Portability | non-portable (uses Data.Array.Base) |
---|---|

Stability | experimental |

Maintainer | libraries@haskell.org |

Immutable arrays, with an overloaded interface. For array types which
can be used with this interface, see the `Array`

type exported by this
module and the Data.Array.Unboxed module. Other packages, such as
diffarray, also provide arrays using this interface.

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

# Array classes

Class of immutable array types.

An array type has the form `(a i e)`

where `a`

is the array type
constructor (kind `* -> * -> *`

), `i`

is the index type (a member of
the class `Ix`

), and `e`

is the element type. The `IArray`

class is
parameterised over both `a`

and `e`

, so that instances specialised to
certain element types can be defined.

module Data.Ix

# Immutable non-strict (boxed) arrays

data Array i e

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

and elements in `e`

.

# Array construction

:: (IArray a e, Ix i) | |

=> (i, i) | bounds of the array: (lowest,highest) |

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

-> a i e |

Constructs an immutable array from a pair of bounds and a list of initial associations.

The bounds are specified as a pair of the lowest and highest bounds in the array respectively. 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)).

An association is a pair of the form `(i,x)`

, which defines the value of
the array at index `i`

to be `x`

. The array is undefined 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 implementation-dependent.
(In GHC, the last value specified for that index is used.
Other implementations will also do this for unboxed arrays, but Haskell
98 requires that for `Array`

the value at such indices is 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. Whether `array`

is strict or non-strict in the elements depends
on the array type: `Data.Array.Array`

is a non-strict array type, but
all of the `Data.Array.Unboxed.UArray`

arrays are strict. Thus in a
non-strict array, 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.

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

Constructs an immutable array from a list of initial elements. The list gives the elements of the array in ascending order beginning with the lowest index.

:: (IArray a e, Ix i) | |

=> (e -> e' -> e) | An accumulating function |

-> e | A default element |

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

-> [(i, e')] | List of associations |

-> a i e | Returns: the array |

Constructs an immutable array from a list of associations. Unlike
`array`

, the same index is allowed to occur multiple times in the list
of associations; an *accumulating function* is used to combine the
values of elements 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]

# Accessing arrays

(!) :: (IArray a e, Ix i) => a i e -> i -> eSource

Returns the element of an immutable array at the specified index.

indices :: (IArray a e, Ix i) => a i e -> [i]Source

Returns a list of all the valid indices in an array.

elems :: (IArray a e, Ix i) => a i e -> [e]Source

Returns a list of all the elements of an array, in the same order as their indices.

assocs :: (IArray a e, Ix i) => a i e -> [(i, e)]Source

Returns the contents of an array as a list of associations.

# Incremental array updates

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

Takes an array and a list of pairs and returns an array identical to
the left 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.

As with the `array`

function, if any two associations in the list have
the same index, the value at that index is implementation-dependent.
(In GHC, the last value specified for that index is used.
Other implementations will also do this for unboxed arrays, but Haskell
98 requires that for `Array`

the value at such indices is bottom.)

For most array types, this operation is O(*n*) where *n* is the size
of the array. However, the diffarray package provides an array type
for which this operation has complexity linear in the number of updates.

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

`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])