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    <blockquote> <p>Is there any concrete performance benefit to using the Logic monad?</p> </blockquote> <p><strong>TL;DR</strong>: Not that I can find; it appears that <code>Maybe</code> outperforms <code>Logic</code> since it has less overhead.</p> <hr> <p>I decided to implement a simple benchmark to check the performance of <code>Logic</code> versus <code>Maybe</code>. In my test, I randomly construct 5000 CNFs with <code>n</code> clauses, each clause containing three literals. Performance is evaluated as the number of clauses <code>n</code> is varied.</p> <p>In my code, I modified <code>dpllLogic</code> as follows:</p> <pre><code>dpllLogic s = listToMaybe $ observeMany 1 $ dpll s </code></pre> <p>I also tested modifying <code>dpll</code> with <em>fair disjunction</em>, like so:</p> <pre><code>dpll goalClauses = dpll' $ S.empty :|-: goalClauses where dpll' sequent@(assms :|-: clauses) = do -- Fail early if falsum is a subgoal guard $ not (S.empty `member` clauses) case concatMap S.toList $ S.toList clauses of -- Return the assumptions if there are no subgoals left [] -&gt; return assms -- Otherwise try various tactics for resolving goals x:_ -&gt; msum [ pureRule sequent , oneRule sequent , return $ unitP x sequent , return $ unitP (neg x) sequent ] &gt;&gt;- dpll' </code></pre> <p>I then tested the using <code>Maybe</code>, <code>Logic</code>, and <code>Logic</code> with fair disjunction.</p> <p>Here are the benchmark results for this test: <img src="https://i.stack.imgur.com/5kdVw.png" alt="Maybe Monad v. Logic Monad v. Logic Monad with Fair Disjunction"></p> <p>As we can see, <code>Logic</code> with or without fair disjunction in this case makes no difference. The <code>dpll</code> solve using the <code>Maybe</code> monad appears to run in linear time in <code>n</code>, while using the <code>Logic</code> monad incurs additional overhead. It appears that the overhead incurred plateaus off. </p> <p>Here is the <code>Main.hs</code> file used to generate these test. Someone wishing to reproduce these benchmarks might wish to review <a href="http://www.haskell.org/ghc/docs/7.2.1/html/users_guide/profiling.html" rel="noreferrer">Haskell's notes on profiling</a>:</p> <pre><code>module Main where import DPLL import System.Environment (getArgs) import System.Random import Control.Monad (replicateM) import Data.Set (fromList) randLit = do let clauses = [ T p | p &lt;- ['a'..'f'] ] ++ [ F p | p &lt;- ['a'..'f'] ] r &lt;- randomRIO (0, (length clauses) - 1) return $ clauses !! r randClause n = fmap fromList $ replicateM n $ fmap fromList $ replicateM 3 randLit main = do args &lt;- getArgs let n = read (args !! 0) :: Int clauses &lt;- replicateM 5000 $ randClause n -- To use the Maybe monad --let satisfiable = filter (/= Nothing) $ map dpll clauses let satisfiable = filter (/= Nothing) $ map dpllLogic clauses putStrLn $ (show $ length satisfiable) ++ " satisfiable out of " ++ (show $ length clauses) </code></pre>
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    1. POUsing the Logic Monad in Haskell
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