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.