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    <p>The two nested loops you wrote are an excellent starting point. That is, we can write a function <code>tokens</code> that delegates its work to two recursive functions <code>outer</code> and <code>inner</code> that correspond to your loops:</p> <pre><code>type Token a = ([a], Int, Int) tokens :: [a] -&gt; [Token a] tokens = outer 0 where outer _ [] = [] outer i l@(_ : xs) = inner i [] l ++ outer (i + 1) xs where inner _ _ [] = [] inner j acc (x : xs) = (acc ++ [x], i, j) : inner (j + 1) (acc ++ [x]) xs </code></pre> <p>Here, <code>outer</code> iterates over the string and, for each start position within that string, calls <code>inner</code> to collect all the segments that start at that position together with their end positions.</p> <p>Although this function meets your requirements,</p> <pre><code>&gt; tokens "blah" [("b",0,0),("bl",0,1),("bla",0,2),("blah",0,3),("l",1,1),("la",1,2),("lah",1,3),("a",2,2),("ah",2,3),("h",3,3)] </code></pre> <p>it is quite inefficient due to the repeated list concatenation. A more efficient version would accumulate its results in so-called <a href="http://www.haskell.org/haskellwiki/Difference_list" rel="nofollow">difference lists</a>:</p> <pre><code>type Token a = ([a], Int, Int) tokens :: [a] -&gt; [Token a] tokens l = outer 0 l [] where outer _ [] = id outer i l@(_ : xs) = inner i id l . outer (i + 1) xs where inner _ _ [] = id inner j acc (x : xs) = ((acc [x], i, j) :) . inner (j + 1) (acc . (x :)) xs </code></pre> <p>How to construct the dictionary of course depends on how you choose to represent it. Here's an approach that uses simple ordered association lists,</p> <pre><code>type Dict a = [([a], [(Int, Int)])] empty :: Dict a empty = [] update :: Ord a =&gt; Token a -&gt; Dict a -&gt; Dict a update (xs, i, j) [] = [(xs, [(i, j)])] update (xs, i, j) ((ys, ns) : dict) = case compare xs ys of LT -&gt; (xs, [(i, j)]) : (ys, ns) : dict EQ -&gt; (ys, (i, j) : ns) : dict GT -&gt; (ys, ns) : update (xs, i, j) dict toDict :: Ord a =&gt; [a] -&gt; Dict a toDict = foldr update empty . tokens </code></pre> <p>but as your keys are strings, <a href="http://en.wikipedia.org/wiki/Trie" rel="nofollow">tries</a> (a.k.a. prefix trees) are probably a better choice.</p> <p>If it's efficient substring queries that you're after, I would recommend looking into <a href="http://en.wikipedia.org/wiki/Suffix_tree" rel="nofollow">suffix trees</a>, although their implementation is somewhat involved. You may want to check out</p> <ul> <li>Robert Giegerich and Stefan Kurtz. A comparison of imperative and purely functional suffix tree constructions. <em>Science of Computer Programming</em> 25(2–3):187–218, 1995</li> </ul> <p>and Bryan O'Sullivan's <a href="http://hackage.haskell.org/package/suffixtree" rel="nofollow">suffixtree</a> package on Hackage.</p>
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    1. POHow to find all substrings of a String with start and end indices
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    1. USStefan Holdermans
    1. USStefan Holdermans
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