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copied!<p>The point is that <code>map</code> and <code>f</code> (<code>check</code> in your example) only communicate regarding how to transform individual elements. They don't communicate about how far down the list to transform elements: <code>map</code> always carries on all the way to the end.</p> <pre><code>map :: (a -> b) -> [a] -> [b] map _ [] = [] map f (x:xs) = f x : map f xs </code></pre> <p>Let's write a new version of <code>map</code> --- I'll call it <code>mapOnce</code> because I can't think of a better name.</p> <pre><code>mapOnce :: (a -> Maybe a) -> [a] -> [a] </code></pre> <p>There are two things to note about this type signature:</p> <ol> <li><p>Because we may stop applying <code>f</code> part-way down the list, the input list and the output list must have the same type. (With <code>map</code>, because the entire list will always be mapped, the type can change.)</p></li> <li><p>The type of <code>f</code> hasn't changed to <code>a -> a</code>, but to <code>a -> Maybe a</code>.</p> <ul> <li><code>Nothing</code> will mean "leave this element unchanged, continue down the list"</li> <li><code>Just y</code> will mean "change this element, and leave the remaining elements unaltered"</li> </ul></li> </ol> <p>So:</p> <pre><code>mapOnce _ [] = [] mapOnce f (x:xs) = case f x of Nothing -> x : mapOnce f xs Just y -> y : xs </code></pre> <p>Your example is now:</p> <pre><code>replaceX :: [Int] -> Int -> Int -> [Int] replaceX items old new = mapOnce check items where check item | item == old = Just new | otherwise = Nothing </code></pre>

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