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If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. + diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/mcmc-synthesis.cabal b/mcmc-synthesis.cabal new file mode 100644 --- /dev/null +++ b/mcmc-synthesis.cabal @@ -0,0 +1,52 @@ +-- Initial mcmc-synthesis.cabal generated by cabal init. For further +-- documentation, see http://haskell.org/cabal/users-guide/ + +-- The name of the package. +name: mcmc-synthesis + +-- The package version. See the Haskell package versioning policy (PVP) +-- for standards guiding when and how versions should be incremented. +-- http://www.haskell.org/haskellwiki/Package_versioning_policy +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.4 + +-- A short (one-line) description of the package. +synopsis: MCMC applied to probabilistic program synthesis + +-- A longer description of the package. +-- description: + +-- The license under which the package is released. +license: GPL-3 + +-- The file containing the license text. +license-file: LICENSE + +-- The package author(s). +author: Jacob Taylor + +-- An email address to which users can send suggestions, bug reports, and +-- patches. +maintainer: jacobltaylor@gmail.com + +-- A copyright notice. +-- copyright: + +category: Language + +build-type: Simple + +-- Constraint on the version of Cabal needed to build this package. +cabal-version: >=1.8 + + +library + build-depends: base ==4.5.*, MonadRandom ==0.1.* + hs-source-dirs: src + exposed-modules: Language.Synthesis.Distribution, Language.Synthesis.MCMC, + Language.Synthesis.Synthesis, Language.Synthesis.Mutations + GHC-options: -Wall -O2 + + diff --git a/src/Language/Synthesis/Distribution.hs b/src/Language/Synthesis/Distribution.hs new file mode 100644 --- /dev/null +++ b/src/Language/Synthesis/Distribution.hs @@ -0,0 +1,70 @@ +{-# LANGUAGE RankNTypes #-} +module Language.Synthesis.Distribution ( + Distr (Distr), sample, logProbability, negativeInfinity, sumByLogs, + categorical, uniform, randInt, replicate, mix +) where + +import Prelude hiding (replicate) + +import Control.Monad (replicateM) +import Control.Monad.Random (Rand, Random, RandomGen, getRandom, + getRandomR) + +-- |Represents a discrete probability distribution. +data Distr a = Distr { + -- |Sample a random item from the distribution. + sample :: forall g. RandomGen g => Rand g a, + -- |Compute the log probability of a given value. + logProbability :: a -> Double +} + +-- |Negative infinity, the log of 0 probability. +negativeInfinity :: Double +negativeInfinity = read "-Infinity" + +-- |Computes (log . sum . map exp), with more numeric precision. +sumByLogs :: [Double] -> Double +sumByLogs xs = log (sum [exp (x - high) | x <- xs]) + high + where high = maximum xs + +-- |Samples from an (item, weight) list. +sampleCategorical :: RandomGen g => [(a, Double)] -> Rand g a +sampleCategorical items = go items . sum $ map snd items + where go [] _ = error "Cannot sample from an empty list." + go [(x, _)] _ = return x + go ((x, weight):rest) total = do + acceptance <- getRandom + if weight/total >= acceptance + then return x + else go rest $ total - weight + +-- |A distribution from an (item, weight) list. +categorical :: Eq a => [(a, Double)] -> Distr a +categorical items = Distr (sampleCategorical items) logProb + where total = sum (map snd items) + logProb item = case lookup item items of + Nothing -> negativeInfinity + Just weight -> log (weight/total) + +-- |Uniform distribution. +uniform :: Eq a => [a] -> Distr a +uniform xs = categorical [(x, 1.0) | x <- xs] + +-- |A distribution over some integral type, inclusively between the 2 +-- values. +randInt :: (Integral i, Random i) => (i, i) -> Distr i +randInt range@(low, high) = Distr (getRandomR range) logProb + where logProb item = if low <= item && item <= high + then -log (fromIntegral $ high - low + 1) + else negativeInfinity + +-- |Generate n independent draws from a distribution. +replicate :: Int -> Distr a -> Distr [a] +replicate n orig = Distr (replicateM n $ sample orig) logProb + where logProb xs = sum [logProbability orig x | x <- xs] + +-- |Given (distribution, weight) pairs, mix the distributions. +mix :: [(Distr a, Double)] -> Distr a +mix distrs = Distr (sampleCategorical distrs >>= sample) logProb + where logProb x = sumByLogs [log prob + logProbability distr x | + (distr, prob) <- distrs] diff --git a/src/Language/Synthesis/MCMC.hs b/src/Language/Synthesis/MCMC.hs new file mode 100644 --- /dev/null +++ b/src/Language/Synthesis/MCMC.hs @@ -0,0 +1,44 @@ +module Language.Synthesis.MCMC (mhList) where + +import Control.Monad +import Control.Monad.Random (Rand, RandomGen, getRandom, + getSplit, runRand) +import Control.Monad.Random.Class () + +import Language.Synthesis.Distribution (Distr) +import qualified Language.Synthesis.Distribution as Distr + + +-- These functions work on triples, (value, aux, density). +-- Density functions take a value and return auxilary and density. + + +mhNext :: RandomGen g => (a, b, Double) -> (a -> (b, Double)) -> + (a -> Distr a) -> Rand g (a, b, Double) +mhNext (orig, origAux, origDensity) density jump = do + next <- Distr.sample (jump orig) + let origToNext = Distr.logProbability (jump orig) next + nextToOrig = Distr.logProbability (jump next) orig + (nextAux, nextDensity) = density next + score = nextDensity - origDensity + nextToOrig - origToNext + acceptance <- getRandom + return $ if score >= log acceptance + then (next, nextAux, nextDensity) + else (orig, origAux, origDensity) + + +mhList' :: RandomGen g => (a, b, Double) -> (a -> (b, Double)) -> + (a -> Distr a) -> g -> [(a, b, Double)] +mhList' orig density jump g = orig : mhList' next density jump g' + where (next, g') = runRand (mhNext orig density jump) g + + +-- |Use the Metropolis-Hastings algorithm to sample a list of values. +mhList :: RandomGen g => + a -- ^The initial value. + -> (a -> (b, Double)) -- ^Density function. + -> (a -> Distr a) -- ^Jumping distribution. + -> Rand g [(a, b, Double)] -- ^List of (value, aux, density). +mhList orig density jump = + liftM (mhList' (orig, origAux, origDensity) density jump) getSplit + where (origAux, origDensity) = density orig diff --git a/src/Language/Synthesis/Mutations.hs b/src/Language/Synthesis/Mutations.hs new file mode 100644 --- /dev/null +++ b/src/Language/Synthesis/Mutations.hs @@ -0,0 +1,45 @@ +module Language.Synthesis.Mutations ( + mutateInstruction, swapInstructions, mix, Mutation +) where + +import Language.Synthesis.Distribution (Distr (Distr)) +import qualified Language.Synthesis.Distribution as Distr + +type Mutation a = a -> Distr a + +splitSelectingAt :: Int -> [a] -> ([a], a, [a]) +splitSelectingAt i xs = (take i xs, xs !! i, drop (i+1) xs) + +mutateInstructionAt :: Eq a => Distr a -> Int -> [a] -> Distr [a] +mutateInstructionAt instrDistr i codes = Distr (samp ()) logProb + where (before, _, after) = splitSelectingAt i codes + -- samp (), to get around the monomorphism restriction + samp () = do + elem' <- Distr.sample instrDistr + return (before ++ [elem'] ++ after) + logProb other = + let (before', elem', after') = splitSelectingAt i other in + if (before', after') == (before, after) + then Distr.logProbability instrDistr elem' + else Distr.negativeInfinity + +-- |Given a distribution over instructions, mutates a random instruction. +mutateInstruction :: Eq a => Distr a -> Mutation [a] +mutateInstruction instrDistr codes = + Distr.mix [(mutateInstructionAt instrDistr i codes, 1.0) | i <- [0 .. length codes - 1]] + +replaceAt :: Int -> a -> [a] -> [a] +replaceAt i x xs = before ++ [x] ++ after + where (before, _, after) = splitSelectingAt i xs + +swapAt :: Int -> Int -> [a] -> [a] +swapAt i j xs = replaceAt i (xs !! j) $ replaceAt j (xs !! i) xs + +-- |Swaps 2 random instructions. +swapInstructions :: Eq a => Mutation [a] +swapInstructions codes = + Distr.uniform [swapAt i j codes | i <- [1 .. length codes - 1], j <- [0 .. i - 1]] + +-- |Given (mutation, weight) list, mixes the mutations. +mix :: [(Mutation a, Double)] -> Mutation a +mix muts program = Distr.mix [(mut program, weight) | (mut, weight) <- muts] diff --git a/src/Language/Synthesis/Synthesis.hs b/src/Language/Synthesis/Synthesis.hs new file mode 100644 --- /dev/null +++ b/src/Language/Synthesis/Synthesis.hs @@ -0,0 +1,48 @@ +{-# LANGUAGE NamedFieldPuns #-} +module Language.Synthesis.Synthesis ( + Mutation, synthesizeMhList, runningBest, Problem(..) +) where + +import Control.Monad.Random + +import Language.Synthesis.Distribution (Distr) +import qualified Language.Synthesis.Distribution as Distr +import Language.Synthesis.MCMC +import Language.Synthesis.Mutations (Mutation) + +-- | This type specifies which program to synthesize. It comes with a +-- specification, which is a program that already works, some inputs +-- and a distance function. +data Problem program = Problem { score :: program -> Double + , prior :: Distr program + , jump :: Mutation program + } + +-- |Given a prior distribution, score function, mutation distribution, generate +-- a list of (program, score) values through MH sampling. +synthesizeMhList :: RandomGen gen => Problem program -> Rand gen [(program, Double)] +synthesizeMhList Problem {prior, score, jump} = do + first <- Distr.sample prior + let density prog = (sc, sc + Distr.logProbability prior prog) + where sc = score prog + list <- mhList first density jump + return [(prog, sc) | (prog, sc, _) <- list] + + +scanl' :: (a -> b -> a) -> a -> [b] -> [a] +scanl' f q xs = q : (case xs of + [] -> [] + first:rest -> next `seq` scanl f next rest + where next = f q first) + +-- |Given (value, score) pairs, return a running list of the best pair so far. +runningBest [] = [] +runningBest (first:rest) = scanl' maxScore first rest + where maxScore (p, ps) (q, qs) | qs >= ps = (q, qs) + | otherwise = (p, ps) + +-- runningBest :: [(a, Double)] -> [(a, Double)] +-- runningBest [] = [] +-- runningBest [only] = [only] +-- runningBest ((p,ps):(q,qs):rest) | qs >= ps = (p, ps) : runningBest ((q,qs):rest) +-- | otherwise = (p, ps) : runningBest ((p,ps):rest)