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README
Boltzmann samplers 
Boltzmann.Data
Define sized random generators for Data.Data generic types.
{-# LANGUAGE DeriveDataTypeable #-}
import Data.Data
import Test.QuickCheck
import Boltzmann.Data
data Term = Lambda Int Term | App Term Term | Var Int
deriving (Show, Data)
instance Arbitrary Term where
arbitrary = sized $ generatorPWith [positiveInts]
positiveInts :: Alias Gen
positiveInts =
alias $ \() -> fmap getPositive arbitrary :: Gen Int
main = sample (arbitrary :: Gen Term)
- Objects of the same size (number of constructors) occur with the same probability (see Duchon et al., references below).
- Implements rejection sampling and pointing.
- Works with QuickCheck and MonadRandom, but also similar user-defined monads
for randomness (just implement
MonadRandomLike). - Can be tweaked somewhat with user defined generators.
Boltzmann.Species
An experimental interface to obtain Boltzmann samplers from an applicative specification of a combinatorial system.
No documentation (yet).
References
The core theory of Boltzmann samplers is described in Boltzmann Samplers for the Random Generation of Combinatorial Structures, P. Duchon, P. Flajolet, G. Louchard, G. Schaeffer.
The numerical evaluation of recursively defined generating functions is taken from Boltzmann Oracle for Combinatorial Systems, C. Pivoteau, B. Salvy, M. Soria.
See also
- boltzmann-brain, Boltzmann sampler compiler for combinatorial systems.