>Reader r a</code>? <code>runReader</code> has a type <code>Reader r a -> r -> a</code>, so if we call <code>runReader</code> on <code>m</code> we will get <code>(r -> a)</code> but we were looking for value of <code>a</code> type and what we got is <code>(r -> a)</code> and it seems we don't have any <code>r</code> value to get <code>a</code>. It seems we are stuck as we don't have any other parameter to look for. Let's assume we somehow has some <code>r</code> value (called <code>r_val</code>) so that we can do: <code>let a_val = runReader m r_val</code> gives us value of type <code>a</code>. from <code>a</code> we need to get <code>Reader r b</code> using k <code>let reader_r_b_val = k a_val</code> gives us value of type <code>Reader r b</code> and that's it, we got what we need to return, lets combine all the above 2 lets: <code>k (runReader m r_val)</code> which is <code>Reader r b</code> BUT we are not done yet, we need to do something of <code>r_val</code> which was just a placeholder. Lets say we take <code>r_val</code> as param <code>\r_val -> k (runReader m r_val)</code> which is of type <code>r -> Reader r b</code> ... Hmmm but we only need to return <code>Reader r b</code> .. can we somehow wrap <code>r -> Reader r b</code> into a <code>Reader r b</code> ? <code>Reader $ (\r_val -> k (runReader m r_val))</code> has a type <code>Reader r (Reader r b)</code> .. looks like we are almost there we just need to convert <code>Reader r (Reader r b)</code> to <code>Reader r b</code> i.e we need the to convert inner <code>Reader r b</code> to just <code>b</code> and for that we can use <code>runReader</code> so: <code>Reader $ (\r_val -> runReader (k (runReader m r_val)) r_val)</code>
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1. POReader monad, how bind readers works?
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1. POReader monad, how bind readers works?
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