map
:: (a -> b) -> [a] -> [b]

map
:: (a -> b) -> [a] -> [b]

Module
Map

*Note:* You should use Data.Map.Strict instead of this module if:

- You will eventually need all the values stored.
- The stored values don't represent large virtual data structures to be lazily computed.

An efficient implementation of ordered maps from keys to values (dictionaries).

These modules are intended to be imported qualified, to avoid name clashes with Prelude functions, e.g.

import qualified Data.Map as Map

The implementation of `Map`

is based on *size balanced* binary trees (or
trees of *bounded balance*) as described by:

- Stephen Adams, "
*Efficient sets: a balancing act*", Journal of Functional Programming 3(4):553-562, October 1993, http://www.swiss.ai.mit.edu/~adams/BB/. - J. Nievergelt and E.M. Reingold,
"
*Binary search trees of bounded balance*", SIAM journal of computing 2(1), March 1973.

Note that the implementation is *left-biased* -- the elements of a
first argument are always preferred to the second, for example in
`union`

or `insert`

.

Operation comments contain the operation time complexity in the Big-O notation (http://en.wikipedia.org/wiki/Big_O_notation).

map
:: (Word8 -> Word8) -> ByteString -> ByteString

*O(n)* `map`

`f xs`

is the ByteString obtained by applying `f`

to each
element of `xs`

.

map
:: (Char -> Char) -> ByteString -> ByteString

bytestring - Data.ByteString.Char8

*O(n)* `map`

`f xs`

is the ByteString obtained by applying `f`

to each element of `xs`

map
:: (Word8 -> Word8) -> ByteString -> ByteString

bytestring - Data.ByteString.Lazy

*O(n)* `map`

`f xs`

is the ByteString obtained by applying `f`

to each
element of `xs`

.

map
:: (Char -> Char) -> ByteString -> ByteString

bytestring - Data.ByteString.Lazy.Char8

*O(n)* `map`

`f xs`

is the ByteString obtained by applying `f`

to each element of `xs`

map
:: (a -> b) -> Map k a -> Map k b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> Map k a -> Map k b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> IntMap a -> IntMap b

containers - Data.IntMap.Strict

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (a -> b) -> IntMap a -> IntMap b

*O(n)*. Map a function over all values in the map.

map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]

map
:: (Char -> Char) -> Text -> Text

map
:: (Char -> Char) -> Stream Char -> Stream Char

text - Data.Text.Internal.Fusion.Common

*O(n)* `map`

`f `

xs is the Stream Char obtained by applying `f`

to each element of `xs`

.

map
:: (Char -> Char) -> Text -> Text

map
:: (a -> b) -> Set a -> Set b

*O(n*log n)*.

is the set obtained by applying `map`

f s`f`

to each element of `s`

.

It's worth noting that the size of the result may be smaller if,
for some `(x,y)`

, `x /= y && f x == f y`

map
:: (Key -> Key) -> IntSet -> IntSet

*O(n*min(n,W))*.

is the set obtained by applying `map`

f s`f`

to each element of `s`

.

It's worth noting that the size of the result may be smaller if,
for some `(x,y)`

, `x /= y && f x == f y`

Module
Instances

uniplate - Data.Generics.Uniplate.Data.Instances

In some cases, `Data`

instances for abstract types are incorrect,
and fail to work correctly with Uniplate. This module defines three helper
types (`Hide`

, `Trigger`

and `Invariant`

) to assist when writing instances
for abstract types. The `Hide`

type is useful when you want to mark some part
of your data type as being ignored by Data.Generics.Uniplate.Data
(and any other `Data`

based generics libraries, such as `syb`

).

Using the helper types, this module defines wrappers for types in
the `containers`

package, namely `Map`

, `Set`

, `IntMap`

and `IntSet`

.
The standard `containers`

`Data`

instances all treat the types as abstract,
but the wrapper types allow you to traverse within the data types, ensuring
the necessary invariants are maintained. In particular, if you do not modify
the keys reconstruct will be *O(n)* instead of *O(n log n)*.

As an example of how to implement your own abstract type wrappers, the `Map`

data
type is defined as:

newtype Map k v = Map (`Invariant`

(`Trigger`

[k],`Trigger`

[v], Hide (Map.Map k v))) deriving (Data, Typeable)

The `Map`

type is defined as an `Invariant`

of three components - the keys, the values, and
the underlying `Map`

. We use `Invariant`

to ensure that the keys*values*map always remain in sync.
We use `Trigger`

on the keys and values to ensure that whenever the keys or values change we
rebuild the `Map`

, but if they don't, we reuse the previous `Map`

. The `fromMap`

function is
implemented by pattern matching on the `Map`

type:

`fromMap`

(`Map`

(`Invariant`

_ (_,_,`Hide`

x))) = x

The `toMap`

function is slightly harder, as we need to come up with an invariant restoring function:

toMap :: Ord k => Map.Map k v -> Map k v toMap x = Map $ Invariant inv $ create x where create x = (Trigger False ks, Trigger False vs, Hide x) where (ks,vs) = unzip $ Map.toAscList x inv (ks,vs,x) | trigger ks = create $ Map.fromList $ zip (fromTrigger ks) (fromTrigger vs) | trigger vs = create $ Map.fromDistinctAscList $ zip (fromTrigger ks) (fromTrigger vs) | otherwise = (ks,vs,x)

The `create`

function creates a value from a `Map`

, getting the correct keys and values. The `inv`

function looks at the triggers on the keys/values. If the keys trigger has been tripped, then we
reconstruct the `Map`

using `fromList`

. If the values trigger has been tripped, but they keys trigger
has not, we can use `fromDistinctAscList`

, reducing the complexity of constructing the `Map`

. If nothing
has changed we can reuse the previous value.

The end result is that all Uniplate (or `syb`

) traversals over `Map`

result in a valid value, which has
had all appropriate transformations applied.

Data
Map

A Map from keys `k`

to values `a`

.

Data
Map

A Map from keys `k`

to values `a`

.

map
:: (a -> b) -> Stream a -> Stream b

vector - Data.Vector.Fusion.Stream

Map a function over a `Stream`