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sourcecode:
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module PFLP
( Probability
, Dist
, enum
, uniform
, certainly
, (>>>=)
, joinWith
, (??)
, RT
, pick
, replicateDist
) where
import Control.Search.Unsafe (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') < 0.0001 && 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 Functor Dist where
fmap f (Dist x p) = Dist (f x) p
instance Applicative Dist where
pure = certainly
(<*>) = joinWith ($)
instance Monad Dist where
return = certainly
(>>=) = (>>>=)
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