HaskellWorks.Data.FingerTree

A general sequence representation with arbitrary annotations, for use as a base for implementations of various collection types, as described in section 4 of

• Ralf Hinze and Ross Paterson, "Finger trees: a simple general-purpose data structure", Journal of Functional Programming 16:2 (2006) pp 197-217. http://staff.city.ac.uk/~ross/papers/FingerTree.html

For a directly usable sequence type, see Data.Sequence, which is a specialization of this structure.

An amortized running time is given for each operation, with n referring to the length of the sequence. These bounds hold even in a persistent (shared) setting.

Note: Many of these operations have the same names as similar operations on lists in the Prelude. The ambiguity may be resolved using either qualification or the hiding clause.

Documentation

data FingerTree v a

A representation of a sequence of values of type a, allowing access to the ends in constant time, and append and split in time logarithmic in the size of the smaller piece.

The collection is also parameterized by a measure type v, which is used to specify a position in the sequence for the split operation. The types of the operations enforce the constraint Measured v a, which also implies that the type v is determined by a.

A variety of abstract data types can be implemented by using different element types and measurements.

Constructors

Empty

Single a

Deep !v !(Digit a) (FingerTree v (Node v a)) !(Digit a)

Instances

Measured v a => Measured v (FingerTree v a)

O(1). The cached measure of a tree.

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: FingerTree v a -> v

Foldable (FingerTree v)

Defined in HaskellWorks.Data.FingerTree

Methods

fold :: Monoid m => FingerTree v m -> m

foldMap :: Monoid m => (a -> m) -> FingerTree v a -> m

foldr :: (a -> b -> b) -> b -> FingerTree v a -> b

foldr' :: (a -> b -> b) -> b -> FingerTree v a -> b

foldl :: (b -> a -> b) -> b -> FingerTree v a -> b

foldl' :: (b -> a -> b) -> b -> FingerTree v a -> b

foldr1 :: (a -> a -> a) -> FingerTree v a -> a

foldl1 :: (a -> a -> a) -> FingerTree v a -> a

toList :: FingerTree v a -> [a]

null :: FingerTree v a -> Bool

length :: FingerTree v a -> Int

elem :: Eq a => a -> FingerTree v a -> Bool

maximum :: Ord a => FingerTree v a -> a

minimum :: Ord a => FingerTree v a -> a

sum :: Num a => FingerTree v a -> a

product :: Num a => FingerTree v a -> a

Eq a => Eq (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Methods

(==) :: FingerTree v a -> FingerTree v a -> Bool

(/=) :: FingerTree v a -> FingerTree v a -> Bool

Ord a => Ord (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Methods

compare :: FingerTree v a -> FingerTree v a -> Ordering

(<) :: FingerTree v a -> FingerTree v a -> Bool

(<=) :: FingerTree v a -> FingerTree v a -> Bool

(>) :: FingerTree v a -> FingerTree v a -> Bool

(>=) :: FingerTree v a -> FingerTree v a -> Bool

max :: FingerTree v a -> FingerTree v a -> FingerTree v a

min :: FingerTree v a -> FingerTree v a -> FingerTree v a

Show a => Show (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Methods

showsPrec :: Int -> FingerTree v a -> ShowS

show :: FingerTree v a -> String

showList :: [FingerTree v a] -> ShowS

Generic (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

type Rep (FingerTree v a) :: Type -> Type

Methods

from :: FingerTree v a -> Rep (FingerTree v a) x

to :: Rep (FingerTree v a) x -> FingerTree v a

Measured v a => Semigroup (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Methods

(<>) :: FingerTree v a -> FingerTree v a -> FingerTree v a

sconcat :: NonEmpty (FingerTree v a) -> FingerTree v a

stimes :: Integral b => b -> FingerTree v a -> FingerTree v a

Measured v a => Monoid (FingerTree v a)

empty and ><.

Defined in HaskellWorks.Data.FingerTree

Methods

mempty :: FingerTree v a

mappend :: FingerTree v a -> FingerTree v a -> FingerTree v a

mconcat :: [FingerTree v a] -> FingerTree v a

(NFData a, NFData v) => NFData (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Methods

rnf :: FingerTree v a -> ()

Measured v a => Snoc (FingerTree v a)

O(1). Add an element to the right end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

Defined in HaskellWorks.Data.FingerTree

Methods

snoc :: FingerTree v a -> Elem (FingerTree v a) -> FingerTree v a

Measured v a => Cons (FingerTree v a)

O(1). Add an element to the left end of a sequence. Mnemonic: a triangle with the single element at the pointy end.

Defined in HaskellWorks.Data.FingerTree

Methods

cons :: Elem (FingerTree v a) -> FingerTree v a -> FingerTree v a

Container (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

type Elem (FingerTree v a) :: Type

type Rep (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

type Rep (FingerTree v a) = D1 (MetaData "FingerTree" "HaskellWorks.Data.FingerTree" "hw-fingertree-0.1.2.0-3DwksjKuN7xALuwqw6iuem" False) (C1 (MetaCons "Empty" PrefixI False) (U1 :: Type -> Type) :+: (C1 (MetaCons "Single" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Deep" PrefixI False) ((S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 v) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit a))) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (FingerTree v (Node v a))) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (Digit a))))))

type Elem (FingerTree v a)

Defined in HaskellWorks.Data.FingerTree

type Elem (FingerTree v a) = a

data Digit a

Constructors

One a

Two a a

Three a a a

Four a a a a

Instances

Functor Digit

Defined in HaskellWorks.Data.FingerTree

Methods

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

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

Foldable Digit

Defined in HaskellWorks.Data.FingerTree

Methods

fold :: Monoid m => Digit m -> m

foldMap :: Monoid m => (a -> m) -> Digit a -> m

foldr :: (a -> b -> b) -> b -> Digit a -> b

foldr' :: (a -> b -> b) -> b -> Digit a -> b

foldl :: (b -> a -> b) -> b -> Digit a -> b

foldl' :: (b -> a -> b) -> b -> Digit a -> b

foldr1 :: (a -> a -> a) -> Digit a -> a

foldl1 :: (a -> a -> a) -> Digit a -> a

toList :: Digit a -> [a]

null :: Digit a -> Bool

length :: Digit a -> Int

elem :: Eq a => a -> Digit a -> Bool

maximum :: Ord a => Digit a -> a

minimum :: Ord a => Digit a -> a

sum :: Num a => Digit a -> a

product :: Num a => Digit a -> a

Measured v a => Measured v (Digit a)

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: Digit a -> v

Show a => Show (Digit a)

Defined in HaskellWorks.Data.FingerTree

Methods

showsPrec :: Int -> Digit a -> ShowS

show :: Digit a -> String

showList :: [Digit a] -> ShowS

Generic (Digit a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

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

Methods

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

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

NFData a => NFData (Digit a)

Defined in HaskellWorks.Data.FingerTree

Methods

rnf :: Digit a -> ()

type Rep (Digit a)

Defined in HaskellWorks.Data.FingerTree

type Rep (Digit a) = D1 (MetaData "Digit" "HaskellWorks.Data.FingerTree" "hw-fingertree-0.1.2.0-3DwksjKuN7xALuwqw6iuem" False) ((C1 (MetaCons "One" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :+: C1 (MetaCons "Two" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) :+: (C1 (MetaCons "Three" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) :+: C1 (MetaCons "Four" PrefixI False) ((S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))))

data Node v a

Constructors

Node2 !v a a

Node3 !v a a a

Instances

Monoid v => Measured v (Node v a)

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: Node v a -> v

Foldable (Node v)

Defined in HaskellWorks.Data.FingerTree

Methods

fold :: Monoid m => Node v m -> m

foldMap :: Monoid m => (a -> m) -> Node v a -> m

foldr :: (a -> b -> b) -> b -> Node v a -> b

foldr' :: (a -> b -> b) -> b -> Node v a -> b

foldl :: (b -> a -> b) -> b -> Node v a -> b

foldl' :: (b -> a -> b) -> b -> Node v a -> b

foldr1 :: (a -> a -> a) -> Node v a -> a

foldl1 :: (a -> a -> a) -> Node v a -> a

toList :: Node v a -> [a]

null :: Node v a -> Bool

length :: Node v a -> Int

elem :: Eq a => a -> Node v a -> Bool

maximum :: Ord a => Node v a -> a

minimum :: Ord a => Node v a -> a

sum :: Num a => Node v a -> a

product :: Num a => Node v a -> a

(Show v, Show a) => Show (Node v a)

Defined in HaskellWorks.Data.FingerTree

Methods

showsPrec :: Int -> Node v a -> ShowS

show :: Node v a -> String

showList :: [Node v a] -> ShowS

Generic (Node v a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

type Rep (Node v a) :: Type -> Type

Methods

from :: Node v a -> Rep (Node v a) x

to :: Rep (Node v a) x -> Node v a

(NFData v, NFData a) => NFData (Node v a)

Defined in HaskellWorks.Data.FingerTree

Methods

rnf :: Node v a -> ()

type Rep (Node v a)

Defined in HaskellWorks.Data.FingerTree

type Rep (Node v a) = D1 (MetaData "Node" "HaskellWorks.Data.FingerTree" "hw-fingertree-0.1.2.0-3DwksjKuN7xALuwqw6iuem" False) (C1 (MetaCons "Node2" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 v) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))) :+: C1 (MetaCons "Node3" PrefixI False) ((S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 v) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)) :*: (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a))))

deep :: Measured v a => Digit a -> FingerTree v (Node v a) -> Digit a -> FingerTree v a

node2 :: Measured v a => a -> a -> Node v a

node3 :: Measured v a => a -> a -> a -> Node v a

class Monoid v => Measured v a | a -> v where

Things that can be measured.

Methods

measure :: a -> v

Instances

Measured v a => Measured v (Digit a)

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: Digit a -> v

Measured v a => Measured v (FingerTree v a)

O(1). The cached measure of a tree.

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: FingerTree v a -> v

Monoid v => Measured v (Node v a)

Defined in HaskellWorks.Data.FingerTree

Methods

measure :: Node v a -> v

Construction

empty :: Measured v a => FingerTree v a

O(1). The empty sequence.

singleton :: Measured v a => a -> FingerTree v a

O(1). A singleton sequence.

append :: Measured v a => FingerTree v a -> FingerTree v a -> FingerTree v a

O(log(min(n1,n2))). Concatenate two sequences.

fromList :: Measured v a => [a] -> FingerTree v a

O(n). Create a sequence from a finite list of elements.

Deconstruction

null :: Measured v a => FingerTree v a -> Bool

O(1). Is this the empty sequence?

data ViewL s a

View of the left end of a sequence.

Constructors

EmptyL

empty sequence

a :< (s a) infixr 5

leftmost element and the rest of the sequence

Instances

Functor s => Functor (ViewL s)

Defined in HaskellWorks.Data.FingerTree

Methods

fmap :: (a -> b) -> ViewL s a -> ViewL s b

(<$) :: a -> ViewL s b -> ViewL s a

(Eq a, Eq (s a)) => Eq (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Methods

(==) :: ViewL s a -> ViewL s a -> Bool

(/=) :: ViewL s a -> ViewL s a -> Bool

(Ord a, Ord (s a)) => Ord (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Methods

compare :: ViewL s a -> ViewL s a -> Ordering

(<) :: ViewL s a -> ViewL s a -> Bool

(<=) :: ViewL s a -> ViewL s a -> Bool

(>) :: ViewL s a -> ViewL s a -> Bool

(>=) :: ViewL s a -> ViewL s a -> Bool

max :: ViewL s a -> ViewL s a -> ViewL s a

min :: ViewL s a -> ViewL s a -> ViewL s a

(Read a, Read (s a)) => Read (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Methods

readsPrec :: Int -> ReadS (ViewL s a)

readList :: ReadS [ViewL s a]

readPrec :: ReadPrec (ViewL s a)

readListPrec :: ReadPrec [ViewL s a]

(Show a, Show (s a)) => Show (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Methods

showsPrec :: Int -> ViewL s a -> ShowS

show :: ViewL s a -> String

showList :: [ViewL s a] -> ShowS

Generic (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

type Rep (ViewL s a) :: Type -> Type

Methods

from :: ViewL s a -> Rep (ViewL s a) x

to :: Rep (ViewL s a) x -> ViewL s a

(NFData a, NFData (s a)) => NFData (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

Methods

rnf :: ViewL s a -> ()

type Rep (ViewL s a)

Defined in HaskellWorks.Data.FingerTree

type Rep (ViewL s a) = D1 (MetaData "ViewL" "HaskellWorks.Data.FingerTree" "hw-fingertree-0.1.2.0-3DwksjKuN7xALuwqw6iuem" False) (C1 (MetaCons "EmptyL" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons ":<" (InfixI RightAssociative 5) False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (s a))))

data ViewR s a

View of the right end of a sequence.

Constructors

EmptyR

empty sequence

(s a) :> a infixl 5

the sequence minus the rightmost element, -- and the rightmost element

Instances

Functor s => Functor (ViewR s)

Defined in HaskellWorks.Data.FingerTree

Methods

fmap :: (a -> b) -> ViewR s a -> ViewR s b

(<$) :: a -> ViewR s b -> ViewR s a

(Eq a, Eq (s a)) => Eq (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Methods

(==) :: ViewR s a -> ViewR s a -> Bool

(/=) :: ViewR s a -> ViewR s a -> Bool

(Ord a, Ord (s a)) => Ord (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Methods

compare :: ViewR s a -> ViewR s a -> Ordering

(<) :: ViewR s a -> ViewR s a -> Bool

(<=) :: ViewR s a -> ViewR s a -> Bool

(>) :: ViewR s a -> ViewR s a -> Bool

(>=) :: ViewR s a -> ViewR s a -> Bool

max :: ViewR s a -> ViewR s a -> ViewR s a

min :: ViewR s a -> ViewR s a -> ViewR s a

(Read a, Read (s a)) => Read (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Methods

readsPrec :: Int -> ReadS (ViewR s a)

readList :: ReadS [ViewR s a]

readPrec :: ReadPrec (ViewR s a)

readListPrec :: ReadPrec [ViewR s a]

(Show a, Show (s a)) => Show (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Methods

showsPrec :: Int -> ViewR s a -> ShowS

show :: ViewR s a -> String

showList :: [ViewR s a] -> ShowS

Generic (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Associated Types

type Rep (ViewR s a) :: Type -> Type

Methods

from :: ViewR s a -> Rep (ViewR s a) x

to :: Rep (ViewR s a) x -> ViewR s a

(NFData a, NFData (s a)) => NFData (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

Methods

rnf :: ViewR s a -> ()

type Rep (ViewR s a)

Defined in HaskellWorks.Data.FingerTree

type Rep (ViewR s a) = D1 (MetaData "ViewR" "HaskellWorks.Data.FingerTree" "hw-fingertree-0.1.2.0-3DwksjKuN7xALuwqw6iuem" False) (C1 (MetaCons "EmptyR" PrefixI False) (U1 :: Type -> Type) :+: C1 (MetaCons ":>" (InfixI LeftAssociative 5) False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (s a)) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 a)))

viewl :: Measured v a => FingerTree v a -> ViewL (FingerTree v) a

O(1). Analyse the left end of a sequence.

viewr :: Measured v a => FingerTree v a -> ViewR (FingerTree v) a

O(1). Analyse the right end of a sequence.

split :: Measured v a => (v -> Bool) -> FingerTree v a -> (FingerTree v a, FingerTree v a)

O(log(min(i,n-i))). Split a sequence at a point where the predicate on the accumulated measure changes from False to True.

For predictable results, one should ensure that there is only one such point, i.e. that the predicate is monotonic.

takeUntil :: Measured v a => (v -> Bool) -> FingerTree v a -> FingerTree v a

O(log(min(i,n-i))). Given a monotonic predicate p, takeUntil p t is the largest prefix of t whose measure does not satisfy p.

• takeUntil p t = fst (split p t)

dropUntil :: Measured v a => (v -> Bool) -> FingerTree v a -> FingerTree v a

O(log(min(i,n-i))). Given a monotonic predicate p, dropUntil p t is the rest of t after removing the largest prefix whose measure does not satisfy p.

• dropUntil p t = snd (split p t)

Transformation

reverse :: Measured v a => FingerTree v a -> FingerTree v a

O(n). The reverse of a sequence.

fmap' :: (Measured v1 a1, Measured v2 a2) => (a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2

Like fmap, but with a more constrained type.

fmapWithPos :: (Measured v1 a1, Measured v2 a2) => (v1 -> a1 -> a2) -> FingerTree v1 a1 -> FingerTree v2 a2

Map all elements of the tree with a function that also takes the measure of the prefix of the tree to the left of the element.

unsafeFmap :: (a -> b) -> FingerTree v a -> FingerTree v b

Like fmap, but safe only if the function preserves the measure.

traverse' :: (Measured v1 a1, Measured v2 a2, Applicative f) => (a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)

Like traverse, but with a more constrained type.

traverseWithPos :: (Measured v1 a1, Measured v2 a2, Applicative f) => (v1 -> a1 -> f a2) -> FingerTree v1 a1 -> f (FingerTree v2 a2)

Traverse the tree with a function that also takes the measure of the prefix of the tree to the left of the element.

unsafeTraverse :: Applicative f => (a -> f b) -> FingerTree v a -> f (FingerTree v b)

Like traverse, but safe only if the function preserves the measure.

Example

Particular abstract data types may be implemented by defining element types with suitable Measured instances.

(from section 4.5 of the paper) Simple sequences can be implemented using a Sum monoid as a measure:

newtype Elem a = Elem { getElem :: a }

instance Measured (Sum Int) (Elem a) where
    measure (Elem _) = Sum 1

newtype Seq a = Seq (FingerTree (Sum Int) (Elem a))

Then the measure of a subsequence is simply its length. This representation supports log-time extraction of subsequences:

take :: Int -> Seq a -> Seq a
take k (Seq xs) = Seq (takeUntil (> Sum k) xs)

drop :: Int -> Seq a -> Seq a
drop k (Seq xs) = Seq (dropUntil (> Sum k) xs)

The module Data.Sequence is an optimized instantiation of this type.

For further examples, see Data.IntervalMap.FingerTree and Data.PriorityQueue.FingerTree.

(><) :: (Semigroup v, Container v) => v -> v -> v infixr 5

(<|) :: Cons v => Elem v -> v -> v infixr 5

(|>) :: Snoc v => v -> Elem v -> v infixl 5