We also applied the approach to biological modeling, as can be found in the paper “Modeling Genome Evolution with a DSEL for Probabilistic Programming” which made LtU back when it was fresh. This one is also on the website.

    Does nbsp work? (testing)

Here’s the last bit of my code again with the less-than replaced by the unicode symbol “precedes”

die = optionP [(n,1/6) | n ≺- [1..6]]
test = collect $ liftM2 (+) die die

{-# OPTIONS_GHC -fglasgow-exts #-}
import Control.Monad.Writer
import Data.Ratio
import Data.Monoid
import qualified Data.Map as M

newtype Dist a = D (WriterT Probability [] a)
deriving (Functor, Monad)

newtype Probability = P Rational
deriving (Eq, Ord, Show, Num, Fractional)

instance Monoid Probability where
mempty = 1
mappend = (*)
mconcat = product

runDist :: Dist a -> [(a, Probability)]
runDist (D x) = runWriterT x

optionP :: [(a, Probability)] -> Dist a
optionP xs = D (WriterT xs)

(??) p = sum . map snd . filter (p . fst) . runDist

collect :: (Ord a) => Dist a -> Dist a
collect x = optionP . M.toList . M.fromListWith (+) $ runDist x

die = optionP [(n,1/6) | n

Using ratios would seem a lot more intuitive to me. I’d rather see 1%6 instead of 16.7% for the probability of any given number on a six sided die.

Might it make sense to parameterize the Probability class so it could use any of the Fractional numbers? (Probability Float, or Probability Rational, etc)

> dice = D [(1,1/6), (2,1/6), (3,1/6),(4,1/6),(5,1/6),(6/16)]

It’s either a weird (DWIM-eval) typo or it really works, since you also wrote this:

> fmap (*2) dice == D [ 2*x, p | (x,p)