```1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 ``` ```--- Library for Probabilistic Functional Logic Programming --- @author Sandra Dylus, Jan Christiansen, Finn Teegen, Jan Tikovsky --- @version June 2018 module PFLP ( Probability , Dist , enum , uniform , certainly , (>>>=) , joinWith , (??) , RT , pick , replicateDist ) where import Control.Findall (allValues) infixl 1 >>>= infixr 1 ?? --- Probabilities. --- Floating point numbers are used to model probabilities. type Probability = Float --- Probability distributions. --- Distributions are abstract and can only be created using the functions --- provided by this library, e.g., 'enum' and 'uniform'. Internally, Curry's --- built-in non-determinism is used to model distributions with more than one --- event-probability pair. data Dist a = Dist { event :: a, prob :: Probability } deriving Show member :: [a] -> a member = foldr (?) failed --- Creates a distribution based on a given list of events and another list --- providing the corresponding probabilities. This function also ensures that --- the relevant probabilities add up to `1.0` and are strictly positive. enum :: [a] -> [Probability] -> Dist a enum xs ps | 1.0 - (foldl (+) 0.0 ps') < 1.0e-4 && all (> 0.0) ps' = member (zipWith Dist xs ps') | otherwise = error ("PFLP.enum: probabilities do not add up to 1.0 " ++ "or are not strictly positive") where ps' = take (length xs) ps --- Creates a uniform distribution based on a given list of events. The list --- of events must be non-empty. uniform :: [a] -> Dist a uniform [] = error "PFLP.uniform: list of events must be non-empty" uniform xs@(_:_) = enum xs (repeat (1.0 / fromInt (length xs))) --- Creates a single-event-distribution with probability `1.0`. certainly :: a -> Dist a certainly x = Dist x 1.0 --- Combines two (dependent) distributions. (>>>=) :: Dist a -> (a -> Dist b) -> Dist b d >>>= f = let Dist x p = d Dist y q = f x in Dist y (p * q) --- Combines two (independent) distributions with respect to a given function. joinWith :: (a -> b -> c) -> Dist a -> Dist b -> Dist c joinWith f d1 d2 = do x <- d1 y <- d2 return (f x y) filterDist :: (a -> Bool) -> Dist a -> Dist a filterDist p d | p (event d) = d --- Queries a distribution for the probabilitiy of events that satisfy a given --- predicate. (??) :: (a -> Bool) -> Dist a -> Probability (??) p = foldr (+) 0.0 . allValues . prob . filterDist p --- Run-time choice values. Currently, the only way to construct a run-time --- choice value is to explicitly use a lambda abstraction. The evaluation of --- a run-time choice can be triggered by the function 'pick'. type RT a = () -> a --- Triggers the evaluation of a run-time choice value (see type synonym 'RT'). --- Everytime a run-time choice value is evaluated, a new choice is made. pick :: RT a -> a pick rt = rt () --- Independently replicates a distribution a given number of times. In order --- to behave properly, the given distribution is required to be a run-time --- choice value (see type synonym 'RT'). replicateDist :: Int -> RT (Dist a) -> Dist [a] replicateDist n rt | n == 0 = certainly [] | otherwise = joinWith (:) (pick rt) (replicateDist (n - 1) rt) instance Monad Dist where return = certainly (>>=) = (>>>=) ```