Data.NonEmpty

Documentation

data T f a

The type T can be used for many kinds of list-like structures with restrictions on the size.

• T [] a is a lazy list containing at least one element.
• T (T []) a is a lazy list containing at least two elements.
• T Vector a is a vector with at least one element. You may also use unboxed vectors but the first element will be stored in a box and you will not be able to use many functions from this module.
• T Maybe a is a list that contains one or two elements.
• Maybe is isomorphic to Optional Empty.
• T Empty a is a list that contains exactly one element.
• T (T Empty) a is a list that contains exactly two elements.
• Optional (T Empty) a is a list that contains zero or two elements.
• You can create a list type for every finite set of allowed list length by nesting Optional and NonEmpty constructors. If list length n is allowed, then place Optional at depth n, if it is disallowed then place NonEmpty. The maximum length is marked by Empty.

Constructors

Cons

Fields

head :: a

tail :: f a

Instances

(Monad f, Empty f, Cons f, Append f) => Monad (T f)

Functor f => Functor (T f)

(Applicative f, Empty f, Cons f, Append f) => Applicative (T f)

Foldable f => Foldable (T f)

Traversable f => Traversable (T f)

Arbitrary f => Arbitrary (T f)

Show f => Show (T f)

(Traversable f, Reverse f) => Reverse (T f)

(SortBy f, InsertBy f) => SortBy (T f)

(Sort f, InsertBy f) => Sort (T f)

If you nest too many non-empty lists then the efficient merge-sort (linear-logarithmic runtime) will degenerate to an inefficient insert-sort (quadratic runtime).

Iterate f => Iterate (T f)

Repeat f => Repeat (T f)

Zip f => Zip (T f)

(Cons f, Append f) => Append (T f)

Empty f => Singleton (T f)

ViewL f => ViewL (T f)

Caution: viewL (NonEmpty.Cons x []) = Nothing because the tail is empty, and thus cannot be NonEmpty!

This instance mainly exist to allow cascaded applications of fetch.

Snoc f => Snoc (T f)

Cons f => Cons (T f)

Tails f => Tails (T f)

RemoveEach f => RemoveEach (T f)

InsertBy f => InsertBy (T f)

Insert f => Insert (T f)

Choose f => Choose (T f)

(Eq a, Eq (f a)) => Eq (T f a)

(Ord a, Ord (f a)) => Ord (T f a)

(Show f, Show a) => Show (T f a)

(Arbitrary a, Arbitrary f) => Arbitrary (T f a)

(!:) :: a -> f a -> T f a infixr 5

force :: T f a -> T f a

Force immediate generation of Cons.

apply :: (Applicative f, Cons f, Append f) => T f (a -> b) -> T f a -> T f b

Implementation of <*> without the Empty constraint that is needed for pure.

bind :: (Monad f, Cons f, Append f) => T f a -> (a -> T f b) -> T f b

Implementation of >>= without the Empty constraint that is needed for return.

toList :: Foldable f => T f a -> [a]

flatten :: Cons f => T f a -> f a

fetch :: ViewL f => f a -> Maybe (T f a)

cons :: a -> f a -> T f a

Synonym for Cons. For symmetry to snoc.

snoc :: Traversable f => f a -> a -> T f a

singleton :: Empty f => a -> T f a

reverse :: (Traversable f, Reverse f) => T f a -> T f a

mapHead :: (a -> a) -> T f a -> T f a

mapTail :: (f a -> g a) -> T f a -> T g a

viewL :: T f a -> (a, f a)

viewR :: Traversable f => T f a -> (f a, a)

init :: Traversable f => T f a -> f a

last :: Foldable f => T f a -> a

foldl1 :: Foldable f => (a -> a -> a) -> T f a -> a

foldl1Map :: Foldable f => (b -> b -> b) -> (a -> b) -> T f a -> b

It holds:

foldl1Map f g = foldl1 f . fmap g

but foldl1Map does not need a Functor instance.

foldBalanced :: (a -> a -> a) -> T [] a -> a

Fold a non-empty list in a balanced way. Balanced means that each element has approximately the same depth in the operator tree. Approximately the same depth means that the difference between maximum and minimum depth is at most 1. The accumulation operation must be associative and commutative in order to get the same result as foldl1 or foldr1.

maximum :: (Ord a, Foldable f) => T f a -> a

maximum is a total function

maximumBy :: Foldable f => (a -> a -> Ordering) -> T f a -> a

maximumBy is a total function

maximumKey :: (Ord b, Foldable f) => (a -> b) -> T f a -> a

maximumKey is a total function

minimum :: (Ord a, Foldable f) => T f a -> a

minimum is a total function

minimumBy :: Foldable f => (a -> a -> Ordering) -> T f a -> a

minimumBy is a total function

minimumKey :: (Ord b, Foldable f) => (a -> b) -> T f a -> a

minimumKey is a total function

sum :: (Num a, Foldable f) => T f a -> a

sum does not need a zero for initialization

product :: (Num a, Foldable f) => T f a -> a

product does not need a one for initialization

append :: (Append f, Traversable f) => T f a -> T f a -> T (T f) a infixr 5

appendLeft :: (Append f, Traversable f) => f a -> T f a -> T f a infixr 5

appendRight :: Append f => T f a -> f a -> T f a infixr 5

cycle :: (Cons f, Append f) => T f a -> T f a

generic variants: cycle or better Semigroup.cycle

zipWith :: Zip f => (a -> b -> c) -> T f a -> T f b -> T f c

mapAdjacent :: Traversable f => (a -> a -> b) -> T f a -> f b

class Insert f where

Methods

insert :: Ord a => a -> f a -> T f a

Insert an element into an ordered list while preserving the order.

Instances

Insert []

Insert Maybe

Insert Seq

Insert T

Insert f => Insert (T f)

Insert f => Insert (T f)

insertDefault :: (Ord a, InsertBy f, SortBy f) => a -> f a -> T f a

Default implementation for insert based on insertBy.

class Insert f => InsertBy f where

Methods

insertBy :: (a -> a -> Ordering) -> a -> f a -> T f a

Instances

InsertBy []

InsertBy Maybe

InsertBy Seq

InsertBy T

InsertBy f => InsertBy (T f)

InsertBy f => InsertBy (T f)

scanl :: Traversable f => (b -> a -> b) -> b -> f a -> T f b

scanr :: Traversable f => (a -> b -> b) -> b -> f a -> T f b

class Tails f where

Methods

tails :: (Cons g, Empty g) => f a -> T f (g a)

Instances

Tails []

Tails Maybe

Tails Seq

Tails T

Tails f => Tails (T f)

Tails f => Tails (T f)

inits :: (Traversable f, Snoc g, Empty g) => f a -> T f (g a)

Only advised for structures with efficient appending of single elements like Sequence. Alternatively you may consider initsRev.

initsRev :: (Traversable f, Cons g, Empty g, Reverse g) => f a -> T f (g a)

class Functor f => RemoveEach f where

Methods

removeEach :: T f a -> T f (a, f a)

Instances

RemoveEach []

RemoveEach Maybe

RemoveEach T

RemoveEach f => RemoveEach (T f)

RemoveEach f => RemoveEach (T f)