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copied!<p>The previous solutions do compile, but won't give the expected result. The function <code>f</code> is never applied to the arguments. A correct code is:</p> <pre><code>let rec list_map f ?(accum = []) l = match l with | head :: tail -> list_map f ~accum:(f head :: accum) tail | [] -> accum;; </code></pre> <p>The inferred type is:</p> <pre><code>val list_map : ('a -> 'b) -> ?accum:'b list -> 'a list -> 'b list = <fun> </code></pre> <p>... in contrast to the wrong one:</p> <pre><code>val list_map : 'a -> ?accum:'b list -> 'b list -> 'b list = <fun> </code></pre> <hr> <p>Please note, that the result list is reversed:</p> <pre><code># list_map ( ( ** ) 2.) [1.;2.;3.;4.];; - : float list = [16.; 8.; 4.; 2.] </code></pre> <p>... and equals the function <a href="http://caml.inria.fr/pub/docs/manual-ocaml/libref/List.html#VALrev_map" rel="nofollow noreferrer">rev_list from the List module</a>:</p> <pre><code># List.rev_map ( ( ** ) 2.) [1.;2.;3.;4.];; - : float list = [16.; 8.; 4.; 2.] </code></pre> <hr> <p>So you may want to change your function into:</p> <pre><code>let rec list_map f ?(accum = []) l = match l with | head :: tail -> list_map f ~accum:(f head :: accum) tail | [] -> List.rev accum;; </code></pre> <p>... which should be tail-recursive as well (according to the manual) and returns the list in the original order:</p> <pre><code># list_map ( ( ** ) 2.) [1.;2.;3.;4.];; - : float list = [2.; 4.; 8.; 16.] </code></pre>

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