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    <p>This largely follows <a href="http://www.haskell.org/haskellwiki/Memoization" rel="noreferrer">http://www.haskell.org/haskellwiki/Memoization</a>.</p> <p>You want a function of type (a -> b). If it doesn't call itself, then you can just write a simple wrapper that caches the return values. The best way to store this mapping depends on what properties of a you can exploit. Ordering is pretty much a minimum. With integers you can construct an infinite lazy list or tree holding the values.</p> <pre><code>type Cacher a b = (a -&gt; b) -&gt; a -&gt; b positive_list_cacher :: Cacher Int b positive_list_cacher f n = (map f [0..]) !! n </code></pre> <p>or</p> <pre><code>integer_list_cacher :: Cacher Int b integer_list_cacher f n = (map f (interleave [0..] [-1, -2, ..]) !! index n where index n | n &lt; 0 = 2*abs(n) - 1 index n | n &gt;= 0 = 2 * n </code></pre> <p>So, suppose it is recursive. Then you need it to call not itself, but the memoized version, so you pass that in instead:</p> <pre><code>f_with_memo :: (a -&gt; b) -&gt; a -&gt; b f_with_memo memoed base = base_answer f_with_memo memoed arg = calc (memoed (simpler arg)) </code></pre> <p>The memoized version is, of course, what we're trying to define.</p> <p>But we can start by creating a function that caches its inputs:</p> <p>We could construct one level by passing in a function that creates a structure that caches values. Except we need to create the version of f that <em>already has</em> the cached function passed in.</p> <p>Thanks to laziness, this is no problem:</p> <pre><code>memoize cacher f = cached where cached = cacher (f cached) </code></pre> <p>then all we need is to use it: </p> <pre><code>exposed_f = memoize cacher_for_f f </code></pre> <p>The article gives hints as to how to use a type class selecting on the input to the function to do the above, rather than choosing an explicit caching function. This can be really nice -- rather than explicitly constructing a cache for each combination of input types, we can implicitly combine caches for types a and b into a cache for a function taking a and b.</p> <p>One final caveat: using this lazy technique means the cache never shrinks, it only grows. If you instead use the IO monad, you can manage this, but doing it wisely depends on usage patterns.</p>
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    1. POHow do you make a generic memoize function in Haskell?
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    1. POHow do you make a generic memoize function in Haskell?
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    1. COI read the link. I guess you would have to create a new type class and implement its interface for any type you'd like to be memoized. Is there any way to code that once in the Memoize module to save work for users of this module?
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    2. COYou can code up common types to cache on, and a few rules for combining them. If they use types you haven't defined, they'll need to create instances themselves.
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    3. COYou can also create instances based on type classes such as Ord or Bound, but each should really be put in separate modules -- they may need a different caching scheme, so need the option to not use these.
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