Array

Documentation

data Array i e

The type of immutable non-strict (boxed) arrays with indices in i and elements in e.

Instances

NFData2 Array

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf2 :: (a -> ()) -> (b -> ()) -> Array a b -> ()

Functor (Array i)

Since: base-2.1

Defined in GHC.Arr

Methods

fmap :: (a -> b) -> Array i a -> Array i b

(<$) :: a -> Array i b -> Array i a

Foldable (Array i)

Since: base-4.8.0.0

Defined in Data.Foldable

Methods

fold :: Monoid m => Array i m -> m

foldMap :: Monoid m => (a -> m) -> Array i a -> m

foldr :: (a -> b -> b) -> b -> Array i a -> b

foldr' :: (a -> b -> b) -> b -> Array i a -> b

foldl :: (b -> a -> b) -> b -> Array i a -> b

foldl' :: (b -> a -> b) -> b -> Array i a -> b

foldr1 :: (a -> a -> a) -> Array i a -> a

foldl1 :: (a -> a -> a) -> Array i a -> a

toList :: Array i a -> [a]

null :: Array i a -> Bool

length :: Array i a -> Int

elem :: Eq a => a -> Array i a -> Bool

maximum :: Ord a => Array i a -> a

minimum :: Ord a => Array i a -> a

sum :: Num a => Array i a -> a

product :: Num a => Array i a -> a

Ix i => Traversable (Array i)

Since: base-2.1

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Array i a -> f (Array i b)

sequenceA :: Applicative f => Array i (f a) -> f (Array i a)

mapM :: Monad m => (a -> m b) -> Array i a -> m (Array i b)

sequence :: Monad m => Array i (m a) -> m (Array i a)

NFData a => NFData1 (Array a)

Since: deepseq-1.4.3.0

Defined in Control.DeepSeq

Methods

liftRnf :: (a0 -> ()) -> Array a a0 -> ()

(Ix i, Eq e) => Eq (Array i e)

Since: base-2.1

Defined in GHC.Arr

Methods

(==) :: Array i e -> Array i e -> Bool

(/=) :: Array i e -> Array i e -> Bool

(Data a, Data b, Ix a) => Data (Array a b)

Since: base-4.8.0.0

Defined in Data.Data

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Array a b -> c (Array a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Array a b)

toConstr :: Array a b -> Constr

dataTypeOf :: Array a b -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Array a b))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Array a b))

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Array a b -> Array a b

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Array a b -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Array a b -> r

gmapQ :: (forall d. Data d => d -> u) -> Array a b -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Array a b -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Array a b -> m (Array a b)

(Ix i, Ord e) => Ord (Array i e)

Since: base-2.1

Defined in GHC.Arr

Methods

compare :: Array i e -> Array i e -> Ordering

(<) :: Array i e -> Array i e -> Bool

(<=) :: Array i e -> Array i e -> Bool

(>) :: Array i e -> Array i e -> Bool

(>=) :: Array i e -> Array i e -> Bool

max :: Array i e -> Array i e -> Array i e

min :: Array i e -> Array i e -> Array i e

(Ix a, Read a, Read b) => Read (Array a b)

Since: base-2.1

Defined in GHC.Read

Methods

readsPrec :: Int -> ReadS (Array a b)

readList :: ReadS [Array a b]

readPrec :: ReadPrec (Array a b)

readListPrec :: ReadPrec [Array a b]

(Ix a, Show a, Show b) => Show (Array a b)

Since: base-2.1

Defined in GHC.Arr

Methods

showsPrec :: Int -> Array a b -> ShowS

show :: Array a b -> String

showList :: [Array a b] -> ShowS

(NFData a, NFData b) => NFData (Array a b)

Defined in Control.DeepSeq

Methods

rnf :: Array a b -> ()

Ix i => Ixed (Array i e)

arr ! i ≡ arr ^. ix i
arr // [(i,e)] ≡ ix i .~ e $ arr

Defined in Control.Lens.At

Methods

ix :: Index (Array i e) -> Traversal' (Array i e) (IxValue (Array i e))

(Ix i, i ~ j) => Each (Array i a) (Array j b) a b

each :: Ix i => Traversal (Array i a) (Array i b) a b

Defined in Control.Lens.Each

Methods

each :: Traversal (Array i a) (Array j b) a b

type Index (Array i e)

Defined in Control.Lens.At

type Index (Array i e) = i

type IxValue (Array i e)

Defined in Control.Lens.At

type IxValue (Array i e) = e

array

Arguments

:: Ix i

=> (i, i)

a pair of bounds, each of the index type of the array. These bounds are the lowest and highest indices in the array, in that order. For example, a one-origin vector of length '10' has bounds '(1,10)', and a one-origin '10' by '10' matrix has bounds '((1,1),(10,10))'.

-> [(i, e)]

a list of associations of the form (index, value). Typically, this list will be expressed as a comprehension. An association '(i, x)' defines the value of the array at index i to be x.

-> Array i e

Construct an array with the specified bounds and containing values for given indices within these bounds.

The array is undefined (i.e. bottom) if any index in the list is out of bounds. The Haskell 2010 Report further specifies that if any two associations in the list have the same index, the value at that index is undefined (i.e. bottom). However in GHC's implementation, the value at such an index is the value part of the last association with that index in the list.

Because the indices must be checked for these errors, array is strict in the bounds argument and in the indices of the association list, but non-strict in the values. Thus, recurrences such as the following are possible:

a = array (1,100) ((1,1) : [(i, i * a!(i-1)) | i <- [2..100]])

Not every index within the bounds of the array need appear in the association list, but the values associated with indices that do not appear will be undefined (i.e. bottom).

If, in any dimension, the lower bound is greater than the upper bound, then the array is legal, but empty. Indexing an empty array always gives an array-bounds error, but bounds still yields the bounds with which the array was constructed.

bounds :: Array i e -> (i, i)

The bounds with which an array was constructed.

indices :: Ix i => Array i e -> [i]

The list of indices of an array in ascending order.

assocs :: Ix i => Array i e -> [(i, e)]

The list of associations of an array in index order.

(//) :: Ix i => Array i e -> [(i, e)] -> Array i e infixl 9

Constructs an array identical to the first argument except that it has been updated by the associations in the right argument. For example, if m is a 1-origin, n by n matrix, then

m//[((i,i), 0) | i <- [1..n]]

is the same matrix, except with the diagonal zeroed.

Repeated indices in the association list are handled as for array: Haskell 2010 specifies that the resulting array is undefined (i.e. bottom), but GHC's implementation uses the last association for each index.

accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e

accum f takes an array and an association list and accumulates pairs from the list into the array with the accumulating function f. Thus accumArray can be defined using accum:

accumArray f z b = accum f (array b [(i, z) | i <- range b])

ixmap :: (Ix i, Ix j) => (i, i) -> (i -> j) -> Array j e -> Array i e

ixmap allows for transformations on array indices. It may be thought of as providing function composition on the right with the mapping that the original array embodies.

A similar transformation of array values may be achieved using fmap from the Array instance of the Functor class.