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copied!<p>Here's how I'd write your code:</p> <pre><code>increasing :: Integer -> [Integer] increasing 1 = [1..9] increasing n = let allEndings x = map (10*x +) [x `mod` 10 .. 9] in concatMap allEndings $ increasing (n - 1) </code></pre> <p>I arrived at this code as follows. The first thing I did was to use pattern matching instead of guards, since it's clearer here. The next thing I did was to eliminate the <code>liftM2</code>s. They're unnecessary here, because they're always called with one size-one list; in that case, it's the same as calling <code>map</code>. So <code>liftM2 (*) ps [10]</code> is just <code>map (* 10) ps</code>, and similarly for the other call sites. If you want a general replacement for <code>liftM2</code>, though, you can use <code>Control.Applicative</code>'s <code><$></code> (which is just <code>fmap</code>) and <code><*></code> to replace <code>liftMn</code> for any <code>n</code>: <code>liftMn f a b c ... z</code> becomes <code>f <$> a <*> b <*> c <*> ... <*> z</code>. Whether or not it's nicer is a matter of taste; I happen to like it.<sup>1</sup> But here, we can eliminate that entirely.</p> <p>The next place I simplified the original code is the <code>do ...</code>. You never actually take advantage of the fact that you're in a <code>do</code>-block, and so that code can become</p> <pre><code>let ps = increasing (n - 1) last = map (`mod` 10) ps next = map (* 10) ps in alternateEndings next last </code></pre> <p>From here, arriving at my code essentially involved writing fusing all of your <code>map</code>s together. One of the only remaining calls that wasn't a <code>map</code> was <code>zipWith</code>. But because you effectively have <code>zipWith alts next last</code>, you only work with <code>10*p</code> and <code>p `mod` 10</code> at the same time, so we can calculate them in the same function. This leads to</p> <pre><code>let ps = increasing (n - 1) in concat $ map alts ps where alts p = map (10*p +) [y `mod` 10..9] </code></pre> <p>And this is basically my code: <code>concat $ map ...</code> should always become <code>concatMap</code> (which, incidentally, is <code>=<<</code> in the list monad), we only use <code>ps</code> once so we can fold it in, and I prefer <code>let</code> to <code>where</code>.</p> <hr> <p><strong>1:</strong> Technically, this only works for <code>Applicative</code>s, so if you happen to be using a monad which hasn't been made one, <code><$></code> is <code>`liftM`</code> and <code><*></code> is <code>`ap`</code>. All monads can be made applicative functors, though, and many of them have been.</p>

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