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module List exposing
( singleton, repeat, range, (::)
, map, indexedMap, foldl, foldr, filter, filterMap
, length, reverse, member, all, any, maximum, minimum, sum, product
, append, concat, concatMap, intersperse, map2, map3, map4, map5
, sort, sortBy, sortWith
, isEmpty, head, tail, take, drop, partition, unzip
)
{-| You can create a `List` in Elm with the `[1,2,3]` syntax, so lists are
used all over the place. This module has a bunch of functions to help you work
with them!
# Create
@docs singleton, repeat, range, (::)
# Transform
@docs map, indexedMap, foldl, foldr, filter, filterMap
# Utilities
@docs length, reverse, member, all, any, maximum, minimum, sum, product
# Combine
@docs append, concat, concatMap, intersperse, map2, map3, map4, map5
# Sort
@docs sort, sortBy, sortWith
# Deconstruct
@docs isEmpty, head, tail, take, drop, partition, unzip
-}
import Basics exposing (..)
import Elm.Kernel.List
import Maybe exposing ( Maybe(..) )
infix right 5 (::) = cons
-- CREATE
{-| Create a list with only one element:
singleton 1234 == [1234]
singleton "hi" == ["hi"]
-}
singleton : a -> List a
singleton value =
[value]
{-| Create a list with *n* copies of a value:
repeat 3 (0,0) == [(0,0),(0,0),(0,0)]
-}
repeat : Int -> a -> List a
repeat n value =
repeatHelp [] n value
repeatHelp : List a -> Int -> a -> List a
repeatHelp result n value =
if n <= 0 then
result
else
repeatHelp (cons value result) (n-1) value
{-| Create a list of numbers, every element increasing by one.
You give the lowest and highest number that should be in the list.
range 3 6 == [3, 4, 5, 6]
range 3 3 == [3]
range 6 3 == []
-}
range : Int -> Int -> List Int
range lo hi =
rangeHelp lo hi []
rangeHelp : Int -> Int -> List Int -> List Int
rangeHelp lo hi list =
if lo <= hi then
rangeHelp lo (hi - 1) (cons hi list)
else
list
{-| Add an element to the front of a list.
1 :: [2,3] == [1,2,3]
1 :: [] == [1]
This operator is pronounced *cons* for historical reasons, but you can think
of it like pushing an entry onto a stack.
-}
cons : a -> List a -> List a
cons =
Elm.Kernel.List.cons
-- TRANSFORM
{-| Apply a function to every element of a list.
map sqrt [1,4,9] == [1,2,3]
map not [True,False,True] == [False,True,False]
So `map func [ a, b, c ]` is the same as `[ func a, func b, func c ]`
-}
map : (a -> b) -> List a -> List b
map f xs =
foldr (\x acc -> cons (f x) acc) [] xs
{-| Same as `map` but the function is also applied to the index of each
element (starting at zero).
indexedMap Tuple.pair ["Tom","Sue","Bob"] == [ (0,"Tom"), (1,"Sue"), (2,"Bob") ]
-}
indexedMap : (Int -> a -> b) -> List a -> List b
indexedMap f xs =
map2 f (range 0 (length xs - 1)) xs
{-| Reduce a list from the left.
foldl (+) 0 [1,2,3] == 6
foldl (::) [] [1,2,3] == [3,2,1]
So `foldl step state [1,2,3]` is like saying:
state
|> step 1
|> step 2
|> step 3
-}
foldl : (a -> b -> b) -> b -> List a -> b
foldl func acc list =
case list of
[] ->
acc
x :: xs ->
foldl func (func x acc) xs
{-| Reduce a list from the right.
foldr (+) 0 [1,2,3] == 6
foldr (::) [] [1,2,3] == [1,2,3]
So `foldr step state [1,2,3]` is like saying:
state
|> step 3
|> step 2
|> step 1
-}
foldr : (a -> b -> b) -> b -> List a -> b
foldr fn acc ls =
foldrHelper fn acc 0 ls
foldrHelper : (a -> b -> b) -> b -> Int -> List a -> b
foldrHelper fn acc ctr ls =
case ls of
[] ->
acc
a :: r1 ->
case r1 of
[] ->
fn a acc
b :: r2 ->
case r2 of
[] ->
fn a (fn b acc)
c :: r3 ->
case r3 of
[] ->
fn a (fn b (fn c acc))
d :: r4 ->
let
res =
if ctr > 500 then
foldl fn acc (reverse r4)
else
foldrHelper fn acc (ctr + 1) r4
in
fn a (fn b (fn c (fn d res)))
{-| Keep elements that satisfy the test.
filter isEven [1,2,3,4,5,6] == [2,4,6]
-}
filter : (a -> Bool) -> List a -> List a
filter isGood list =
foldr (\x xs -> if isGood x then cons x xs else xs) [] list
{-| Filter out certain values. For example, maybe you have a bunch of strings
from an untrusted source and you want to turn them into numbers:
numbers : List Int
numbers =
filterMap String.toInt ["3", "hi", "12", "4th", "May"]
-- numbers == [3, 12]
-}
filterMap : (a -> Maybe b) -> List a -> List b
filterMap f xs =
foldr (maybeCons f) [] xs
maybeCons : (a -> Maybe b) -> a -> List b -> List b
maybeCons f mx xs =
case f mx of
Just x ->
cons x xs
Nothing ->
xs
-- UTILITIES
{-| Determine the length of a list.
length [1,2,3] == 3
-}
length : List a -> Int
length xs =
foldl (\_ i -> i + 1) 0 xs
{-| Reverse a list.
reverse [1,2,3,4] == [4,3,2,1]
-}
reverse : List a -> List a
reverse list =
foldl cons [] list
{-| Figure out whether a list contains a value.
member 9 [1,2,3,4] == False
member 4 [1,2,3,4] == True
-}
member : a -> List a -> Bool
member x xs =
any (\a -> a == x) xs
{-| Determine if all elements satisfy some test.
all isEven [2,4] == True
all isEven [2,3] == False
all isEven [] == True
-}
all : (a -> Bool) -> List a -> Bool
all isOkay list =
not (any (not << isOkay) list)
{-| Determine if any elements satisfy some test.
any isEven [2,3] == True
any isEven [1,3] == False
any isEven [] == False
-}
any : (a -> Bool) -> List a -> Bool
any isOkay list =
case list of
[] ->
False
x :: xs ->
-- note: (isOkay x || any isOkay xs) would not get TCO
if isOkay x then
True
else
any isOkay xs
{-| Find the maximum element in a non-empty list.
maximum [1,4,2] == Just 4
maximum [] == Nothing
-}
maximum : List comparable -> Maybe comparable
maximum list =
case list of
x :: xs ->
Just (foldl max x xs)
_ ->
Nothing
{-| Find the minimum element in a non-empty list.
minimum [3,2,1] == Just 1
minimum [] == Nothing
-}
minimum : List comparable -> Maybe comparable
minimum list =
case list of
x :: xs ->
Just (foldl min x xs)
_ ->
Nothing
{-| Get the sum of the list elements.
sum [1,2,3,4] == 10
-}
sum : List number -> number
sum numbers =
foldl (+) 0 numbers
{-| Get the product of the list elements.
product [1,2,3,4] == 24
-}
product : List number -> number
product numbers =
foldl (*) 1 numbers
-- COMBINE
{-| Put two lists together.
append [1,1,2] [3,5,8] == [1,1,2,3,5,8]
append ['a','b'] ['c'] == ['a','b','c']
You can also use [the `(++)` operator](Basics#++) to append lists.
-}
append : List a -> List a -> List a
append xs ys =
case ys of
[] ->
xs
_ ->
foldr cons ys xs
{-| Concatenate a bunch of lists into a single list:
concat [[1,2],[3],[4,5]] == [1,2,3,4,5]
-}
concat : List (List a) -> List a
concat lists =
foldr append [] lists
{-| Map a given function onto a list and flatten the resulting lists.
concatMap f xs == concat (map f xs)
-}
concatMap : (a -> List b) -> List a -> List b
concatMap f list =
concat (map f list)
{-| Places the given value between all members of the given list.
intersperse "on" ["turtles","turtles","turtles"] == ["turtles","on","turtles","on","turtles"]
-}
intersperse : a -> List a -> List a
intersperse sep xs =
case xs of
[] ->
[]
hd :: tl ->
let
step x rest =
cons sep (cons x rest)
spersed =
foldr step [] tl
in
cons hd spersed
{-| Combine two lists, combining them with the given function.
If one list is longer, the extra elements are dropped.
totals : List Int -> List Int -> List Int
totals xs ys =
List.map2 (+) xs ys
-- totals [1,2,3] [4,5,6] == [5,7,9]
pairs : List a -> List b -> List (a,b)
pairs xs ys =
List.map2 Tuple.pair xs ys
-- pairs ["alice","bob","chuck"] [2,5,7,8]
-- == [("alice",2),("bob",5),("chuck",7)]
-}
map2 : (a -> b -> result) -> List a -> List b -> List result
map2 =
Elm.Kernel.List.map2
{-|-}
map3 : (a -> b -> c -> result) -> List a -> List b -> List c -> List result
map3 =
Elm.Kernel.List.map3
{-|-}
map4 : (a -> b -> c -> d -> result) -> List a -> List b -> List c -> List d -> List result
map4 =
Elm.Kernel.List.map4
{-|-}
map5 : (a -> b -> c -> d -> e -> result) -> List a -> List b -> List c -> List d -> List e -> List result
map5 =
Elm.Kernel.List.map5
-- SORT
{-| Sort values from lowest to highest
sort [3,1,5] == [1,3,5]
-}
sort : List comparable -> List comparable
sort xs =
sortBy identity xs
{-| Sort values by a derived property.
alice = { name="Alice", height=1.62 }
bob = { name="Bob" , height=1.85 }
chuck = { name="Chuck", height=1.76 }
sortBy .name [chuck,alice,bob] == [alice,bob,chuck]
sortBy .height [chuck,alice,bob] == [alice,chuck,bob]
sortBy String.length ["mouse","cat"] == ["cat","mouse"]
-}
sortBy : (a -> comparable) -> List a -> List a
sortBy =
Elm.Kernel.List.sortBy
{-| Sort values with a custom comparison function.
sortWith flippedComparison [1,2,3,4,5] == [5,4,3,2,1]
flippedComparison a b =
case compare a b of
LT -> GT
EQ -> EQ
GT -> LT
This is also the most general sort function, allowing you
to define any other: `sort == sortWith compare`
-}
sortWith : (a -> a -> Order) -> List a -> List a
sortWith =
Elm.Kernel.List.sortWith
-- DECONSTRUCT
{-| Determine if a list is empty.
isEmpty [] == True
**Note:** It is usually preferable to use a `case` to test this so you do not
forget to handle the `(x :: xs)` case as well!
-}
isEmpty : List a -> Bool
isEmpty xs =
case xs of
[] ->
True
_ ->
False
{-| Extract the first element of a list.
head [1,2,3] == Just 1
head [] == Nothing
**Note:** It is usually preferable to use a `case` to deconstruct a `List`
because it gives you `(x :: xs)` and you can work with both subparts.
-}
head : List a -> Maybe a
head list =
case list of
x :: xs ->
Just x
[] ->
Nothing
{-| Extract the rest of the list.
tail [1,2,3] == Just [2,3]
tail [] == Nothing
**Note:** It is usually preferable to use a `case` to deconstruct a `List`
because it gives you `(x :: xs)` and you can work with both subparts.
-}
tail : List a -> Maybe (List a)
tail list =
case list of
x :: xs ->
Just xs
[] ->
Nothing
{-| Take the first *n* members of a list.
take 2 [1,2,3,4] == [1,2]
-}
take : Int -> List a -> List a
take n list =
takeFast 0 n list
takeFast : Int -> Int -> List a -> List a
takeFast ctr n list =
if n <= 0 then
[]
else
case ( n, list ) of
( _, [] ) ->
list
( 1, x :: _ ) ->
[ x ]
( 2, x :: y :: _ ) ->
[ x, y ]
( 3, x :: y :: z :: _ ) ->
[ x, y, z ]
( _, x :: y :: z :: w :: tl ) ->
if ctr > 1000 then
cons x (cons y (cons z (cons w (takeTailRec (n - 4) tl))))
else
cons x (cons y (cons z (cons w (takeFast (ctr + 1) (n - 4) tl))))
_ ->
list
takeTailRec : Int -> List a -> List a
takeTailRec n list =
reverse (takeReverse n list [])
takeReverse : Int -> List a -> List a -> List a
takeReverse n list kept =
if n <= 0 then
kept
else
case list of
[] ->
kept
x :: xs ->
takeReverse (n - 1) xs (cons x kept)
{-| Drop the first *n* members of a list.
drop 2 [1,2,3,4] == [3,4]
-}
drop : Int -> List a -> List a
drop n list =
if n <= 0 then
list
else
case list of
[] ->
list
x :: xs ->
drop (n-1) xs
{-| Partition a list based on some test. The first list contains all values
that satisfy the test, and the second list contains all the value that do not.
partition (\x -> x < 3) [0,1,2,3,4,5] == ([0,1,2], [3,4,5])
partition isEven [0,1,2,3,4,5] == ([0,2,4], [1,3,5])
-}
partition : (a -> Bool) -> List a -> (List a, List a)
partition pred list =
let
step x (trues, falses) =
if pred x then
(cons x trues, falses)
else
(trues, cons x falses)
in
foldr step ([],[]) list
{-| Decompose a list of tuples into a tuple of lists.
unzip [(0, True), (17, False), (1337, True)] == ([0,17,1337], [True,False,True])
-}
unzip : List (a,b) -> (List a, List b)
unzip pairs =
let
step (x,y) (xs,ys) =
(cons x xs, cons y ys)
in
foldr step ([], []) pairs