- module Data.Ix
- data Ix i => Array i e
- array :: Ix i => (i, i) -> [(i, e)] -> Array i e
- listArray :: Ix i => (i, i) -> [e] -> Array i e
- accumArray :: Ix i => (e -> a -> e) -> e -> (i, i) -> [(i, a)] -> Array i e
- (!) :: Ix i => Array i e -> i -> e
- bounds :: Ix i => Array i e -> (i, i)
- indices :: Ix i => Array i e -> [i]
- elems :: Ix i => Array i e -> [e]
- assocs :: Ix i => Array i e -> [(i, e)]
- (//) :: Ix i => Array i e -> [(i, e)] -> Array i e
- accum :: Ix i => (e -> a -> e) -> Array i e -> [(i, a)] -> Array i e
- ixmap :: (Ix i, Ix j) => (i, i) -> (i -> j) -> Array j e -> Array i e

# Immutable non-strict arrays

Haskell provides indexable *arrays*, which may be thought of as functions
whose domains are isomorphic to contiguous subsets of the integers.
Functions restricted in this way can be implemented efficiently;
in particular, a programmer may reasonably expect rapid access to
the components. To ensure the possibility of such an implementation,
arrays are treated as data, not as general functions.

Since most array functions involve the class `Ix`

, the contents of the
module Data.Ix are re-exported from Data.Array for convenience:

module Data.Ix

The type of immutable non-strict (boxed) arrays
with indices in `i`

and elements in `e`

.

# Array construction

:: Ix i | |

=> (i, i) | a pair of |

-> [(i, e)] | a list of |

-> 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. If any two associations in the list have the same index, the value at that index is undefined (i.e. bottom).

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.

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

Construct an array from a pair of bounds and a list of values in index order.

:: Ix i | |

=> (e -> a -> e) | accumulating function |

-> e | initial value |

-> (i, i) | bounds of the array |

-> [(i, a)] | association list |

-> Array i e |

The `accumArray`

function deals with repeated indices in the association
list using an *accumulating function* which combines the values of
associations with the same index.
For example, given a list of values of some index type, `hist`

produces a histogram of the number of occurrences of each index within
a specified range:

hist :: (Ix a, Num b) => (a,a) -> [a] -> Array a b hist bnds is = accumArray (+) 0 bnds [(i, 1) | i<-is, inRange bnds i]

If the accumulating function is strict, then `accumArray`

is strict in
the values, as well as the indices, in the association list. Thus,
unlike ordinary arrays built with `array`

, accumulated arrays should
not in general be recursive.

# Accessing arrays

# Incremental array updates

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

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`

:
the resulting array is undefined (i.e. bottom),

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

takes an array and an association list and accumulates
pairs from the list into the array with the accumulating function `accum`

f`f`

.
Thus `accumArray`

can be defined using `accum`

:

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

# Derived arrays

# Specification

module Array ( module Data.Ix, -- export all of Data.Ix Array, array, listArray, (!), bounds, indices, elems, assocs, accumArray, (//), accum, ixmap ) where import Data.Ix import Data.List( (\\) ) infixl 9 !, // data (Ix a) => Array a b = MkArray (a,a) (a -> b) deriving () array :: (Ix a) => (a,a) -> [(a,b)] -> Array a b array b ivs | any (not . inRange b. fst) ivs = error "Data.Array.array: out-of-range array association" | otherwise = MkArray b arr where arr j = case [ v | (i,v) <- ivs, i == j ] of [v] -> v [] -> error "Data.Array.!: undefined array element" _ -> error "Data.Array.!: multiply defined array element" listArray :: (Ix a) => (a,a) -> [b] -> Array a b listArray b vs = array b (zipWith (\ a b -> (a,b)) (range b) vs) (!) :: (Ix a) => Array a b -> a -> b (!) (MkArray _ f) = f bounds :: (Ix a) => Array a b -> (a,a) bounds (MkArray b _) = b indices :: (Ix a) => Array a b -> [a] indices = range . bounds elems :: (Ix a) => Array a b -> [b] elems a = [a!i | i <- indices a] assocs :: (Ix a) => Array a b -> [(a,b)] assocs a = [(i, a!i) | i <- indices a] (//) :: (Ix a) => Array a b -> [(a,b)] -> Array a b a // new_ivs = array (bounds a) (old_ivs ++ new_ivs) where old_ivs = [(i,a!i) | i <- indices a, i `notElem` new_is] new_is = [i | (i,_) <- new_ivs] accum :: (Ix a) => (b -> c -> b) -> Array a b -> [(a,c)] -> Array a b accum f = foldl (\a (i,v) -> a // [(i,f (a!i) v)]) accumArray :: (Ix a) => (b -> c -> b) -> b -> (a,a) -> [(a,c)] -> Array a b accumArray f z b = accum f (array b [(i,z) | i <- range b]) ixmap :: (Ix a, Ix b) => (a,a) -> (a -> b) -> Array b c -> Array a c ixmap b f a = array b [(i, a ! f i) | i <- range b] instance (Ix a) => Functor (Array a) where fmap fn (MkArray b f) = MkArray b (fn . f) instance (Ix a, Eq b) => Eq (Array a b) where a == a' = assocs a == assocs a' instance (Ix a, Ord b) => Ord (Array a b) where a <= a' = assocs a <= assocs a' instance (Ix a, Show a, Show b) => Show (Array a b) where showsPrec p a = showParen (p > arrPrec) ( showString "array " . showsPrec (arrPrec+1) (bounds a) . showChar ' ' . showsPrec (arrPrec+1) (assocs a) ) instance (Ix a, Read a, Read b) => Read (Array a b) where readsPrec p = readParen (p > arrPrec) (\r -> [ (array b as, u) | ("array",s) <- lex r, (b,t) <- readsPrec (arrPrec+1) s, (as,u) <- readsPrec (arrPrec+1) t ]) -- Precedence of the 'array' function is that of application itself arrPrec = 10