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Lazy list implementation in Elm.

type alias LazyList a =
Lazy (LazyListView a)

Lazy List type.

type LazyListView a
= Nil
| Cons a (LazyList a)

Analogous to `List`

type. This is the actual implementation type for the
`LazyList`

type. This type is exposed to the user if the user so wishes to
do pattern matching or understand how the list type works. It is not
recommended to work with this type directly. Try working solely with the
provided functions in the package.

cons : a -> LazyList a -> LazyList a

Add a value to the front of a list.

empty : LazyList a

Create an empty list.

singleton : a -> LazyList a

Create a singleton list.

isEmpty : LazyList a -> Bool

Detect if a list is empty or not.

head : LazyList a -> Maybe a

Get the head of a list.

tail : LazyList a -> Maybe (LazyList a)

Get the tail of a list.

headAndTail : LazyList a -> Maybe ( a, LazyList a )

Get the head and tail of a list.

member : a -> LazyList a -> Bool

Test if a value is a member of a list.

length : LazyList a -> Int

Get the length of a lazy list.

Warning: This will not terminate if the list is infinite.

toList : LazyList a -> List a

Convert a lazy list to a normal list.

fromList : List a -> LazyList a

Convert a normal list to a lazy list.

toArray : LazyList a -> Array a

Convert a lazy list to an array.

fromArray : Array a -> LazyList a

Convert an array to a lazy list.

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

Map a function to a list.

zip : LazyList a -> LazyList b -> LazyList ( a, b )

reduce : (a -> b -> b) -> b -> LazyList a -> b

Reduce a list with a given reducer and an initial value.

Example : reduce (+) 0 (1 ::: 2 ::: 3 ::: 4 ::: empty) == 10

flatten : LazyList (LazyList a) -> LazyList a

Flatten a list of lists into a single list by appending all the inner lists into one big list.

append : LazyList a -> LazyList a -> LazyList a

Append a list to another list.

foldl : (a -> b -> b) -> b -> LazyList a -> b

Analogous to `List.foldl`

. Is an alias for `reduce`

.

foldr : (a -> b -> b) -> b -> LazyList a -> b

Analogous to `List.foldr`

.

intersperse : a -> LazyList a -> LazyList a

Places the given value between all members of the given list.

interleave : LazyList a -> LazyList a -> LazyList a

Interleave the elements of a list in another list. The two lists get interleaved at the end.

reverse : LazyList a -> LazyList a

Reverse a list.

cycle : LazyList a -> LazyList a

Take a list and repeat it ad infinitum. This cycles a finite list by putting the front after the end of the list. This results in a no-op in the case of an infinite list.

iterate : (a -> a) -> a -> LazyList a

Create an infinite list of applications of a function on some value.

Equivalent to:

```
x ::: f x ::: f (f x) ::: f (f (f x)) ::: ... -- etc...
```

repeat : a -> LazyList a

Repeat a value ad infinitum.
Be careful when you use this. The result of this is a truly infinite list.
Do not try calling `reduce`

or `toList`

on an infinite list as it'll never
finish computing. Make sure you then filter it down to a finite list with `head`

or `take`

or something.

take : Int -> LazyList a -> LazyList a

Take at most `n`

many values from a list.

takeWhile : (a -> Bool) -> LazyList a -> LazyList a

Take elements from a list as long as the predicate is satisfied.

drop : Int -> LazyList a -> LazyList a

Drop at most `n`

many values from a list.

dropWhile : (a -> Bool) -> LazyList a -> LazyList a

Drop elements from a list as long as the predicate is satisfied.

keepIf : (a -> Bool) -> LazyList a -> LazyList a

Keep all elements in a list that satisfy the given predicate.

dropIf : (a -> Bool) -> LazyList a -> LazyList a

Drop all elements in a list that satisfy the given predicate.

filterMap : (a -> Maybe b) -> LazyList a -> LazyList b

Map a function that may fail over a lazy list, keeping only the values that were successfully transformed.

unique : LazyList a -> LazyList a

Remove all duplicates from a list and return a list of distinct elements.

andMap : LazyList a -> LazyList (a -> b) -> LazyList b

Known as `mapN`

in some circles. Allows you to apply `map`

in cases
where then number of arguments are greater than 5.

The argument order is such that it works well with `|>`

chains.

andThen : (a -> LazyList b) -> LazyList a -> LazyList b

Chain list producing operations. Map then flatten.

numbers : LazyList number

The infinite list of counting numbers.

i.e.:

```
1 ::: 2 ::: 3 ::: 4 ::: 5 ::: ... -- etc...
```

sum : LazyList number -> number

Get the sum of a list of numbers.

product : LazyList number -> number

Get the product of a list of numbers.

map2 : (a -> b -> c) -> LazyList a -> LazyList b -> LazyList c

map3 : (a -> b -> c -> d) -> LazyList a -> LazyList b -> LazyList c -> LazyList d

map4 : (a -> b -> c -> d -> e) -> LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e

map5 : (a -> b -> c -> d -> e -> f) -> LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList f

zip3 : LazyList a -> LazyList b -> LazyList c -> LazyList ( a, b, c )

zip4 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList ( a, b, c, d )

zip5 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList ( a, b, c, d, e )

**Warning:** Calling these functions on large lists and then calling `toList`

can easily overflow the stack. Consider
passing the results to `take aConstantNumber`

.

product2 : LazyList a -> LazyList b -> LazyList ( a, b )

Create a lazy list containing all possible pairs in the given lazy lists.

product3 : LazyList a -> LazyList b -> LazyList c -> LazyList ( a, b, c )

Create a lazy list containing all possible triples in the given lazy lists.

product4 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList ( a, b, c, d )

Create a lazy list containing all possible 4-tuples in the given lazy lists.

product5 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList ( a, b, c, d, e )

Create a lazy list containing all possible 5-tuples in the given lazy lists.

```
module Lazy.List exposing (..)
{-| Lazy list implementation in Elm.
# Types
@docs LazyList, LazyListView
# Constructors
@docs cons, empty, singleton
# Query operations
@docs isEmpty, head, tail, headAndTail, member, length
# Conversions
@docs toList, fromList, toArray, fromArray
# Map-reduce et al.
@docs map, zip, reduce, flatten, append, foldl, foldr
# Common operations
@docs intersperse, interleave, reverse, cycle, iterate, repeat, take, takeWhile, drop, dropWhile
# Filtering operations
@docs keepIf, dropIf, filterMap, unique
# Chaining operations
@docs andMap, andThen
# Useful math stuff
@docs numbers, sum, product
# All the maps!
@docs map2, map3, map4, map5
# All the zips!
@docs zip3, zip4, zip5
# All the Cartesian products!
**Warning:** Calling these functions on large lists and then calling `toList` can easily overflow the stack. Consider
passing the results to `take aConstantNumber`.
@docs product2, product3, product4, product5
# Infix Operators
@docs (:::), (+++)
-}
import Array exposing (Array)
import List
import Random exposing (Generator, Seed)
import Lazy exposing (Lazy, lazy, force)
{-| Analogous to `List` type. This is the actual implementation type for the
`LazyList` type. This type is exposed to the user if the user so wishes to
do pattern matching or understand how the list type works. It is not
recommended to work with this type directly. Try working solely with the
provided functions in the package.
-}
type LazyListView a
= Nil
| Cons a (LazyList a)
{-| Lazy List type.
-}
type alias LazyList a =
Lazy (LazyListView a)
{-| Create an empty list.
-}
empty : LazyList a
empty =
lazy <|
\() -> Nil
{-| Create a singleton list.
-}
singleton : a -> LazyList a
singleton a =
cons a empty
{-| Detect if a list is empty or not.
-}
isEmpty : LazyList a -> Bool
isEmpty list =
case force list of
Nil ->
True
_ ->
False
{-| Add a value to the front of a list.
-}
cons : a -> LazyList a -> LazyList a
cons a list =
lazy <|
\() ->
Cons a list
{-| Get the head of a list.
-}
head : LazyList a -> Maybe a
head list =
case force list of
Nil ->
Nothing
Cons first _ ->
Just first
{-| Get the tail of a list.
-}
tail : LazyList a -> Maybe (LazyList a)
tail list =
case force list of
Nil ->
Nothing
Cons _ rest ->
Just rest
{-| Get the head and tail of a list.
-}
headAndTail : LazyList a -> Maybe ( a, LazyList a )
headAndTail list =
case force list of
Nil ->
Nothing
Cons first rest ->
Just ( first, rest )
{-| Repeat a value ad infinitum.
Be careful when you use this. The result of this is a truly infinite list.
Do not try calling `reduce` or `toList` on an infinite list as it'll never
finish computing. Make sure you then filter it down to a finite list with `head`
or `take` or something.
-}
repeat : a -> LazyList a
repeat a =
lazy <|
\() ->
Cons a (repeat a)
{-| Append a list to another list.
-}
append : LazyList a -> LazyList a -> LazyList a
append list1 list2 =
lazy <|
\() ->
case force list1 of
Nil ->
force list2
Cons first rest ->
force (first ::: rest +++ list2)
{-| Interleave the elements of a list in another list. The two lists get
interleaved at the end.
-}
interleave : LazyList a -> LazyList a -> LazyList a
interleave list1 list2 =
lazy <|
\() ->
case force list1 of
Nil ->
force list2
Cons first1 rest1 ->
case force list2 of
Nil ->
force list1
Cons first2 rest2 ->
force (first1 ::: first2 ::: interleave rest1 rest2)
{-| Places the given value between all members of the given list.
-}
intersperse : a -> LazyList a -> LazyList a
intersperse a list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
case force rest of
Nil ->
force (first ::: empty)
Cons second tail ->
case force tail of
Nil ->
force (first ::: a ::: second ::: empty)
_ ->
force (first ::: a ::: second ::: a ::: intersperse a tail)
{-| Take a list and repeat it ad infinitum. This cycles a finite list
by putting the front after the end of the list. This results in a no-op in
the case of an infinite list.
-}
cycle : LazyList a -> LazyList a
cycle list =
list
+++ (lazy <|
\() ->
force (cycle list)
)
{-| Create an infinite list of applications of a function on some value.
Equivalent to:
x ::: f x ::: f (f x) ::: f (f (f x)) ::: ... -- etc...
-}
iterate : (a -> a) -> a -> LazyList a
iterate f a =
lazy <|
\() ->
Cons a (iterate f (f a))
{-| The infinite list of counting numbers.
i.e.:
1 ::: 2 ::: 3 ::: 4 ::: 5 ::: ... -- etc...
-}
numbers : LazyList number
numbers =
iterate ((+) 1) 1
{-| Take at most `n` many values from a list.
-}
take : Int -> LazyList a -> LazyList a
take n list =
lazy <|
\() ->
if n <= 0 then
Nil
else
case force list of
Nil ->
Nil
Cons first rest ->
Cons first (take (n - 1) rest)
{-| Take elements from a list as long as the predicate is satisfied.
-}
takeWhile : (a -> Bool) -> LazyList a -> LazyList a
takeWhile predicate list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
if predicate first then
Cons first (takeWhile predicate rest)
else
Nil
{-| Drop at most `n` many values from a list.
-}
drop : Int -> LazyList a -> LazyList a
drop n list =
lazy <|
\() ->
if n <= 0 then
force list
else
case force list of
Nil ->
Nil
Cons first rest ->
force (drop (n - 1) rest)
{-| Drop elements from a list as long as the predicate is satisfied.
-}
dropWhile : (a -> Bool) -> LazyList a -> LazyList a
dropWhile predicate list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
if predicate first then
force (dropWhile predicate rest)
else
force list
{-| Test if a value is a member of a list.
-}
member : a -> LazyList a -> Bool
member a list =
case force list of
Nil ->
False
Cons first rest ->
first == a || member a rest
{-| Get the length of a lazy list.
Warning: This will not terminate if the list is infinite.
-}
length : LazyList a -> Int
length =
reduce (\_ n -> n + 1) 0
{-| Remove all duplicates from a list and return a list of distinct elements.
-}
unique : LazyList a -> LazyList a
unique list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
if member first rest then
force (unique rest)
else
Cons first (unique rest)
{-| Keep all elements in a list that satisfy the given predicate.
-}
keepIf : (a -> Bool) -> LazyList a -> LazyList a
keepIf predicate list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
if predicate first then
Cons first (keepIf predicate rest)
else
force (keepIf predicate rest)
{-| Drop all elements in a list that satisfy the given predicate.
-}
dropIf : (a -> Bool) -> LazyList a -> LazyList a
dropIf predicate =
keepIf (\n -> not (predicate n))
{-| Map a function that may fail over a lazy list, keeping only
the values that were successfully transformed.
-}
filterMap : (a -> Maybe b) -> LazyList a -> LazyList b
filterMap transform list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
case transform first of
Just val ->
Cons val (filterMap transform rest)
Nothing ->
force (filterMap transform rest)
{-| Reduce a list with a given reducer and an initial value.
Example :
reduce (+) 0 (1 ::: 2 ::: 3 ::: 4 ::: empty) == 10
-}
reduce : (a -> b -> b) -> b -> LazyList a -> b
reduce reducer b list =
case force list of
Nil ->
b
Cons first rest ->
reduce reducer (reducer first b) rest
{-| Analogous to `List.foldl`. Is an alias for `reduce`.
-}
foldl : (a -> b -> b) -> b -> LazyList a -> b
foldl =
reduce
{-| Analogous to `List.foldr`.
-}
foldr : (a -> b -> b) -> b -> LazyList a -> b
foldr reducer b list =
Array.foldr reducer b (toArray list)
{-| Get the sum of a list of numbers.
-}
sum : LazyList number -> number
sum =
reduce (+) 0
{-| Get the product of a list of numbers.
-}
product : LazyList number -> number
product =
reduce (*) 1
{-| Flatten a list of lists into a single list by appending all the inner
lists into one big list.
-}
flatten : LazyList (LazyList a) -> LazyList a
flatten list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
force (first +++ flatten rest)
{-| Chain list producing operations. Map then flatten.
-}
andThen : (a -> LazyList b) -> LazyList a -> LazyList b
andThen f list =
map f list |> flatten
{-| Reverse a list.
-}
reverse : LazyList a -> LazyList a
reverse =
reduce cons empty
{-| Map a function to a list.
-}
map : (a -> b) -> LazyList a -> LazyList b
map f list =
lazy <|
\() ->
case force list of
Nil ->
Nil
Cons first rest ->
Cons (f first) (map f rest)
{-| -}
map2 : (a -> b -> c) -> LazyList a -> LazyList b -> LazyList c
map2 f list1 list2 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
case force list2 of
Nil ->
Nil
Cons first2 rest2 ->
Cons (f first1 first2) (map2 f rest1 rest2)
{-| Known as `mapN` in some circles. Allows you to apply `map` in cases
where then number of arguments are greater than 5.
The argument order is such that it works well with `|>` chains.
-}
andMap : LazyList a -> LazyList (a -> b) -> LazyList b
andMap listVal listFuncs =
map2 (<|) listFuncs listVal
{-| -}
map3 : (a -> b -> c -> d) -> LazyList a -> LazyList b -> LazyList c -> LazyList d
map3 f list1 list2 list3 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
case force list2 of
Nil ->
Nil
Cons first2 rest2 ->
case force list3 of
Nil ->
Nil
Cons first3 rest3 ->
Cons (f first1 first2 first3) (map3 f rest1 rest2 rest3)
{-| -}
map4 : (a -> b -> c -> d -> e) -> LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e
map4 f list1 list2 list3 list4 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
case force list2 of
Nil ->
Nil
Cons first2 rest2 ->
case force list3 of
Nil ->
Nil
Cons first3 rest3 ->
case force list4 of
Nil ->
Nil
Cons first4 rest4 ->
Cons (f first1 first2 first3 first4) (map4 f rest1 rest2 rest3 rest4)
{-| -}
map5 : (a -> b -> c -> d -> e -> f) -> LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList f
map5 f list1 list2 list3 list4 list5 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
case force list2 of
Nil ->
Nil
Cons first2 rest2 ->
case force list3 of
Nil ->
Nil
Cons first3 rest3 ->
case force list4 of
Nil ->
Nil
Cons first4 rest4 ->
case force list5 of
Nil ->
Nil
Cons first5 rest5 ->
Cons
(f first1 first2 first3 first4 first5)
(map5 f rest1 rest2 rest3 rest4 rest5)
{-| -}
zip : LazyList a -> LazyList b -> LazyList ( a, b )
zip =
map2 (,)
{-| -}
zip3 : LazyList a -> LazyList b -> LazyList c -> LazyList ( a, b, c )
zip3 =
map3 (,,)
{-| -}
zip4 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList ( a, b, c, d )
zip4 =
map4 (,,,)
{-| -}
zip5 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList ( a, b, c, d, e )
zip5 =
map5 (,,,,)
{-| Create a lazy list containing all possible pairs in the given lazy lists.
-}
product2 : LazyList a -> LazyList b -> LazyList ( a, b )
product2 list1 list2 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
case force list2 of
Nil ->
Nil
Cons _ _ ->
force <| map ((,) first1) list2 +++ product2 rest1 list2
{-| Create a lazy list containing all possible triples in the given lazy lists.
-}
product3 : LazyList a -> LazyList b -> LazyList c -> LazyList ( a, b, c )
product3 list1 list2 list3 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
force <| map (\( b, c ) -> ( first1, b, c )) (product2 list2 list3) +++ product3 rest1 list2 list3
{-| Create a lazy list containing all possible 4-tuples in the given lazy lists.
-}
product4 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList ( a, b, c, d )
product4 list1 list2 list3 list4 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
force <| map (\( b, c, d ) -> ( first1, b, c, d )) (product3 list2 list3 list4) +++ product4 rest1 list2 list3 list4
{-| Create a lazy list containing all possible 5-tuples in the given lazy lists.
-}
product5 : LazyList a -> LazyList b -> LazyList c -> LazyList d -> LazyList e -> LazyList ( a, b, c, d, e )
product5 list1 list2 list3 list4 list5 =
lazy <|
\() ->
case force list1 of
Nil ->
Nil
Cons first1 rest1 ->
force <| map (\( b, c, d, e ) -> ( first1, b, c, d, e )) (product4 list2 list3 list4 list5) +++ product5 rest1 list2 list3 list4 list5
{-| Convert a lazy list to a normal list.
-}
toList : LazyList a -> List a
toList list =
case force list of
Nil ->
[]
Cons first rest ->
first :: toList rest
{-| Convert a normal list to a lazy list.
-}
fromList : List a -> LazyList a
fromList =
List.foldr cons empty
{-| Convert a lazy list to an array.
-}
toArray : LazyList a -> Array a
toArray list =
case force list of
Nil ->
Array.empty
Cons first rest ->
Array.append (Array.push first Array.empty) (toArray rest)
{-| Convert an array to a lazy list.
-}
fromArray : Array a -> LazyList a
fromArray =
Array.foldr cons empty
---------------------
-- INFIX OPERATORS --
---------------------
infixr 5 :::
{-| Alias for `cons`. Analogous to `::` for lists.
-}
(:::) : a -> LazyList a -> LazyList a
(:::) =
cons
infixr 5 +++
{-| Alias for `append`. Analogous to `++` for lists.
-}
(+++) : LazyList a -> LazyList a -> LazyList a
(+++) =
append
```