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copied!<p>Ok let's start from scratch. A pure strategy is a function that given a state of knowledge yields a guess. <code>state -> Guess</code>. For any given state, there's some way to add new knowledge to it -- <code>Answer -> state -> state</code>. Rather than an initial guess, we now just need an initial state.</p> <pre><code>data Strategy state = Strategy { initialState :: state, extractGuess :: state -> Guess, updateState :: Answer -> state -> state } </code></pre> <p>So now lets see what happns when we compose these functions.</p> <pre><code>type Oracle = Guess -> Maybe Answer -- we'll encode success as Nothing stepState :: Oracle -> Strategy state -> state -> Maybe state stepState oracle str state = fmap (\ans -> updateState str ans state) $ oracle (extractGuess str state) stepMany :: Strategy state -> Oracle -> [state] stepMany str oracle = go (initialState str) where go state = case stepState oracle str state of Nothing -> [] Just newState -> newState : go newState </code></pre> <p>So <code>stepMany</code> is 90% of what we want, but its still polymorphic in that pesky state param. That's easy enough to work around -- after all we want the number of steps, not the intermediate states of the steps themselves.</p> <pre><code>type packedStrategy = Oracle -> Int packStrategy :: Strategy state -> PackedStrategy packStrategy str oracle = length $ stepMany str oracle </code></pre> <p>And now you can write <code>[packStrategy stratOne, packStrategy stratTwo]</code> etc. And along the way, we've discovered something important -- what you care about from your strategy is just that it is a function from some problem (represented by an oracle) to the steps it takes to solve the problem. And one way (not the only way) to produce such stratgies is to provide a way to ask for new knowledge (to guess) and a way to update our knowledge (update state). </p> <p>This is not the only answer, and maybe not ideal for your purposes, but it should help to move you towards thinking with functions and types rather than objects and capabilities.</p>

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