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    copied!<p>The heart is the <code>bits</code> function:</p> <pre><code>-- | Memoize an ordered type with a bits instance. bits :: (Ord a, Bits a) =&gt; Memo a bits f = IntTrie.apply (fmap f IntTrie.identity) </code></pre> <p>It is the only function (except the trivial <code>unit :: Memo ()</code>) which can give you a <code>Memo a</code> value. It uses the same idea as in this <a href="http://www.haskell.org/haskellwiki/Memoization" rel="noreferrer">page</a> about Haskell memoization. Section 2 shows the simplest memoization strategy using a list and section 3 does the same using a binary tree of naturals similar to the <code>IntTree</code> used in memocombinators.</p> <p>The basic idea is to use a construction like <code>(map fib [0 ..] !!)</code> or in the memocombinators case - <code>IntTrie.apply (fmap f IntTrie.identity)</code>. The thing to notice here is the correspondance between <code>IntTie.apply</code> and <code>!!</code> and also between <code>IntTrie.identity</code> and <code>[0..]</code>.</p> <p>The next step is memoizing functions with other types of arguments. This is done with the <code>wrap</code> function which uses an isomorphism between types <code>a</code> and <code>b</code> to construct a <code>Memo b</code> from a <code>Memo a</code>. For example:</p> <pre><code>Memo.integral f =&gt; wrap fromInteger toInteger bits f =&gt; bits (f . fromInteger) . toInteger =&gt; IntTrie.apply (fmap (f . fromInteger) IntTrie.identity) . toInteger ~&gt; (semantically equivalent) (map (f . fromInteger) [0..] !!) . toInteger </code></pre> <p>The rest of the source code deals with types like List, Maybe, Either and memoizing multiple arguments.</p>
 

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