Markov

Three type classes for deterministically analyzing Markov chains with known parameters. Markov0 is intended to list possible outcomes, Markov should allow for more sophisticated analysis. See Examples for examples. See README for a detailed description.

Markov0

class Eq m => Markov0 m where

A basic implementation of Markov chains.

Minimal complete definition

transition0 | step0

Methods

transition0 :: m -> [m -> m]

step0 :: m -> [m]

Instances

Markov0 Simple

Defined in Markov.Example

Methods

transition0 :: Simple -> [Simple -> Simple]

step0 :: Simple -> [Simple]

chain0 :: Markov0 m => [m] -> [[m]]

Itterated steps, with equal states combined.

Markov

class (Applicative t, Comonad t) => Markov t m where

An implementation of Markov chains.

Minimal complete definition

transition | step | sequential

Methods

transition :: m -> [t (m -> m)]

step :: t m -> [t m]

sequential :: [m -> [t (m -> m)]]

Instances

Markov ((,) (Product Rational, Merge String)) Room

Defined in Markov.Example

Methods

transition :: Room -> [((Product Rational, Merge String), Room -> Room)]

step :: ((Product Rational, Merge String), Room) -> [((Product Rational, Merge String), Room)]

sequential :: [Room -> [((Product Rational, Merge String), Room -> Room)]]

Markov ((,) (Sum Int, Product Rational)) Extinction

Defined in Markov.Example

Methods

transition :: Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]

step :: ((Sum Int, Product Rational), Extinction) -> [((Sum Int, Product Rational), Extinction)]

sequential :: [Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]]

Markov ((,) (Product Double)) FillBin

Defined in Markov.Example

Methods

transition :: FillBin -> [(Product Double, FillBin -> FillBin)]

step :: (Product Double, FillBin) -> [(Product Double, FillBin)]

sequential :: [FillBin -> [(Product Double, FillBin -> FillBin)]]

Markov ((,) (Product Double)) Tidal

Defined in Markov.Example

Methods

transition :: Tidal -> [(Product Double, Tidal -> Tidal)]

step :: (Product Double, Tidal) -> [(Product Double, Tidal)]

sequential :: [Tidal -> [(Product Double, Tidal -> Tidal)]]

Markov ((,) (Product Double)) Urn

Defined in Markov.Example

Methods

transition :: Urn -> [(Product Double, Urn -> Urn)]

step :: (Product Double, Urn) -> [(Product Double, Urn)]

sequential :: [Urn -> [(Product Double, Urn -> Urn)]]

Markov ((,) (Product Double)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Product Double, Simple -> Simple)]

step :: (Product Double, Simple) -> [(Product Double, Simple)]

sequential :: [Simple -> [(Product Double, Simple -> Simple)]]

Markov ((,) (Product Double)) FromLists

Defined in Markov.Example

Methods

transition :: FromLists -> [(Product Double, FromLists -> FromLists)]

step :: (Product Double, FromLists) -> [(Product Double, FromLists)]

sequential :: [FromLists -> [(Product Double, FromLists -> FromLists)]]

Markov ((,) (Product Int)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Product Int, Simple -> Simple)]

step :: (Product Int, Simple) -> [(Product Int, Simple)]

sequential :: [Simple -> [(Product Int, Simple -> Simple)]]

Markov ((,) (Sum Int)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Sum Int, Simple -> Simple)]

step :: (Sum Int, Simple) -> [(Sum Int, Simple)]

sequential :: [Simple -> [(Sum Int, Simple -> Simple)]]

chain :: (Combine (t m), Grouping (t m), Markov t m) => [t m] -> [[t m]]

Iterated steps, with equal states combined using summarize operation. WARNING: group does not currently respect equivalence classes, only Grouping.

Combine

class Combine a where

Within equivalence classes, combine should be associative, commutative, and should be idempotent up to equivalence. I.e. if x == y == z,

(x `combine` y) `combine` z = x `combine` (y `combine` z)

x `combine` y = y `combine` x

x `combine` x == x

Minimal complete definition

combine | summarize

Methods

combine :: a -> a -> a

summarize :: NonEmpty a -> a

Instances

Combine FillBin

Defined in Markov.Example

Methods

combine :: FillBin -> FillBin -> FillBin

summarize :: NonEmpty FillBin -> FillBin

Combine Room

Defined in Markov.Example

Methods

combine :: Room -> Room -> Room

summarize :: NonEmpty Room -> Room

Combine Tidal

Defined in Markov.Example

Methods

combine :: Tidal -> Tidal -> Tidal

summarize :: NonEmpty Tidal -> Tidal

Combine Extinction

Defined in Markov.Example

Methods

combine :: Extinction -> Extinction -> Extinction

summarize :: NonEmpty Extinction -> Extinction

Combine Urn

Defined in Markov.Example

Methods

combine :: Urn -> Urn -> Urn

summarize :: NonEmpty Urn -> Urn

Combine Simple

Defined in Markov.Example

Methods

combine :: Simple -> Simple -> Simple

summarize :: NonEmpty Simple -> Simple

Combine FromLists

Defined in Markov.Example

Methods

combine :: FromLists -> FromLists -> FromLists

summarize :: NonEmpty FromLists -> FromLists

Num a => Combine (Product a)

Defined in Markov

Methods

combine :: Product a -> Product a -> Product a

summarize :: NonEmpty (Product a) -> Product a

Combine (Sum a)

Defined in Markov

Methods

combine :: Sum a -> Sum a -> Sum a

summarize :: NonEmpty (Sum a) -> Sum a

Combine (Merge a)

Defined in Markov

Methods

combine :: Merge a -> Merge a -> Merge a

summarize :: NonEmpty (Merge a) -> Merge a

(Combine a, Combine b) => Combine (a, b)

Defined in Markov

Methods

combine :: (a, b) -> (a, b) -> (a, b)

summarize :: NonEmpty (a, b) -> (a, b)

(Combine a, Combine b, Combine c) => Combine (a, b, c)

Defined in Markov

Methods

combine :: (a, b, c) -> (a, b, c) -> (a, b, c)

summarize :: NonEmpty (a, b, c) -> (a, b, c)

newtype Merge a

Values from a Monoid which have the respective binary operation applied each step, where different values mean states should not be combined. E.g., strings with concatenation.

Constructors

Merge a

Instances

Enum a => Enum (Merge a)

Defined in Markov

Methods

succ :: Merge a -> Merge a

pred :: Merge a -> Merge a

toEnum :: Int -> Merge a

fromEnum :: Merge a -> Int

enumFrom :: Merge a -> [Merge a]

enumFromThen :: Merge a -> Merge a -> [Merge a]

enumFromTo :: Merge a -> Merge a -> [Merge a]

enumFromThenTo :: Merge a -> Merge a -> Merge a -> [Merge a]

Eq a => Eq (Merge a)

Defined in Markov

Methods

(==) :: Merge a -> Merge a -> Bool

(/=) :: Merge a -> Merge a -> Bool

Fractional a => Fractional (Merge a)

Defined in Markov

Methods

(/) :: Merge a -> Merge a -> Merge a

recip :: Merge a -> Merge a

fromRational :: Rational -> Merge a

Num a => Num (Merge a)

Defined in Markov

Methods

(+) :: Merge a -> Merge a -> Merge a

(-) :: Merge a -> Merge a -> Merge a

(*) :: Merge a -> Merge a -> Merge a

negate :: Merge a -> Merge a

abs :: Merge a -> Merge a

signum :: Merge a -> Merge a

fromInteger :: Integer -> Merge a

Show a => Show (Merge a)

Defined in Markov

Methods

showsPrec :: Int -> Merge a -> ShowS

show :: Merge a -> String

showList :: [Merge a] -> ShowS

Generic (Merge a)

Defined in Markov

Associated Types

type Rep (Merge a) :: Type -> Type

Methods

from :: Merge a -> Rep (Merge a) x

to :: Rep (Merge a) x -> Merge a

Semigroup a => Semigroup (Merge a)

Defined in Markov

Methods

(<>) :: Merge a -> Merge a -> Merge a

sconcat :: NonEmpty (Merge a) -> Merge a

stimes :: Integral b => b -> Merge a -> Merge a

Monoid a => Monoid (Merge a)

Defined in Markov

Methods

mempty :: Merge a

mappend :: Merge a -> Merge a -> Merge a

mconcat :: [Merge a] -> Merge a

Grouping a => Grouping (Merge a)

Defined in Markov

Methods

grouping :: Group (Merge a)

Combine (Merge a)

Defined in Markov

Methods

combine :: Merge a -> Merge a -> Merge a

summarize :: NonEmpty (Merge a) -> Merge a

Markov ((,) (Product Rational, Merge String)) Room

Defined in Markov.Example

Methods

transition :: Room -> [((Product Rational, Merge String), Room -> Room)]

step :: ((Product Rational, Merge String), Room) -> [((Product Rational, Merge String), Room)]

sequential :: [Room -> [((Product Rational, Merge String), Room -> Room)]]

type Rep (Merge a)

Defined in Markov

type Rep (Merge a) = D1 (MetaData "Merge" "Markov" "markov-realization-0.3.0-5G6aaFp9qxGCG9ox1pSRBj" True) (C1 (MetaCons "Merge" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

newtype Sum a

Values which are added each step where different values mean states should not be combined. E.g., number of times a red ball is picked from an urn.

Constructors

Sum a

Instances

Enum a => Enum (Sum a)

Defined in Markov

Methods

succ :: Sum a -> Sum a

pred :: Sum a -> Sum a

toEnum :: Int -> Sum a

fromEnum :: Sum a -> Int

enumFrom :: Sum a -> [Sum a]

enumFromThen :: Sum a -> Sum a -> [Sum a]

enumFromTo :: Sum a -> Sum a -> [Sum a]

enumFromThenTo :: Sum a -> Sum a -> Sum a -> [Sum a]

Eq a => Eq (Sum a)

Defined in Markov

Methods

(==) :: Sum a -> Sum a -> Bool

(/=) :: Sum a -> Sum a -> Bool

Fractional a => Fractional (Sum a)

Defined in Markov

Methods

(/) :: Sum a -> Sum a -> Sum a

recip :: Sum a -> Sum a

fromRational :: Rational -> Sum a

Num a => Num (Sum a)

Defined in Markov

Methods

(+) :: Sum a -> Sum a -> Sum a

(-) :: Sum a -> Sum a -> Sum a

(*) :: Sum a -> Sum a -> Sum a

negate :: Sum a -> Sum a

abs :: Sum a -> Sum a

signum :: Sum a -> Sum a

fromInteger :: Integer -> Sum a

Show a => Show (Sum a)

Defined in Markov

Methods

showsPrec :: Int -> Sum a -> ShowS

show :: Sum a -> String

showList :: [Sum a] -> ShowS

Generic (Sum a)

Defined in Markov

Associated Types

type Rep (Sum a) :: Type -> Type

Methods

from :: Sum a -> Rep (Sum a) x

to :: Rep (Sum a) x -> Sum a

Num a => Semigroup (Sum a)

Defined in Markov

Methods

(<>) :: Sum a -> Sum a -> Sum a

sconcat :: NonEmpty (Sum a) -> Sum a

stimes :: Integral b => b -> Sum a -> Sum a

Num a => Monoid (Sum a)

Defined in Markov

Methods

mempty :: Sum a

mappend :: Sum a -> Sum a -> Sum a

mconcat :: [Sum a] -> Sum a

Grouping a => Grouping (Sum a)

Defined in Markov

Methods

grouping :: Group (Sum a)

Combine (Sum a)

Defined in Markov

Methods

combine :: Sum a -> Sum a -> Sum a

summarize :: NonEmpty (Sum a) -> Sum a

Markov ((,) (Sum Int, Product Rational)) Extinction

Defined in Markov.Example

Methods

transition :: Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]

step :: ((Sum Int, Product Rational), Extinction) -> [((Sum Int, Product Rational), Extinction)]

sequential :: [Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]]

Markov ((,) (Sum Int)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Sum Int, Simple -> Simple)]

step :: (Sum Int, Simple) -> [(Sum Int, Simple)]

sequential :: [Simple -> [(Sum Int, Simple -> Simple)]]

type Rep (Sum a)

Defined in Markov

type Rep (Sum a) = D1 (MetaData "Sum" "Markov" "markov-realization-0.3.0-5G6aaFp9qxGCG9ox1pSRBj" True) (C1 (MetaCons "Sum" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

newtype Product a

Values which are multiplied each step, and combined additively for equal states. E.g., probabilities.

Constructors

Product a

Instances

Enum a => Enum (Product a)

Defined in Markov

Methods

succ :: Product a -> Product a

pred :: Product a -> Product a

toEnum :: Int -> Product a

fromEnum :: Product a -> Int

enumFrom :: Product a -> [Product a]

enumFromThen :: Product a -> Product a -> [Product a]

enumFromTo :: Product a -> Product a -> [Product a]

enumFromThenTo :: Product a -> Product a -> Product a -> [Product a]

Eq (Product a)

WARNING! Defined _ == _ = True!

Defined in Markov

Methods

(==) :: Product a -> Product a -> Bool

(/=) :: Product a -> Product a -> Bool

Fractional a => Fractional (Product a)

Defined in Markov

Methods

(/) :: Product a -> Product a -> Product a

recip :: Product a -> Product a

fromRational :: Rational -> Product a

Num a => Num (Product a)

Defined in Markov

Methods

(+) :: Product a -> Product a -> Product a

(-) :: Product a -> Product a -> Product a

(*) :: Product a -> Product a -> Product a

negate :: Product a -> Product a

abs :: Product a -> Product a

signum :: Product a -> Product a

fromInteger :: Integer -> Product a

Show a => Show (Product a)

Defined in Markov

Methods

showsPrec :: Int -> Product a -> ShowS

show :: Product a -> String

showList :: [Product a] -> ShowS

Generic (Product a)

Defined in Markov

Associated Types

type Rep (Product a) :: Type -> Type

Methods

from :: Product a -> Rep (Product a) x

to :: Rep (Product a) x -> Product a

Num a => Semigroup (Product a)

Defined in Markov

Methods

(<>) :: Product a -> Product a -> Product a

sconcat :: NonEmpty (Product a) -> Product a

stimes :: Integral b => b -> Product a -> Product a

Num a => Monoid (Product a)

Defined in Markov

Methods

mempty :: Product a

mappend :: Product a -> Product a -> Product a

mconcat :: [Product a] -> Product a

Grouping (Product a)

Defined in Markov

Methods

grouping :: Group (Product a)

Num a => Combine (Product a)

Defined in Markov

Methods

combine :: Product a -> Product a -> Product a

summarize :: NonEmpty (Product a) -> Product a

Markov ((,) (Product Rational, Merge String)) Room

Defined in Markov.Example

Methods

transition :: Room -> [((Product Rational, Merge String), Room -> Room)]

step :: ((Product Rational, Merge String), Room) -> [((Product Rational, Merge String), Room)]

sequential :: [Room -> [((Product Rational, Merge String), Room -> Room)]]

Markov ((,) (Sum Int, Product Rational)) Extinction

Defined in Markov.Example

Methods

transition :: Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]

step :: ((Sum Int, Product Rational), Extinction) -> [((Sum Int, Product Rational), Extinction)]

sequential :: [Extinction -> [((Sum Int, Product Rational), Extinction -> Extinction)]]

Markov ((,) (Product Double)) FillBin

Defined in Markov.Example

Methods

transition :: FillBin -> [(Product Double, FillBin -> FillBin)]

step :: (Product Double, FillBin) -> [(Product Double, FillBin)]

sequential :: [FillBin -> [(Product Double, FillBin -> FillBin)]]

Markov ((,) (Product Double)) Tidal

Defined in Markov.Example

Methods

transition :: Tidal -> [(Product Double, Tidal -> Tidal)]

step :: (Product Double, Tidal) -> [(Product Double, Tidal)]

sequential :: [Tidal -> [(Product Double, Tidal -> Tidal)]]

Markov ((,) (Product Double)) Urn

Defined in Markov.Example

Methods

transition :: Urn -> [(Product Double, Urn -> Urn)]

step :: (Product Double, Urn) -> [(Product Double, Urn)]

sequential :: [Urn -> [(Product Double, Urn -> Urn)]]

Markov ((,) (Product Double)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Product Double, Simple -> Simple)]

step :: (Product Double, Simple) -> [(Product Double, Simple)]

sequential :: [Simple -> [(Product Double, Simple -> Simple)]]

Markov ((,) (Product Double)) FromLists

Defined in Markov.Example

Methods

transition :: FromLists -> [(Product Double, FromLists -> FromLists)]

step :: (Product Double, FromLists) -> [(Product Double, FromLists)]

sequential :: [FromLists -> [(Product Double, FromLists -> FromLists)]]

Markov ((,) (Product Int)) Simple

Defined in Markov.Example

Methods

transition :: Simple -> [(Product Int, Simple -> Simple)]

step :: (Product Int, Simple) -> [(Product Int, Simple)]

sequential :: [Simple -> [(Product Int, Simple -> Simple)]]

type Rep (Product a)

Defined in Markov

type Rep (Product a) = D1 (MetaData "Product" "Markov" "markov-realization-0.3.0-5G6aaFp9qxGCG9ox1pSRBj" True) (C1 (MetaCons "Product" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))