- module Data.Ix
- data 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.
data Array i e
The type of immutable non-strict (boxed) arrays
with indices in
i and elements in
|:: 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
|-> 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,
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.
Construct an array from a pair of bounds and a list of values in index order.
|:: Ix i|
|=> (e -> a -> e)|
|-> (i, i)|
bounds of the array
|-> [(i, a)]|
|-> Array i e|
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,
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.
Incremental array updates
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 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
the resulting array is undefined (i.e. bottom),
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