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copied!<p>Forwards traveling state with a continuation monad looks like this:</p> <pre><code>Cont (fw -> r) a </code></pre> <p>Then the type of the argument to <code>cont</code> is</p> <pre><code>(a -> fw -> r) -> fw -> r </code></pre> <p>So you get a <code>fw</code> passed in from the past which you have to pass on to the continuation.</p> <p>Backwards traveling state looks like this:</p> <pre><code>Cont (bw, r) a </code></pre> <p>Then the type of the argument to <code>cont</code> is</p> <pre><code>(a -> (bw, r)) -> (bw, r) </code></pre> <p>I.e. you get a <code>bw</code> from the continuation which you have to pass on to the past.</p> <p>These can be combined into one continuation monad:</p> <pre><code>Cont (fw -> (bw, r)) a </code></pre> <p>There's a catch when applying this to your parser, because <code>toProgramStep</code> builds the program in reverse, so the list of ']' points is the forward state, and the list of '[' points is the backward state. Also, I got lazy and skipped the Maybe part, which should catch the pattern matching errors in <code>openBrace</code> and <code>closeBrace</code>.</p> <pre><code>type ParseState = Cont ([TapeP] -> ([TapeP], TapeP)) toProgram :: String -> TapeP toProgram = snd . ($ []) . (`runCont` (\a _ -> ([], a))) . toProgramStep openBrace :: ParseState TapeP -> ParseState TapeP openBrace mcontinue = do continue <- mcontinue cont $ \k (break:bs) -> let (cs, r) = k (loopControl continue break) bs in (continue:cs, r) closeBrace :: ParseState TapeP -> ParseState TapeP closeBrace mbreak = do break <- mbreak cont $ \k bs -> let (continue:cs, r) = k (loopControl continue break) (break:bs) in (cs, r) </code></pre>

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