Copyright	(c) Armando Santos 2019-2020
Maintainer	armandoifsantos@gmail.com
Stability	experimental
Safe Haskell	None
Language	Haskell2010

LAoP.Dist

Contents

Dist and Prob type synonyms
Constraint type synonyms
Functor instance equivalent functions
Applicative equivalent functions
Selective equivalent functions
Monad equivalent functions
Distribution construction functions
Converto to list of pairs
Pretty print distribution

Description

LAoP is a library for algebraic (inductive) construction and manipulation of matrices in Haskell. See my Msc Thesis for the motivation behind the library, the underlying theory, and implementation details.

This module exports a type synonym Dist that represents a stochastic distribution matrix and several distribution construction functions.

Synopsis

newtype Dist a = D (Matrix Prob () a)
type Prob = Double
type Countable a = KnownNat (Count a)
type CountableN a = KnownNat (Count (Normalize a))
type CountableDimensionsN a b = (CountableN a, CountableN b)
type FromListsN a b = FromLists Prob (Normalize a) (Normalize b)
type Liftable a b = (Bounded a, Bounded b, Enum a, Enum b, Eq b, Num Prob, Ord Prob)
type TrivialP a b = Normalize (a, b) ~ Normalize (Normalize a, Normalize b)
type TrivialE a b = Normalize (Either a b) ~ Either (Normalize a) (Normalize b)
fmapD :: (Liftable a b, CountableDimensionsN a b, FromListsN b a) => (a -> b) -> Dist a -> Dist b
unitD :: Dist ()
multD :: (CountableDimensionsN a b, CountableN (a, b), FromListsN (a, b) a, FromListsN (a, b) b, TrivialP a b) => Dist a -> Dist b -> Dist (a, b)
selectD :: (TrivialE a b, FromListsN b b, CountableN b) => Dist (Either a b) -> Matrix Prob a b -> Dist b
returnD :: forall a. (Enum a, FromListsN () a, Countable a) => a -> Dist a
bindD :: Dist a -> Matrix Prob a b -> Dist b
choose :: FromListsN () a => Prob -> Dist a
shape :: FromListsN () a => (Prob -> Prob) -> [a] -> Dist a
linear :: FromListsN () a => [a] -> Dist a
uniform :: FromListsN () a => [a] -> Dist a
negExp :: FromListsN () a => [a] -> Dist a
normal :: FromListsN () a => [a] -> Dist a
toValues :: forall a. (Enum a, Countable a, FromListsN () a) => Dist a -> [(a, Prob)]
prettyDist :: forall a. (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> String
prettyPrintDist :: forall a. (Show a, Enum a, Countable a, FromListsN () a) => Dist a -> IO ()

Documentation

If the sum of the rows of a column matrix is equal to 1 then this stochastic matrix can be seen as a probability distribution.

This module is still experimental but it's already possible to model probabilistic programming problems with it. Import Nat or Type to access LAoP matrix combinators and then all you have to do is to define your sample space, either by creating a new data type or by abstracting it out via Natural.

Write manipulation functions and promote them to matrices via fromF or fromF' and you're good to go!