Control.Monad.List.Exotic

The usual list monad is only one of infinitely many ways to turn the List functor into a monad. This module collects a number of such exotic "list monads". Most of them have been introduced in the paper Degrading Lists by Dylan McDermott, Maciej Piróg, Tarmo Uustalu (PPDP 2020).

Notes:

• Types marked with "(?)" have not been formally verified to be monads (yet), though they were thoroughly tested with billions of QuickCheck tests.
• Monads in this module are presented in terms of join rather than >>=. In each case return is singleton (it is not known if there exists a monad on lists with a different return).
• For readability, code snippets in this documentation assume the OverloadedLists and OverloadedStrings extensions, which allow us to omit some newtype constructors. Example definitions of joins of monads always skip the newtype constructors, that is, assume >>= is always defined as follows for a particular local join:

m >>= f = wrap $ join $ map (unwrap . f) $ unwrap m
 where
  join = ...

• The definitions of monads are optimized for readability and not run-time performance. This is because the monads in this module don't seem to be of any practical use, they are more of a theoretical curiosity.

List monads in general

class Monad m => ListMonad m where

In this module, a "list monad" is a monad in which the underlying functor is isomorphic to List. We require:

wrap . unwrap  ==  id
unwrap . wrap  ==  id

There is a default implementation provided if m is known to be a list (meaning m a is an instance of IsList for all a).

Minimal complete definition

Nothing

Methods

wrap :: [a] -> m a

wrap :: (IsList (m a), Item (m a) ~ a) => [a] -> m a

unwrap :: m a -> [a]

unwrap :: (IsList (m a), Item (m a) ~ a) => m a -> [a]

Instances

ListMonad []

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> [a]

unwrap :: [a] -> [a]

ListMonad Odd

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Odd a

unwrap :: Odd a -> [a]

ListMonad Mini

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Mini a

unwrap :: Mini a -> [a]

ListMonad ListUnfold

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> ListUnfold a

unwrap :: ListUnfold a -> [a]

ListMonad DiscreteHybrid

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> DiscreteHybrid a

unwrap :: DiscreteHybrid a -> [a]

ListMonad MazeWalk

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> MazeWalk a

unwrap :: MazeWalk a -> [a]

ListMonad GlobalFailure

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> GlobalFailure a

unwrap :: GlobalFailure a -> [a]

KnownNat n => ListMonad (StutterKeeper n)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> StutterKeeper n a

unwrap :: StutterKeeper n a -> [a]

KnownNat n => ListMonad (Stutter n)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Stutter n a

unwrap :: Stutter n a -> [a]

(KnownNat n, KnownNat p) => ListMonad (ShortStutterKeeper n p)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> ShortStutterKeeper n p a

unwrap :: ShortStutterKeeper n p a -> [a]

(KnownNat n, KnownNat m) => ListMonad (StutterStutter n m)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> StutterStutter n m a

unwrap :: StutterStutter n m a -> [a]

ListMonad m => ListMonad (DualListMonad m)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> DualListMonad m a

unwrap :: DualListMonad m a -> [a]

newtype DualListMonad m a

Every list monad has a dual, in which join is defined as

join . reverse . fmap reverse

(where join is the join of the original list monad), while return is

reverse . return

(where return is the return of the original list monad).

Constructors

DualListMonad

Fields

• unDualListMonad :: m a

Instances

ListMonad m => Monad (DualListMonad m)

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: DualListMonad m a -> (a -> DualListMonad m b) -> DualListMonad m b

(>>) :: DualListMonad m a -> DualListMonad m b -> DualListMonad m b

return :: a -> DualListMonad m a

fail :: String -> DualListMonad m a

Functor m => Functor (DualListMonad m)

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> DualListMonad m a -> DualListMonad m b

(<$) :: a -> DualListMonad m b -> DualListMonad m a

ListMonad m => Applicative (DualListMonad m)

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> DualListMonad m a

(<*>) :: DualListMonad m (a -> b) -> DualListMonad m a -> DualListMonad m b

liftA2 :: (a -> b -> c) -> DualListMonad m a -> DualListMonad m b -> DualListMonad m c

(*>) :: DualListMonad m a -> DualListMonad m b -> DualListMonad m b

(<*) :: DualListMonad m a -> DualListMonad m b -> DualListMonad m a

ListMonad m => ListMonad (DualListMonad m)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> DualListMonad m a

unwrap :: DualListMonad m a -> [a]

(ListMonad m, IsList (m a)) => IsList (DualListMonad m a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (DualListMonad m a) :: Type

Methods

fromList :: [Item (DualListMonad m a)] -> DualListMonad m a

fromListN :: Int -> [Item (DualListMonad m a)] -> DualListMonad m a

toList :: DualListMonad m a -> [Item (DualListMonad m a)]

type Item (DualListMonad m a)

Defined in Control.Monad.List.Exotic

type Item (DualListMonad m a) = Item (m a)

isSingle :: [a] -> Bool

Checks if a given list is a singleton (= list of length one).

Monads with finite presentation

This section contains monads that come about from free algebras of theories with a finite number of operations, represented as type classes. Coincidentally, all theories in this module have one binary and one nullary operation, that is, each is a subclass of PointedMagma with additional laws. (So does the usual list monad, where the subclass is monoid.) It is not known if there exists a list monad that have a finite presentation but necessarily with a different set of operations (there are such monads on non-empty lists, for example, HeadTails and HeadsTail).

Pointed magmas

class PointedMagma a where

Pointed magmas are structures with one binary operation and one constant. In general, no laws are imposed.

Methods

eps :: a

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

Instances

PointedMagma [a]

Defined in Control.Monad.List.Exotic

Methods

eps :: [a]

(<>) :: [a] -> [a] -> [a]

PointedMagma (ListUnfold a)

Defined in Control.Monad.List.Exotic

Methods

eps :: ListUnfold a

(<>) :: ListUnfold a -> ListUnfold a -> ListUnfold a

PointedMagma (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

Methods

eps :: DiscreteHybrid a

(<>) :: DiscreteHybrid a -> DiscreteHybrid a -> DiscreteHybrid a

PointedMagma (MazeWalk a)

Defined in Control.Monad.List.Exotic

Methods

eps :: MazeWalk a

(<>) :: MazeWalk a -> MazeWalk a -> MazeWalk a

PointedMagma (GlobalFailure a)

Defined in Control.Monad.List.Exotic

Methods

eps :: GlobalFailure a

(<>) :: GlobalFailure a -> GlobalFailure a -> GlobalFailure a

KnownNat n => PointedMagma (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

Methods

eps :: StutterKeeper n a

(<>) :: StutterKeeper n a -> StutterKeeper n a -> StutterKeeper n a

KnownNat n => PointedMagma (Stutter n a)

Defined in Control.Monad.List.Exotic

Methods

eps :: Stutter n a

(<>) :: Stutter n a -> Stutter n a -> Stutter n a

(KnownNat n, KnownNat m) => PointedMagma (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

Methods

eps :: StutterStutter n m a

(<>) :: StutterStutter n m a -> StutterStutter n m a -> StutterStutter n m a

class ListMonad m => FreeRBPM m (c :: * -> Constraint) | m -> c where

A class for free right-braketed (subclasses of) pointed magmas.

Most of the monads defined in this module arise from subclasses of PointedMagma, in which we do not assume any additional methods, but require the instances to satisfy additional equations. This means that the monad is not only an instance of such a class that defines a type of algebra, but it is free such algebra.

In particular, we consider theories c in which the equations have the following shapes:

x <> eps       ==  ...
eps <> x       ==  ...
(x <> y) <> z  ==  ...

Moreover, when read left-to-right, they form a terminating and confluent rewriting system with normal forms of the following shape:

eps
x <> (y <> ( ... (z <> t) ... ))

This class offers a witness that a particular list monad m is a free algebra of the theory c. This gives us the function

foldRBPM _ (unwrap -> []) = eps
foldRBPM f (unwrap -> xs) = foldr1 (<>) (map f xs)

which is the unique lifting of an interpretation of generators to a homomorphism (between algebras of this sort) from the list monad to any algebra (an instance) of c.

Note that the default definition of foldRBPM is always the right one for right-bracketed subclasses of PointedMagma, so it is enough to declare the relationship, for example:

instance FreeRBPM [] Monoid

Minimal complete definition

Nothing

Methods

foldRBPM :: (PointedMagma a, c a) => (x -> a) -> m x -> a

Instances

FreeRBPM [] Monoid

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, Monoid a) => (x -> a) -> [x] -> a

FreeRBPM ListUnfold SkewedAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, SkewedAlgebra a) => (x -> a) -> ListUnfold x -> a

FreeRBPM DiscreteHybrid LeaningAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, LeaningAlgebra a) => (x -> a) -> DiscreteHybrid x -> a

FreeRBPM MazeWalk PalindromeAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, PalindromeAlgebra a) => (x -> a) -> MazeWalk x -> a

FreeRBPM GlobalFailure ZeroSemigroup

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, ZeroSemigroup a) => (x -> a) -> GlobalFailure x -> a

KnownNat n => FreeRBPM (StutterKeeper n) (StutterKeeperAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterKeeperAlgebra n a) => (x -> a) -> StutterKeeper n x -> a

KnownNat n => FreeRBPM (Stutter n) (StutterAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterAlgebra n a) => (x -> a) -> Stutter n x -> a

(KnownNat n, KnownNat m) => FreeRBPM (StutterStutter n m) (StutterStutterAlgebra n m)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterStutterAlgebra n m a) => (x -> a) -> StutterStutter n m x -> a

The Global Failure monad

class PointedMagma a => ZeroSemigroup a

A zero semigroup has an associative binary operation and a constant that is absorbing on both sides. That is, the following equations hold:

x <> eps       ==  eps
eps <> x       ==  eps
(x <> y) <> z  ==  x <> (y <> z)

Instances

FreeRBPM GlobalFailure ZeroSemigroup

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, ZeroSemigroup a) => (x -> a) -> GlobalFailure x -> a

ZeroSemigroup (GlobalFailure a)

Defined in Control.Monad.List.Exotic

newtype GlobalFailure a

The Global Failure monad arises from free zero semigroups. It implements a kind of nondeterminism similar to the usual List monad, but failing (= producing an empty list) in one branch makes the entire computation fail. Its join is defined as:

join xss | any null xss = []
         | otherwise    = concat xss

For example:

>>> [1, 2, 3] >>= (\n -> [1..n]) :: GlobalFailure Int
GlobalFailure [1,1,2,1,2,3]
>>> [1, 0, 3] >>= (\n -> [1..n]) :: GlobalFailure Int
GlobalFailure []

Constructors

GlobalFailure

Fields

• unGlobalFailure :: [a]

Instances

Monad GlobalFailure

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: GlobalFailure a -> (a -> GlobalFailure b) -> GlobalFailure b

(>>) :: GlobalFailure a -> GlobalFailure b -> GlobalFailure b

return :: a -> GlobalFailure a

fail :: String -> GlobalFailure a

Functor GlobalFailure

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> GlobalFailure a -> GlobalFailure b

(<$) :: a -> GlobalFailure b -> GlobalFailure a

Applicative GlobalFailure

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> GlobalFailure a

(<*>) :: GlobalFailure (a -> b) -> GlobalFailure a -> GlobalFailure b

liftA2 :: (a -> b -> c) -> GlobalFailure a -> GlobalFailure b -> GlobalFailure c

(*>) :: GlobalFailure a -> GlobalFailure b -> GlobalFailure b

(<*) :: GlobalFailure a -> GlobalFailure b -> GlobalFailure a

ListMonad GlobalFailure

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> GlobalFailure a

unwrap :: GlobalFailure a -> [a]

FreeRBPM GlobalFailure ZeroSemigroup

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, ZeroSemigroup a) => (x -> a) -> GlobalFailure x -> a

IsList (GlobalFailure a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (GlobalFailure a) :: Type

Methods

fromList :: [Item (GlobalFailure a)] -> GlobalFailure a

fromListN :: Int -> [Item (GlobalFailure a)] -> GlobalFailure a

toList :: GlobalFailure a -> [Item (GlobalFailure a)]

Eq a => Eq (GlobalFailure a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (GlobalFailure a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> GlobalFailure a -> ShowS

show :: GlobalFailure a -> String

showList :: [GlobalFailure a] -> ShowS

IsString (GlobalFailure Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> GlobalFailure Char

ZeroSemigroup (GlobalFailure a)

Defined in Control.Monad.List.Exotic

PointedMagma (GlobalFailure a)

Defined in Control.Monad.List.Exotic

Methods

eps :: GlobalFailure a

(<>) :: GlobalFailure a -> GlobalFailure a -> GlobalFailure a

type Item (GlobalFailure a)

Defined in Control.Monad.List.Exotic

type Item (GlobalFailure a) = a

The Maze Walk monad

class PointedMagma a => PalindromeAlgebra a

A palindrome algebra is a pointed magma that satisfies the following equations:

x <> eps       ==  eps
eps <> x       ==  eps
(x <> y) <> z  ==  x <> (y <> (x <> z))

Instances

FreeRBPM MazeWalk PalindromeAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, PalindromeAlgebra a) => (x -> a) -> MazeWalk x -> a

PalindromeAlgebra (MazeWalk a)

Defined in Control.Monad.List.Exotic

palindromize :: [a] -> [a]

Turns a list into a palindrome by appending it and its reversed init. For example:

palindromize []       ==  []
palindromize "Ringo"  ==  "RingogniR"

newtype MazeWalk a

The Maze Walk monad arises from free palindrome algebras. Its join is defined as:

join xss | null xss     = []
         | any null xss = []
         | otherwise    = concatMap palindromize (init xss) ++ last xss

Intuitively, it is a list of values one encounters when walking a path in a maze. The bind operation attaches to each value a new "corridor" to visit. In our walk we explore every such corridor. For example, consider the following expression:

>>> join ["John", "Paul", "George", "Ringo"] :: MazeWalk Char
MazeWalk "JohnhoJPauluaPGeorgegroeGRingo"

It represents a walk through the following maze (the entrance is marked with ">"):

  ┌────┬──────┐
  │L U │ N G O│
  ├─┤A ┴ I┌───┘
 > J P G R│
┌─┘O ┬ E ┌┘
│N H │ O └──┐
└────┤ R G E│
     └──────┘

First, we take the J-O-H-N path. When we reach its end, we turn around and go back to J, so our walk to this point is J-O-H-N-H-O-J (hence the connection with palindromes). Then, we explore the P-A-U-L corridor, adding P-A-U-L-U-A-P to our walk. The same applies to G-E-O-R-G-E. But when at the end of R-I-N-G-O, we have explored the entire maze, so our walk is done (this is why we do not palindromize the last element).

Constructors

MazeWalk

Fields

• unMazeWalk :: [a]

Instances

Monad MazeWalk

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: MazeWalk a -> (a -> MazeWalk b) -> MazeWalk b

(>>) :: MazeWalk a -> MazeWalk b -> MazeWalk b

return :: a -> MazeWalk a

fail :: String -> MazeWalk a

Functor MazeWalk

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> MazeWalk a -> MazeWalk b

(<$) :: a -> MazeWalk b -> MazeWalk a

Applicative MazeWalk

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> MazeWalk a

(<*>) :: MazeWalk (a -> b) -> MazeWalk a -> MazeWalk b

liftA2 :: (a -> b -> c) -> MazeWalk a -> MazeWalk b -> MazeWalk c

(*>) :: MazeWalk a -> MazeWalk b -> MazeWalk b

(<*) :: MazeWalk a -> MazeWalk b -> MazeWalk a

ListMonad MazeWalk

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> MazeWalk a

unwrap :: MazeWalk a -> [a]

FreeRBPM MazeWalk PalindromeAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, PalindromeAlgebra a) => (x -> a) -> MazeWalk x -> a

IsList (MazeWalk a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (MazeWalk a) :: Type

Methods

fromList :: [Item (MazeWalk a)] -> MazeWalk a

fromListN :: Int -> [Item (MazeWalk a)] -> MazeWalk a

toList :: MazeWalk a -> [Item (MazeWalk a)]

Eq a => Eq (MazeWalk a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (MazeWalk a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> MazeWalk a -> ShowS

show :: MazeWalk a -> String

showList :: [MazeWalk a] -> ShowS

IsString (MazeWalk Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> MazeWalk Char

PalindromeAlgebra (MazeWalk a)

Defined in Control.Monad.List.Exotic

PointedMagma (MazeWalk a)

Defined in Control.Monad.List.Exotic

Methods

eps :: MazeWalk a

(<>) :: MazeWalk a -> MazeWalk a -> MazeWalk a

type Item (MazeWalk a)

Defined in Control.Monad.List.Exotic

type Item (MazeWalk a) = a

The Discrete Hybrid monad

class PointedMagma a => LeaningAlgebra a

Instances should satisfy the following:

x <> eps       ==  eps
eps <> x       ==  x
(x <> y) <> z  ==  y <> z

Instances

FreeRBPM DiscreteHybrid LeaningAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, LeaningAlgebra a) => (x -> a) -> DiscreteHybrid x -> a

LeaningAlgebra (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

safeLast :: [a] -> [a]

A singleton list with the last element of the argument, if it exists. Otherwise, empty.

safeLast "Roy"  ==  "y"
safeLast []     ==  []

newtype DiscreteHybrid a

The Discrete Hybrid monad arises from free leaning algebras. Its join is defined as:

join xss | null xss        = []
         | null (last xss) = []
         | otherwise       = concatMap safeLast (init xss) ++ last xss

For example:

>>> join ["Roy", "Kelton", "Orbison"] :: DiscreteHybrid Char
DiscreteHybrid "ynOrbison"
>>> join ["Roy", "", "Orbison"] :: DiscreteHybrid Char
DiscreteHybrid "yOrbison"

Different versions of hybrid monads originate from Renato Neves's PhD thesis.

Constructors

DiscreteHybrid

Fields

• unDiscreteHybrid :: [a]

Instances

Monad DiscreteHybrid

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: DiscreteHybrid a -> (a -> DiscreteHybrid b) -> DiscreteHybrid b

(>>) :: DiscreteHybrid a -> DiscreteHybrid b -> DiscreteHybrid b

return :: a -> DiscreteHybrid a

fail :: String -> DiscreteHybrid a

Functor DiscreteHybrid

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> DiscreteHybrid a -> DiscreteHybrid b

(<$) :: a -> DiscreteHybrid b -> DiscreteHybrid a

Applicative DiscreteHybrid

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> DiscreteHybrid a

(<*>) :: DiscreteHybrid (a -> b) -> DiscreteHybrid a -> DiscreteHybrid b

liftA2 :: (a -> b -> c) -> DiscreteHybrid a -> DiscreteHybrid b -> DiscreteHybrid c

(*>) :: DiscreteHybrid a -> DiscreteHybrid b -> DiscreteHybrid b

(<*) :: DiscreteHybrid a -> DiscreteHybrid b -> DiscreteHybrid a

ListMonad DiscreteHybrid

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> DiscreteHybrid a

unwrap :: DiscreteHybrid a -> [a]

FreeRBPM DiscreteHybrid LeaningAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, LeaningAlgebra a) => (x -> a) -> DiscreteHybrid x -> a

IsList (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (DiscreteHybrid a) :: Type

Methods

fromList :: [Item (DiscreteHybrid a)] -> DiscreteHybrid a

fromListN :: Int -> [Item (DiscreteHybrid a)] -> DiscreteHybrid a

toList :: DiscreteHybrid a -> [Item (DiscreteHybrid a)]

Eq a => Eq (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> DiscreteHybrid a -> ShowS

show :: DiscreteHybrid a -> String

showList :: [DiscreteHybrid a] -> ShowS

IsString (DiscreteHybrid Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> DiscreteHybrid Char

LeaningAlgebra (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

PointedMagma (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

Methods

eps :: DiscreteHybrid a

(<>) :: DiscreteHybrid a -> DiscreteHybrid a -> DiscreteHybrid a

type Item (DiscreteHybrid a)

Defined in Control.Monad.List.Exotic

type Item (DiscreteHybrid a) = a

The List Unfold monad

class PointedMagma a => SkewedAlgebra a

A skewed algebra allows only right-nested composition of the binary operation. Every other expression is equal to eps.

x <> eps       ==  eps
eps <> x       ==  eps
(x <> y) <> z  ==  eps

Instances

FreeRBPM ListUnfold SkewedAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, SkewedAlgebra a) => (x -> a) -> ListUnfold x -> a

SkewedAlgebra (ListUnfold a)

Defined in Control.Monad.List.Exotic

newtype ListUnfold a

The List Unfold monad arises from free skewed algebras. It implements a form of nondeterminism similar to the usual list monad, but new choices may arise only in the last element (so the bind operation can only rename other elements), essentially unfolding a list. If new choices arise in the "init" of the list, the entire computation fails. Also, failure is always global. The join operation is defined as follows:

join xss | null xss                        = []
         | any null xss                    = []
         | any (not . isSingle) (init xss) = []
         | otherwise                       = concat xss

For example:

>>> [1,1,1,4] >>= \x -> [1..x] :: ListUnfold Int
ListUnfold [1,1,1,1,2,3,4]
>>> [1,2,1,4] >>= \x -> [1..x] :: ListUnfold Int
ListUnfold []
>>> [1,0,1,4] >>= \x -> [1..x] :: ListUnfold Int
ListUnfold []

Constructors

ListUnfold

Fields

• unListUnfold :: [a]

Instances

Monad ListUnfold

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: ListUnfold a -> (a -> ListUnfold b) -> ListUnfold b

(>>) :: ListUnfold a -> ListUnfold b -> ListUnfold b

return :: a -> ListUnfold a

fail :: String -> ListUnfold a

Functor ListUnfold

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> ListUnfold a -> ListUnfold b

(<$) :: a -> ListUnfold b -> ListUnfold a

Applicative ListUnfold

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> ListUnfold a

(<*>) :: ListUnfold (a -> b) -> ListUnfold a -> ListUnfold b

liftA2 :: (a -> b -> c) -> ListUnfold a -> ListUnfold b -> ListUnfold c

(*>) :: ListUnfold a -> ListUnfold b -> ListUnfold b

(<*) :: ListUnfold a -> ListUnfold b -> ListUnfold a

ListMonad ListUnfold

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> ListUnfold a

unwrap :: ListUnfold a -> [a]

FreeRBPM ListUnfold SkewedAlgebra

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, SkewedAlgebra a) => (x -> a) -> ListUnfold x -> a

IsList (ListUnfold a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (ListUnfold a) :: Type

Methods

fromList :: [Item (ListUnfold a)] -> ListUnfold a

fromListN :: Int -> [Item (ListUnfold a)] -> ListUnfold a

toList :: ListUnfold a -> [Item (ListUnfold a)]

Eq a => Eq (ListUnfold a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (ListUnfold a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> ListUnfold a -> ShowS

show :: ListUnfold a -> String

showList :: [ListUnfold a] -> ShowS

IsString (ListUnfold Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> ListUnfold Char

SkewedAlgebra (ListUnfold a)

Defined in Control.Monad.List.Exotic

PointedMagma (ListUnfold a)

Defined in Control.Monad.List.Exotic

Methods

eps :: ListUnfold a

(<>) :: ListUnfold a -> ListUnfold a -> ListUnfold a

type Item (ListUnfold a)

Defined in Control.Monad.List.Exotic

type Item (ListUnfold a) = a

The Stutter monad

class (KnownNat n, PointedMagma a) => StutterAlgebra n a

A stutter algebra (for a given natural number n) is a pointed magma that satisfies the following equations:

x <> eps       ==  foldr1 (<>) (replicate (n + 2) x)
eps <> x       ==  eps  
(x <> y) <> z  ==  eps

Instances

KnownNat n => StutterAlgebra n (Stutter n a)

Defined in Control.Monad.List.Exotic

KnownNat n => FreeRBPM (Stutter n) (StutterAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterAlgebra n a) => (x -> a) -> Stutter n x -> a

replicateLast :: Int -> [a] -> [a]

Repeat the last element on the list n additional times, that is:

replicateLast n [] = []
replicateLast n xs = xs ++ replicate n (last xs)

newtype Stutter (n :: Nat) a

The Stutter monad arises from free stutter algebras. Its join is a concat of the longest prefix consisting only of singletons with a "stutter" on the last singleton (that is, the last singleton is additionally repeated n+1 times for an n fixed in the type). It doesn't stutter only when the init consists only of singletons and the last list is non-empty. The join can thus be defined as follows (omitting the conversion of the type-level Nat n to a run-time value):

join xss | null xss
         = []
         | any (not . isSingle) (init xss) || null (last xss)
         = replicateLast (n + 1) (concat $ takeWhile isSingle (init xss))
         | otherwise
         = concat xss

The Stutter monad is quite similar to ListUnfold. The difference is that when the latter fails (that is, its join results in an empty list), the former stutters on the last singleton.

Examples:

>>> join ["1", "2", "buckle", "my", "shoe"] :: Stutter 5 Char
Stutter "12222222"
>>> join ["1", "2", "buckle"] :: Stutter 5 Char
Stutter "12buckle"
>>> join ["1", "2", "", "my", "shoe"] :: Stutter 5 Char
Stutter "12222222"

Constructors

Stutter

Fields

• unStutter :: [a]

Instances

KnownNat n => StutterAlgebra n (Stutter n a)

Defined in Control.Monad.List.Exotic

KnownNat n => Monad (Stutter n)

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: Stutter n a -> (a -> Stutter n b) -> Stutter n b

(>>) :: Stutter n a -> Stutter n b -> Stutter n b

return :: a -> Stutter n a

fail :: String -> Stutter n a

Functor (Stutter n)

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> Stutter n a -> Stutter n b

(<$) :: a -> Stutter n b -> Stutter n a

KnownNat n => Applicative (Stutter n)

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> Stutter n a

(<*>) :: Stutter n (a -> b) -> Stutter n a -> Stutter n b

liftA2 :: (a -> b -> c) -> Stutter n a -> Stutter n b -> Stutter n c

(*>) :: Stutter n a -> Stutter n b -> Stutter n b

(<*) :: Stutter n a -> Stutter n b -> Stutter n a

KnownNat n => ListMonad (Stutter n)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Stutter n a

unwrap :: Stutter n a -> [a]

KnownNat n => FreeRBPM (Stutter n) (StutterAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterAlgebra n a) => (x -> a) -> Stutter n x -> a

KnownNat n => IsList (Stutter n a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (Stutter n a) :: Type

Methods

fromList :: [Item (Stutter n a)] -> Stutter n a

fromListN :: Int -> [Item (Stutter n a)] -> Stutter n a

toList :: Stutter n a -> [Item (Stutter n a)]

Eq a => Eq (Stutter n a)

Defined in Control.Monad.List.Exotic

Methods

(==) :: Stutter n a -> Stutter n a -> Bool

(/=) :: Stutter n a -> Stutter n a -> Bool

Show a => Show (Stutter n a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> Stutter n a -> ShowS

show :: Stutter n a -> String

showList :: [Stutter n a] -> ShowS

KnownNat n => IsString (Stutter n Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> Stutter n Char

KnownNat n => PointedMagma (Stutter n a)

Defined in Control.Monad.List.Exotic

Methods

eps :: Stutter n a

(<>) :: Stutter n a -> Stutter n a -> Stutter n a

type Item (Stutter n a)

Defined in Control.Monad.List.Exotic

type Item (Stutter n a) = a

The Stutter-Keeper monad

class (KnownNat n, PointedMagma a) => StutterKeeperAlgebra n a

A stutter-keeper algebra (for a given natural number n) is a pointed magma that satisfies the following equations:

x <> eps       ==  foldr1 (<>) (replicate (n + 2) x)
eps <> x       ==  eps  
(x <> y) <> z  ==  x <> y

Instances

KnownNat n => StutterKeeperAlgebra n (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

KnownNat n => FreeRBPM (StutterKeeper n) (StutterKeeperAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterKeeperAlgebra n a) => (x -> a) -> StutterKeeper n x -> a

newtype StutterKeeper (n :: Nat) a

The stutter-keeper monad arises from free stutter-keeper algebras. Its join stutters (as in the Stutter monad) if the first non-singleton list in empty. Otherwise, it keeps the singleton prefix, and keeps the first non-singleton list. The join can thus be defined as follows (omitting the conversion of the type-level Nat n to a run-time value):

join xss | null xss
         = []
         | null (head (dropWhile isSingle (init xss) ++ [last xss]))
         = replicateLast (n + 1) (concat $ takeWhile isSingle (init xss))
         | otherwise
         = map head (takeWhile isSingle (init xss))
            ++ head (dropWhile isSingle (init xss) ++ [last xss])

Examples:

>>> join ["1", "2", "buckle", "my", "shoe"] :: StutterKeeper 5 Char
StutterKeeper "12buckle"
>>> join ["1", "2", "buckle"] :: StutterKeeper 5 Char
StutterKeeper "12buckle"
>>> join ["1", "2", "", "my", "shoe"] :: StutterKeeper 5 Char
StutterKeeper "12222222"

Constructors

StutterKeeper

Fields

• unStutterKeeper :: [a]

Instances

KnownNat n => StutterKeeperAlgebra n (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

KnownNat n => Monad (StutterKeeper n)

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: StutterKeeper n a -> (a -> StutterKeeper n b) -> StutterKeeper n b

(>>) :: StutterKeeper n a -> StutterKeeper n b -> StutterKeeper n b

return :: a -> StutterKeeper n a

fail :: String -> StutterKeeper n a

Functor (StutterKeeper n)

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> StutterKeeper n a -> StutterKeeper n b

(<$) :: a -> StutterKeeper n b -> StutterKeeper n a

KnownNat n => Applicative (StutterKeeper n)

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> StutterKeeper n a

(<*>) :: StutterKeeper n (a -> b) -> StutterKeeper n a -> StutterKeeper n b

liftA2 :: (a -> b -> c) -> StutterKeeper n a -> StutterKeeper n b -> StutterKeeper n c

(*>) :: StutterKeeper n a -> StutterKeeper n b -> StutterKeeper n b

(<*) :: StutterKeeper n a -> StutterKeeper n b -> StutterKeeper n a

KnownNat n => ListMonad (StutterKeeper n)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> StutterKeeper n a

unwrap :: StutterKeeper n a -> [a]

KnownNat n => FreeRBPM (StutterKeeper n) (StutterKeeperAlgebra n)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterKeeperAlgebra n a) => (x -> a) -> StutterKeeper n x -> a

KnownNat n => IsList (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (StutterKeeper n a) :: Type

Methods

fromList :: [Item (StutterKeeper n a)] -> StutterKeeper n a

fromListN :: Int -> [Item (StutterKeeper n a)] -> StutterKeeper n a

toList :: StutterKeeper n a -> [Item (StutterKeeper n a)]

Eq a => Eq (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

Methods

(==) :: StutterKeeper n a -> StutterKeeper n a -> Bool

(/=) :: StutterKeeper n a -> StutterKeeper n a -> Bool

Show a => Show (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> StutterKeeper n a -> ShowS

show :: StutterKeeper n a -> String

showList :: [StutterKeeper n a] -> ShowS

KnownNat n => IsString (StutterKeeper n Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> StutterKeeper n Char

KnownNat n => PointedMagma (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

Methods

eps :: StutterKeeper n a

(<>) :: StutterKeeper n a -> StutterKeeper n a -> StutterKeeper n a

type Item (StutterKeeper n a)

Defined in Control.Monad.List.Exotic

type Item (StutterKeeper n a) = a

The Stutter-Stutter monad

class (KnownNat n, KnownNat m, PointedMagma a) => StutterStutterAlgebra n m a

A stutter-stutter algebra (for given natural numbers n and m) is a pointed magma that satisfies the following equations:

x <> eps       ==  foldr1 (<>) (replicate (n + 2) x)
eps <> x       ==  eps  
(x <> y) <> z  ==  foldr1 (<>) (replicate (m + 2) x)

Instances

(KnownNat n, KnownNat m) => StutterStutterAlgebra n m (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

(KnownNat n, KnownNat m) => FreeRBPM (StutterStutter n m) (StutterStutterAlgebra n m)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterStutterAlgebra n m a) => (x -> a) -> StutterStutter n m x -> a

newtype StutterStutter (n :: Nat) (m :: Nat) a

The stutter-stutter monad arises from free stutter-stutter algebras. It is similar to StutterKeeper, but instead of keeping the first non-singleton list, it stutters on its first element (unless the first non-singleton list is also the last list, in which case it is kept in the result). The join can thus be defined as follows (omitting the conversion of the type-level nats to run-time values):

join xss | null xss
         = []
         | null (head (dropWhile isSingle (init xss) ++ [last xss]))
         = replicateLast (n + 1) (concat $ takeWhile isSingle (init xss))
         | any (not . isSingle) (init xss) || null (last xss)
         = concat (takeWhile isSingle (init xss))
            ++ replicate (m + 2) (head (head (dropWhile isSingle (init xss))))
         | otherwise
         = concat xss

Examples:

>>> join ["1", "2", "buckle", "my", "shoe"] :: StutterStutter 5 10 Char
StutterStutter "12bbbbbbbbbbbb"
>>> join ["1", "2", "buckle"] :: StutterStutter 5 10 Char
StutterStutter "12buckle"
>>> join ["1", "2", "", "my", "shoe"] :: StutterStutter 5 10 Char
StutterStutter "12222222"

Constructors

StutterStutter

Fields

• unStutterStutter :: [a]

Instances

(KnownNat n, KnownNat m) => StutterStutterAlgebra n m (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

(KnownNat n, KnownNat m) => Monad (StutterStutter n m)

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: StutterStutter n m a -> (a -> StutterStutter n m b) -> StutterStutter n m b

(>>) :: StutterStutter n m a -> StutterStutter n m b -> StutterStutter n m b

return :: a -> StutterStutter n m a

fail :: String -> StutterStutter n m a

Functor (StutterStutter n m)

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> StutterStutter n m a -> StutterStutter n m b

(<$) :: a -> StutterStutter n m b -> StutterStutter n m a

(KnownNat n, KnownNat m) => Applicative (StutterStutter n m)

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> StutterStutter n m a

(<*>) :: StutterStutter n m (a -> b) -> StutterStutter n m a -> StutterStutter n m b

liftA2 :: (a -> b -> c) -> StutterStutter n m a -> StutterStutter n m b -> StutterStutter n m c

(*>) :: StutterStutter n m a -> StutterStutter n m b -> StutterStutter n m b

(<*) :: StutterStutter n m a -> StutterStutter n m b -> StutterStutter n m a

(KnownNat n, KnownNat m) => ListMonad (StutterStutter n m)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> StutterStutter n m a

unwrap :: StutterStutter n m a -> [a]

(KnownNat n, KnownNat m) => FreeRBPM (StutterStutter n m) (StutterStutterAlgebra n m)

Defined in Control.Monad.List.Exotic

Methods

foldRBPM :: (PointedMagma a, StutterStutterAlgebra n m a) => (x -> a) -> StutterStutter n m x -> a

(KnownNat n, KnownNat m) => IsList (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (StutterStutter n m a) :: Type

Methods

fromList :: [Item (StutterStutter n m a)] -> StutterStutter n m a

fromListN :: Int -> [Item (StutterStutter n m a)] -> StutterStutter n m a

toList :: StutterStutter n m a -> [Item (StutterStutter n m a)]

Eq a => Eq (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

Methods

(==) :: StutterStutter n m a -> StutterStutter n m a -> Bool

(/=) :: StutterStutter n m a -> StutterStutter n m a -> Bool

Show a => Show (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> StutterStutter n m a -> ShowS

show :: StutterStutter n m a -> String

showList :: [StutterStutter n m a] -> ShowS

(KnownNat n, KnownNat m) => IsString (StutterStutter n m Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> StutterStutter n m Char

(KnownNat n, KnownNat m) => PointedMagma (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

Methods

eps :: StutterStutter n m a

(<>) :: StutterStutter n m a -> StutterStutter n m a -> StutterStutter n m a

type Item (StutterStutter n m a)

Defined in Control.Monad.List.Exotic

type Item (StutterStutter n m a) = a

Other monads

While all list monads have presentations in terms of operations and equations, some require infinitely many operations. This section contains monads that are either known to require infinitely many operations, or those for which no finite presentation is known, but we don't know for sure that such a presentation doesn't exist.

The Mini monad

newtype Mini a

The Mini monad is the minimal list monad, meaning that its join fails (= results in an empty list) for all values except the ones that appear in the unit laws (i.e., a singleton or a list of singletons):

join xss | isSingle xss     = concat xss
         | all isSingle xss = concat xss
         | otherwise        = []

For example:

>>> join ["HelloThere"] :: Mini Char
Mini "HelloThere"
>>> join ["Hello", "There"] :: Mini Char
Mini ""

It does not arise from a subclass of PointedMagma (or any algebraic theory with a finite number of operations for that matter).

Constructors

Mini

Fields

• unMini :: [a]

Instances

Monad Mini

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: Mini a -> (a -> Mini b) -> Mini b

(>>) :: Mini a -> Mini b -> Mini b

return :: a -> Mini a

fail :: String -> Mini a

Functor Mini

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> Mini a -> Mini b

(<$) :: a -> Mini b -> Mini a

Applicative Mini

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> Mini a

(<*>) :: Mini (a -> b) -> Mini a -> Mini b

liftA2 :: (a -> b -> c) -> Mini a -> Mini b -> Mini c

(*>) :: Mini a -> Mini b -> Mini b

(<*) :: Mini a -> Mini b -> Mini a

ListMonad Mini

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Mini a

unwrap :: Mini a -> [a]

IsList (Mini a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (Mini a) :: Type

Methods

fromList :: [Item (Mini a)] -> Mini a

fromListN :: Int -> [Item (Mini a)] -> Mini a

toList :: Mini a -> [Item (Mini a)]

Eq a => Eq (Mini a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (Mini a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> Mini a -> ShowS

show :: Mini a -> String

showList :: [Mini a] -> ShowS

IsString (Mini Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> Mini Char

type Item (Mini a)

Defined in Control.Monad.List.Exotic

type Item (Mini a) = a

The Odd monad (?)

newtype Odd a

The join of the Odd monad is a concat of the inner lists provided there is an odd number of them, and that all of them are of odd length themselves. Otherwise (modulo cases needed for the unit laws), it returns an empty list.

join xss | isSingle xss               = concat xss
         | all isSingle xss           = concat xss
         | odd (length xss)
            && all (odd . length) xss = concat xss 
         | otherwise                  = []

For example:

>>> join ["Elvis", "Presley"] :: Odd Char
Odd ""
>>> join ["Elvis", "Aaron", "Presley"] :: Odd Char
Odd "ElvisAaronPresley"
>>> join ["Roy", "Kelton", "Orbison"] :: Odd Char
Odd ""

At the moment, it is unclear whether it comes from a finite algebraic theory (or that it is indeed a monad).

Constructors

Odd

Fields

• unOdd :: [a]

Instances

Monad Odd

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: Odd a -> (a -> Odd b) -> Odd b

(>>) :: Odd a -> Odd b -> Odd b

return :: a -> Odd a

fail :: String -> Odd a

Functor Odd

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> Odd a -> Odd b

(<$) :: a -> Odd b -> Odd a

Applicative Odd

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> Odd a

(<*>) :: Odd (a -> b) -> Odd a -> Odd b

liftA2 :: (a -> b -> c) -> Odd a -> Odd b -> Odd c

(*>) :: Odd a -> Odd b -> Odd b

(<*) :: Odd a -> Odd b -> Odd a

ListMonad Odd

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> Odd a

unwrap :: Odd a -> [a]

IsList (Odd a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (Odd a) :: Type

Methods

fromList :: [Item (Odd a)] -> Odd a

fromListN :: Int -> [Item (Odd a)] -> Odd a

toList :: Odd a -> [Item (Odd a)]

Eq a => Eq (Odd a)

Defined in Control.Monad.List.Exotic

Methods

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

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

Show a => Show (Odd a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> Odd a -> ShowS

show :: Odd a -> String

showList :: [Odd a] -> ShowS

IsString (Odd Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> Odd Char

type Item (Odd a)

Defined in Control.Monad.List.Exotic

type Item (Odd a) = a

The Short Stutter-Keeper monad (?)

newtype ShortStutterKeeper (n :: Nat) (p :: Nat) a

This monad works just like the StutterKeeper monad but it takes a prefix of the result of join of length p+2 (unless the unit laws say otherwise). Thus, its join is defined as follows (omitting the conversion of the type-level Nat p to a run-time value):

join xss | isSingle xss     = concat xss
         | all isSingle xss = concat xss
         | otherwise        = take (p + 2) $ toList
                                ((Control.Monad.join $ StutterKeeper $ fmap StutterKeeper xss)
                                  :: StutterKeeper n _)

For example:

>>> join ["1", "2", "buckle", "my", "shoe"] :: ShortStutterKeeper 5 2 Char
ShortStutterKeeper "12bu"
>>> join ["1", "2", "buckle"] :: ShortStutterKeeper 5 2 Char
ShortStutterKeeper "12bu"
>>> join ["1", "2", "", "my", "shoe"] :: ShortStutterKeeper 5 2 Char
ShortStutterKeeper "1222"

Compare the ShortFront monad on non-empty lists.

Constructors

ShortStutterKeeper

Fields

• unShortStutterKeeper :: [a]

Instances

(KnownNat n, KnownNat p) => Monad (ShortStutterKeeper n p)

Defined in Control.Monad.List.Exotic

Methods

(>>=) :: ShortStutterKeeper n p a -> (a -> ShortStutterKeeper n p b) -> ShortStutterKeeper n p b

(>>) :: ShortStutterKeeper n p a -> ShortStutterKeeper n p b -> ShortStutterKeeper n p b

return :: a -> ShortStutterKeeper n p a

fail :: String -> ShortStutterKeeper n p a

Functor (ShortStutterKeeper n p)

Defined in Control.Monad.List.Exotic

Methods

fmap :: (a -> b) -> ShortStutterKeeper n p a -> ShortStutterKeeper n p b

(<$) :: a -> ShortStutterKeeper n p b -> ShortStutterKeeper n p a

(KnownNat n, KnownNat p) => Applicative (ShortStutterKeeper n p)

Defined in Control.Monad.List.Exotic

Methods

pure :: a -> ShortStutterKeeper n p a

(<*>) :: ShortStutterKeeper n p (a -> b) -> ShortStutterKeeper n p a -> ShortStutterKeeper n p b

liftA2 :: (a -> b -> c) -> ShortStutterKeeper n p a -> ShortStutterKeeper n p b -> ShortStutterKeeper n p c

(*>) :: ShortStutterKeeper n p a -> ShortStutterKeeper n p b -> ShortStutterKeeper n p b

(<*) :: ShortStutterKeeper n p a -> ShortStutterKeeper n p b -> ShortStutterKeeper n p a

(KnownNat n, KnownNat p) => ListMonad (ShortStutterKeeper n p)

Defined in Control.Monad.List.Exotic

Methods

wrap :: [a] -> ShortStutterKeeper n p a

unwrap :: ShortStutterKeeper n p a -> [a]

(KnownNat n, KnownNat p) => IsList (ShortStutterKeeper n p a)

Defined in Control.Monad.List.Exotic

Associated Types

type Item (ShortStutterKeeper n p a) :: Type

Methods

fromList :: [Item (ShortStutterKeeper n p a)] -> ShortStutterKeeper n p a

fromListN :: Int -> [Item (ShortStutterKeeper n p a)] -> ShortStutterKeeper n p a

toList :: ShortStutterKeeper n p a -> [Item (ShortStutterKeeper n p a)]

Eq a => Eq (ShortStutterKeeper n p a)

Defined in Control.Monad.List.Exotic

Methods

(==) :: ShortStutterKeeper n p a -> ShortStutterKeeper n p a -> Bool

(/=) :: ShortStutterKeeper n p a -> ShortStutterKeeper n p a -> Bool

Show a => Show (ShortStutterKeeper n p a)

Defined in Control.Monad.List.Exotic

Methods

showsPrec :: Int -> ShortStutterKeeper n p a -> ShowS

show :: ShortStutterKeeper n p a -> String

showList :: [ShortStutterKeeper n p a] -> ShowS

(KnownNat n, KnownNat p) => IsString (ShortStutterKeeper n p Char)

Defined in Control.Monad.List.Exotic

Methods

fromString :: String -> ShortStutterKeeper n p Char

type Item (ShortStutterKeeper n p a)

Defined in Control.Monad.List.Exotic

type Item (ShortStutterKeeper n p a) = a