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    <p>Ok, so what you need is a function <code>combinations n</code> that will produce all the booleans combinations of length <code>n</code>; let's represent them as lists of lists of booleans (i.e. a single assignment of variables will be a list of booleans). Then this function would do the job:</p> <pre><code>let rec combinations = function | 0 -&gt; [[]] | n -&gt; let rest = combinations (n - 1) in let comb_f = List.map (fun l -&gt; false::l) rest in let comb_t = List.map (fun l -&gt; true::l) rest in comb_t @ comb_f </code></pre> <p>There is only one empty combination of length <code>0</code> and for <code>n &gt; 0</code> we produce combinations of <code>n-1</code> and prefix them with <code>false</code> and with <code>true</code> to produce all possible combinations of length <code>n</code>.</p> <p>You could write a function to print such combinations, let's say:</p> <pre><code>let rec combinations_to_string = function | [] -&gt; "" | x::xs -&gt; let rec bools_to_str = function | [] -&gt; "" | b::bs -&gt; Printf.sprintf "%s%s" (if b then "T" else "F") (bools_to_str bs) in Printf.sprintf "[%s]%s" (bools_to_str x) (combinations_to_string xs) </code></pre> <p>and then test it all with:</p> <pre><code>let _ = let n = int_of_string Sys.argv.(1) in let combs = combinations n in Printf.eprintf "combinations(%d) = %s\n" n (combinations_to_string combs) </code></pre> <p>to get:</p> <pre><code>&gt; ./combinations 3 combinations(3) = [TTT][TTF][TFT][TFF][FTT][FTF][FFT][FFF] </code></pre>
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    1. COthis is incredible! could you explain to me the meaning of @ there? is it the same as List.append? and one more, what's the meaning of fun l -> false::l ?
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    2. CO@zfm: sure, `@` is indeed a shortcut for `List.append` (see http://caml.inria.fr/pub/docs/manual-ocaml/libref/Pervasives.html). `fun l -> false::l` is an anonymous function. You could write `let ff l = false::l in List.map ff rest` but instead you can "inline" the function as I did above. Hope that helps.
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    3. COIf you cannot hold all the combinations in memory, check out a post I made awhile ago (with some ocaml) for creating an index of the combination in lexicographical order, http://stackoverflow.com/questions/127704/algorithm-to-return-all-combinations-of-k-elements-from-n/127856#127856
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