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    <p>You're confusing mutability with data structure. It <em>is</em> a proper list — just not one you're allowed to modify. Haskell is purely functional, meaning values are constant — you can't change an item in a list any more than you could turn the number 2 into 3. Instead, you perform calculations to create new values with the changes you desire.</p> <p>You could define that function most simply this way:</p> <pre><code>add ls idx el = take idx ls ++ el : drop idx ls </code></pre> <p>The list <code>el : drop idx ls</code> reuses the tail of the original list, so you only have to generate a new list up to <code>idx</code> (which is what the <code>take</code> function does). If you want to do it using explicit recursion, you could define it like so:</p> <pre><code>add ls 0 el = el : ls add (x:xs) idx el | idx &lt; 0 = error "Negative index for add" | otherwise = x : add xs (idx - 1) el add [] _ el = [el] </code></pre> <p>This reuses the tail of the list in the same way (that's the <code>el : ls</code> in the first case).</p> <p>Since you seem to be having trouble seeing how this is a linked list, let's be clear about what a linked list is: It's a data structure consisting of cells, where each cell has a value and a reference to the next item. In C, it might be defined as:</p> <pre><code>struct ListCell { void *value; /* This is the head */ struct ListCell *next; /* This is the tail */ } </code></pre> <p>In Lisp, it's defined as <code>(head . tail)</code>, where <code>head</code> is the value and <code>tail</code> is the reference to the next item.</p> <p>In Haskell, it's defined as <code>data [] a = [] | a : [a]</code>, where <code>a</code> is the value and <code>[a]</code> is the reference to the next item.</p> <p>As you can see, these data structures are all equivalent. The only difference is that in C and Lisp, which are not purely functional, the head and tail values are things you can change. In Haskell, you can't change them.</p>
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