Copyright | (c) The University of Glasgow 2001 |
---|---|

License | BSD-style (see the file libraries/base/LICENSE) |

Maintainer | libraries@haskell.org |

Stability | provisional |

Portability | portable |

Safe Haskell | Trustworthy |

Language | Haskell2010 |

Basic non-strict arrays.

*Note:* The Data.Array.IArray module provides a more general interface
to immutable arrays: it defines operations with the same names as
those defined below, but with more general types, and also defines
`Array`

instances of the relevant classes. To use that more general
interface, import Data.Array.IArray but not Data.Array.

- 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.

Since most array functions involve the class `Ix`

, this module is exported
from Data.Array so that modules need not import both Data.Array and
Data.Ix.

module Data.Ix

data Array i e :: * -> * -> *

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. 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.

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

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 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

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])