Returns a new list that contains all pairings of elements from the first and second lists.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: ('T1 * 'T2) list

The resulting list of pairs.

Example

 let people = ["Kirk"; "Spock"; "McCoy"]
 let numbers = [1;2]

 people |> List.allPairs numbers

 [(1, "Kirk"); (1, "Spock"); (1, "McCoy"); (2, "Kirk"); (2, "Spock"); (2, "McCoy")]

Returns a new list that contains the elements of the first list followed by elements of the second.

list1 : 'T list

The first input list.

list2 : 'T list

The second input list.

Returns: 'T list

The resulting list.

Example

 List.append [1..3] [4..7]     //  evaluates [1; 2; 3; 4; 5; 6; 7]
 
 [4..7] |> List.append [1..3]  //  evaluates [1; 2; 3; 4; 5; 6; 7]

Returns the average of the elements in the list.

Raises ArgumentException if list is empty.

list : ^T list

The input list.

Returns: ^T

The resulting average.

Example

 [1.0 .. 9.0] |> List.average  // evaluates 5.0

Example

 [1 .. 9] |> List.average

Returns the average of the elements generated by applying the function to each element of the list.

Raises ArgumentException if list is empty.

projection : 'T -> ^U

The function to transform the list elements into the type to be averaged.

list : 'T list

The input list.

Returns: ^U

The resulting average.

Example

Average the age of persons by extracting the age from records

 type People = 
    {
        Name: string
        Age: int
    }

 let getAgeAsFloat person = float person.age

 let people = 
     [ { Name = "Kirk"; Age = 26 }
       { Name = "Spock"; Age = 90 }
       { Name = "McCoy"; Age = 37 } ]

 people |> List.averageBy getAgeAsFloat  // evaluates 51.0

Example

Average a list of integer numbers by converting to float

 [1 .. 9] |> List.averageBy float  // evaluates 5.0

Applies the given function to each element of the list. Returns the list comprised of the results x for each element where the function returns Some(x)

chooser : 'T -> 'U option

The function to generate options from the elements.

list : 'T list

The input list.

Returns: 'U list

The list comprising the values selected from the chooser function.

Example

 type Happiness =
     | AlwaysHappy
     | MostOfTheTimeGrumpy

 type People =
     {
       Name: string
       Happiness: Happiness
     }

 let takeJustHappyPersons person =
     match person.Happiness with
     | AlwaysHappy -> Some person.Name
     | MostOfTheTimeGrumpy -> None

 let candidatesForTheTrip = 
     [ { Name = "SpongeBob"; Happiness = AlwaysHappy }
       { Name = "Patrick"; Happiness = AlwaysHappy }
       { Name = "Squidward"; Happiness = MostOfTheTimeGrumpy } ]

 candidatesForTheTrip |> List.choose takeJustHappyPersons

Example

Using the identity function id (is defined like fun x -> x):

 
 let input1 = [ Some 1; None; Some 3; None ]

 input1 |> List.choose id  // evaluates [1; 3]

Example

 let input2: int option list = [] 

 input2 |> List.choose id  // evaluates to the empty list

Example

 let input3: string option list = [None; None]

 input3 |> List.choose id  // evaluates to the empty list

Divides the input list into chunks of size at most chunkSize.

chunkSize : int

The maximum size of each chunk.

list : 'T list

The input list.

Returns: 'T list list

The list divided into chunks.

Example

 [1 .. 10 ] |> List.chunkBySize 3  // evaluates

 [1 .. 5 ] |> List.chunkBySize 10

 let input : string list = []

 input |> List.chunkBySize 10

For each element of the list, applies the given function. Concatenates all the results and return the combined list.

mapping : 'T -> 'U list

The function to transform each input element into a sublist to be concatenated.

list : 'T list

The input list.

Returns: 'U list

The concatenation of the transformed sublists.

Example

For each positive number in the array we are generating all the previous positive numbers

 [1..4] |> List.collect (fun x -> [1..x])

Compares two lists using the given comparison function, element by element.

comparer : 'T -> 'T -> int

A function that takes an element from each list and returns an int. If it evaluates to a non-zero value iteration is stopped and that value is returned.

list1 : 'T list

The first input list.

list2 : 'T list

The second input list.

Returns: int

Returns the first non-zero result from the comparison function. If the first list has a larger element, the return value is always positive. If the second list has a larger element, the return value is always negative. When the elements are equal in the two lists, 1 is returned if the first list is longer, 0 is returned if they are equal in length, and -1 is returned when the second list is longer.

Example

 let closerToNextDozen a b =
   (a % 12).CompareTo(b % 12)

 let input1 = [1; 10]
 let input2 = [1; 10]

 (input1, input2) ||> List.compareWith closerToNextDozen

Example

 let closerToNextDozen a b =
   (a % 12).CompareTo(b % 12)

 let input1 = [1; 5]
 let input2 = [1; 8]

 (input1, input2) ||> List.compareWith closerToNextDozen

Example

 let closerToNextDozen a b =
   (a % 12).CompareTo(b % 12)

 let input1 = [1; 11]
 let input2 = [1; 13]

 (input1, input2) ||> List.compareWith closerToNextDozen

Example

 let closerToNextDozen a b =
   (a % 12).CompareTo(b % 12)

 let input1 = [1; 2]
 let input2 = [1]

 (input1, input2) ||> List.compareWith closerToNextDozen

Example

 let closerToNextDozen a b =
   (a % 12).CompareTo(b % 12)

 let input1 = [1]
 let input2 = [1; 2]

 (input1, input2) ||> List.compareWith closerToNextDozen

Returns a new list that contains the elements of each the lists in order.

lists : seq<'T list>

The input sequence of lists.

Returns: 'T list

The resulting concatenated list.

Example

 let input = [ [1;2]
               [3;4;5]
               [6;7;8;9] ]
 input |> List.concat  // evaluates [1; 2; 3; 4; 5; 6; 7; 8; 9]

Tests if the list contains the specified element.

value : 'T

The value to locate in the input list.

source : 'T list

The input list.

Returns: bool

True if the input list contains the specified element; false otherwise.

Example

 [1..9] |> List.contains 0

Example

 [1..9] |> List.contains 3

Example

 let input = [1, "SpongeBob"; 2, "Patrick"; 3, "Squidward"; 4, "Mr. Krabs"]

 input |> List.contains (2, "Patrick")

Example

 let input = [1, "SpongeBob"; 2, "Patrick"; 3, "Squidward"; 4, "Mr. Krabs"]

 input |> List.contains (22, "Patrick")

Applies a key-generating function to each element of a list and returns a list yielding unique keys and their number of occurrences in the original list.

projection : 'T -> 'Key

A function transforming each item of the input list into a key to be compared against the others.

list : 'T list

The input list.

Returns: ('Key * int) list

The result list.

Example

Counting the number of occurrences of chars

 let input = ['H'; 'a'; 'p'; 'p'; 'y']

 input |> List.countBy id

Returns a list that contains no duplicate entries according to generic hash and equality comparisons on the entries. If an element occurs multiple times in the list then the later occurrences are discarded.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let input = [6;1;2;3;1;4;5;5]

 input |> List.distinct

Returns a list that contains no duplicate entries according to the generic hash and equality comparisons on the keys returned by the given key-generating function. If an element occurs multiple times in the list then the later occurrences are discarded.

projection : 'T -> 'Key

A function transforming the list items into comparable keys.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let isEven x = 0 = x % 2

 let input = [6;1;2;3;1;4;5;5]

 input |> List.distinctBy isEven  // evaluates [6; 1]

Returns an empty list of the given type.

Returns: 'T list

Returns the only element of the list.

list : 'T list

The input list.

Returns: 'T

The only element of the list.

Example

 ["the chosen one"] |> List.exactlyOne // evaluates "the chosen one"

Example

 let input : string list = []

 input |> List.exactlyOne

Example

 [1..5] |> List.exactlyOne

Returns a new list with the distinct elements of the input list which do not appear in the itemsToExclude sequence, using generic hash and equality comparisons to compare values.

itemsToExclude : seq<'T>

A sequence whose elements that also occur in the input list will cause those elements to be removed from the result.

list : 'T list

A list whose elements that are not also in itemsToExclude will be returned.

Returns: 'T list

A list that contains the distinct elements of list that do not appear in itemsToExclude.

Example

 let input = [1, "Kirk"; 2, "Spock"; 3, "Kenobi"] 

 input |> List.except [3, "Kenobi"]

Example

 [0..10] |> List.except [1..5]  // evaluates [0; 6; 7; 8; 9; 10]

Example

 [1..5] |> List.except [0..10]  // evaluates []

Tests if any element of the list satisfies the given predicate.

The predicate is applied to the elements of the input list. If any application returns true then the overall result is true and no further elements are tested. Otherwise, false is returned.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: bool

True if any element satisfies the predicate.

Example

 let input = [1, "Kirk"; 2, "Spock"; 3, "Kenobi"] 
 
 input |> List.exists (fun x -> x = (3, "Kenobi"))  // evaluates true
 
 input |> List.exists (fun (n, name) -> n > 5)      // evaluates false

Tests if any pair of corresponding elements of the lists satisfies the given predicate.

The predicate is applied to matching elements in the two collections up to the lesser of the two lengths of the collections. If any application returns true then the overall result is true and no further elements are tested. Otherwise, if one collections is longer than the other then the ArgumentException exception is raised. Otherwise, false is returned.

predicate : 'T1 -> 'T2 -> bool

The function to test the input elements.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: bool

True if any pair of elements satisfy the predicate.

Example

Check if the sum of pairs (from 2 different lists) have at least one even number

 let anEvenSum a b  = 0 = (a + b) % 2
 
 ([1..4], [2..5]) 
 ||> List.exists2 anEvenSum     // evaluates false
 
 ([1..4], [2;4;5;6])
 ||> List.exists2 anEvenSum   // evaluates true

Returns a new collection containing only the elements of the collection for which the given predicate returns "true"

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T list

A list containing only the elements that satisfy the predicate.

Example

 let input = [1, "Luke"; 2, "Kirk"; 3, "Kenobi"; 4, "Spock"]

 let isComingFromStarTrek (x,_) = isEven x
 
 input |> List.filter isComingFromStarTrek

Returns the first element for which the given function returns True. Raises KeyNotFoundException if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T

The first element that satisfies the predicate.

Example

 let isEven x  = 0 = x % 2

 let isGreaterThan x y = y > x

 let input = [1, "Luke"; 2, "Kirk"; 3, "Spock"; 4, "Kenobi"]
 
 input |> List.find (fun (x,_) -> isEven x)              // evaluates (2, "Kirk")
 input |> List.find (fun (x,_) -> x |> isGreaterThan 6)  // raises an exception

Returns the last element for which the given function returns True. Raises KeyNotFoundException if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T

The last element that satisfies the predicate.

Example

 let isEven x  = 0 = x % 2

 let isGreaterThan x y = y > x

 let input = [1, "Luke"; 2, "Kirk"; 3, "Spock"; 4, "Kenobi"]
 
 input |> List.findBack (fun (x,_) -> isEven x)              // evaluates (4, "Kenobi")
 input |> List.findBack (fun (x,_) -> x |> isGreaterThan 6)  // raises an exception

Returns the index of the first element in the list that satisfies the given predicate. Raises KeyNotFoundException if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: int

The index of the first element that satisfies the predicate.

Example

 let isEven x  = 0 = x % 2

 let isGreaterThan x y = y > x

 let input = [1, "Luke"; 2, "Kirk"; 3, "Spock"; 4, "Kenobi"]
 
 input |> List.findIndex (fun (x,_) -> isEven x)              // evaluates 1
 input |> List.findIndex (fun (x,_) -> x |> isGreaterThan 6)  // raises an exception

Returns the index of the last element in the list that satisfies the given predicate. Raises KeyNotFoundException if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: int

The index of the last element that satisfies the predicate.

Example

 let isEven x  = 0 = x % 2

 let isGreaterThan x y = y > x

 let input = [1, "Luke"; 2, "Kirk"; 3, "Spock"; 4, "Kenobi"]
 
 input |> List.findIndexBack (fun (x,_) -> isEven x)              // evaluates 3
 input |> List.findIndexBack (fun (x,_) -> x |> isGreaterThan 6)  // raises an exception

Applies a function to each element of the collection, threading an accumulator argument through the computation. Take the second argument, and apply the function to it and the first element of the list. Then feed this result into the function along with the second element and so on. Return the final result. If the input function is f and the elements are i0...iN then computes f (... (f s i0) i1 ...) iN.

folder : 'State -> 'T -> 'State

The function to update the state given the input elements.

state : 'State

The initial state.

list : 'T list

The input list.

Returns: 'State

The final state value.

Example

Making the sum of squares for the first 5 natural numbers

 (0, [1..5]) ||> List.fold (fun s v -> s + v * v)  // evaluates 55

Example

Shopping for fruits hungry, you tend to take more of each as the hunger grows

 type Fruit = Apple | Pear | Orange

 type BagItem = { fruit: Fruit; quantity: int }

 let takeMore (previous: BagItem list) fruit = 
     let toTakeThisTime = 
         match previous with 
         | bagItem :: otherBagItems -> bagItem.quantity + 1 
         | [] -> 1 
     { fruit = fruit; quantity = toTakeThisTime } :: previous

 let inputs = [ Apple; Pear; Orange ]
 
 ([], inputs) ||> List.fold takeMore

  [{ fruit = Orange; quantity = 3 }
   { fruit = Pear; quantity = 2 }
   { fruit = Apple; quantity = 1 }]

Applies a function to corresponding elements of two collections, threading an accumulator argument through the computation. The collections must have identical sizes. If the input function is f and the elements are i0...iN and j0...jN then computes f (... (f s i0 j0)...) iN jN.

folder : 'State -> 'T1 -> 'T2 -> 'State

The function to update the state given the input elements.

state : 'State

The initial state.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: 'State

The final state value.

Example

Count the numer of times the coins match:
 type CoinToss = Head | Tails

 let inputs1 = [Tails; Head; Tails]
 let inputs2 = [Tails; Head; Head]

 (0, inputs1, inputs2) |||> List.fold2 (fun acc input1 input2 ->
     match (input1, input2) with
     | Head, Head -> acc + 1
     | Tails, Tails -> acc + 1
     | _ -> acc - 1)

Applies a function to each element of the collection, starting from the end, threading an accumulator argument through the computation. If the input function is f and the elements are i0...iN then computes f i0 (...(f iN s)).

folder : 'T -> 'State -> 'State

The function to update the state given the input elements.

list : 'T list

The input list.

state : 'State

The initial state.

Returns: 'State

The state object after the folding function is applied to each element of the list.

Example

Making the sum of squares for the first 5 natural numbers

 ([1..5], 0) ||> List.foldBack (fun v acc -> acc + v * v)  // evaluates 55

Example

Shopping for fruits hungry, you tend to take more of each as the hunger grows

 type Fruit = Apple | Pear | Orange

 type BagItem = { fruit: Fruit; quantity: int }

 let takeMore fruit (previous: BagItem list) =
     let toTakeThisTime = 
         match previous with 
         | bagItem :: otherBagItems -> bagItem.quantity + 1 
         | [] -> 1 
     { fruit = fruit; quantity = toTakeThisTime } :: previous

 let input = [ Apple; Pear; Orange ]
 
 (input, []) ||> List.foldBack takeMore

  [{ fruit = Apple; quantity = 3 }
   { fruit = Pear; quantity = 2 }
   { fruit = Orange; quantity = 1 }]

Applies a function to corresponding elements of two collections, threading an accumulator argument through the computation. The collections must have identical sizes. If the input function is f and the elements are i0...iN and j0...jN then computes f i0 j0 (...(f iN jN s)).

folder : 'T1 -> 'T2 -> 'State -> 'State

The function to update the state given the input elements.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

state : 'State

The initial state.

Returns: 'State

The final state value.

Example

Count the positives, negatives and accumulate some text from back to front:
 type Count =
   { Positive: int
     Negative: int
     Text: string }

 let inputs1 = [ -1; -2; -3 ]
 let inputs2 = [ 3; 2; 1 ]
 let initialState = {Positive = 0; Negative = 0; Text = ""}

 (inputs1, inputs2, initialState) |||> List.foldBack2 (fun a b acc  ->
     let text = acc.Text + "(" + string a + "," + string b + ") "
     if a + b >= 0 then
         { acc with
             Positive = acc.Positive + 1
             Text = text }
     else
         { acc with
             Negative = acc.Negative + 1
             Text = text }
 )

 { Positive = 2
   Negative = 1
   Text = "(-3,1) (-2,2) (-1,3) " }

Tests if all elements of the collection satisfy the given predicate.

The predicate is applied to the elements of the input list. If any application returns false then the overall result is false and no further elements are tested. Otherwise, true is returned.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: bool

True if all of the elements satisfy the predicate.

Example

 let isEven a = a % 2 = 0

 [2; 42] |> List.forall isEven // evaluates to true

 [1; 2] |> List.forall isEven // evaluates to false

Tests if all corresponding elements of the collection satisfy the given predicate pairwise.

The predicate is applied to matching elements in the two collections up to the lesser of the two lengths of the collections. If any application returns false then the overall result is false and no further elements are tested. Otherwise, if one collection is longer than the other then the ArgumentException exception is raised. Otherwise, true is returned.

predicate : 'T1 -> 'T2 -> bool

The function to test the input elements.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: bool

True if all of the pairs of elements satisfy the predicate.

Example

 let inputs1 = [1; 2; 3]
 let inputs2 = [1; 2; 3]

 (inputs1, inputs2) ||> List.forall2 (=)

Example

 let items1 = [2017; 1; 1]
 let items2 = [2019; 19; 8]

 (items1, items2) ||> List.forall2 (=)

Example

 let items1 = [1; 2; 3]
 let items2 = [1; 2]

 (items1, items2) ||> List.forall2 (=)

Applies a key-generating function to each element of a list and yields a list of unique keys. Each unique key contains a list of all elements that match to this key.

projection : 'T -> 'Key

A function that transforms an element of the list into a comparable key.

list : 'T list

The input list.

Returns: ('Key * 'T list) list

The result list.

Example

 let inputs = [1; 2; 3; 4; 5]

 inputs |> List.groupBy (fun n -> n % 2)

Returns the first element of the list.

list : 'T list

The input list.

Returns: 'T

The first element of the list.

Example

 let inputs = ["banana"; "pear"]

 inputs |> List.head

Example

 [] |> List.head

Returns a new list whose elements are the corresponding elements of the input list paired with the index (from 0) of each element.

list : 'T list

The input list.

Returns: (int * 'T) list

The list of indexed elements.

Example

 let inputs = ["a"; "b"; "c"]

 inputs |> List.indexed

Creates a list by calling the given generator on each index.

length : int

The length of the list to generate.

initializer : int -> 'T

The function to generate an element from an index.

Returns: 'T list

The list of generated elements.

Example

 List.init 4 (fun v -> v + 5)

Example

 List.init -5 (fun v -> v + 5)

Return a new list with a new item inserted before the given index.

index : int

The index where the item should be inserted.

value : 'T

The value to insert.

source : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = [ 0; 1; 2 ]

 inputs |> List.insertAt 1 9

Return a new list with new items inserted before the given index.

index : int

The index where the items should be inserted.

values : seq<'T>

The values to insert.

source : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = [ 0; 1; 2 ]

 inputs |> List.insertManyAt 1 [ 8; 9 ]
 Evaluates to [ 0; 8; 9; 1; 2 ].

Returns true if the list contains no elements, false otherwise.

list : 'T list

The input list.

Returns: bool

True if the list is empty.

Example

 [ ] |> List.isEmpty

Example

 [ "pear"; "banana" ] |> List.isEmpty

Indexes into the list. The first element has index 0.

index : int

The index to retrieve.

list : 'T list

The input list.

Returns: 'T

The value at the given index.

Example

 let inputs = [ "a"; "b"; "c" ]

 inputs |> List.item 1

Example

 let inputs = [ "a"; "b"; "c" ]

 inputs |> List.item 4

Applies the given function to each element of the collection.

action : 'T -> unit

The function to apply to elements from the input list.

list : 'T list

The input list.

Example

 let inputs = [ "a"; "b"; "c" ]

 inputs |> List.iter (printfn "%s")

 a
 b
 c

Applies the given function to two collections simultaneously. The collections must have identical size.

action : 'T1 -> 'T2 -> unit

The function to apply to pairs of elements from the input lists.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Example

 let inputs1 = [ "a"; "b"; "c" ]
 let inputs2 = [ 1; 2; 3 ]

 (inputs1, inputs2) ||> List.iter2 (printfn "%s: %i")

 a: 1
 b: 2
 c: 3

Applies the given function to each element of the collection. The integer passed to the function indicates the index of element.

action : int -> 'T -> unit

The function to apply to the elements of the list along with their index.

list : 'T list

The input list.

Example

 let inputs = [ "a"; "b"; "c" ]

 inputs |> List.iteri (fun i v -> printfn "{i}: {v}")

 0: a
 1: b
 2: c

Applies the given function to two collections simultaneously. The collections must have identical size. The integer passed to the function indicates the index of element.

action : int -> 'T1 -> 'T2 -> unit

The function to apply to a pair of elements from the input lists along with their index.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Example

 let inputs1 = [ "a"; "b"; "c" ]
 let inputs2 = [ "banana"; "pear"; "apple" ]

 (inputs1, inputs2) ||> List.iteri2 (fun i s1 s2 -> printfn "Index {i}: {s1} - {s2}")

 Index 0: a - banana
 Index 1: b - pear
 Index 2: c - apple

Returns the last element of the list.

list : 'T list

The input list.

Returns: 'T

The last element of the list.

Example

 [ "pear"; "banana" ] |> List.last

Example

 [ ] |> List.last

Returns the length of the list.

The notation array.Length is preferred.

list : 'T list

The input list.

Returns: int

The length of the list.

Example

 let inputs = [ "a"; "b"; "c" ]

 inputs |> List.length

Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection.

mapping : 'T -> 'U

The function to transform elements from the input list.

list : 'T list

The input list.

Returns: 'U list

The list of transformed elements.

Example

 let inputs = [ "a"; "bbb"; "cc" ]

 inputs |> List.map (fun x -> x.Length)

Builds a new collection whose elements are the results of applying the given function to the corresponding elements of the two collections pairwise.

mapping : 'T1 -> 'T2 -> 'U

The function to transform pairs of elements from the input lists.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: 'U list

The list of transformed elements.

Example

 let inputs1 = ["a"; "bad"; "good"]
 let inputs2 = [0; 2; 1]

 (inputs1, inputs2) ||> List.map2 (fun x y -> x.[y])

Builds a new collection whose elements are the results of applying the given function to the corresponding elements of the three collections simultaneously.

mapping : 'T1 -> 'T2 -> 'T3 -> 'U

The function to transform triples of elements from the input lists.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

list3 : 'T3 list

The third input list.

Returns: 'U list

The list of transformed elements.

Example

 let inputs1 = [ "a"; "t"; "ti" ]
 let inputs2 = [ "l"; "h"; "m" ]
 let inputs3 = [ "l"; "e"; "e" ]

 (inputs1, inputs2, inputs3) |||> List.map3 (fun x y z -> x + y + z)

Combines map and fold. Builds a new list whose elements are the results of applying the given function to each of the elements of the input list. The function is also used to accumulate a final value.

mapping : 'State -> 'T -> 'Result * 'State

The function to transform elements from the input list and accumulate the final value.

state : 'State

The initial state.

list : 'T list

The input list.

Returns: 'Result list * 'State

The list of transformed elements, and the final accumulated value.

Example

Accumulate the charges, and double them as well
 type Charge =
     | In of int
     | Out of int

 let inputs = [ In 1; Out 2; In 3 ]

 let newCharges, balance =
     (0, inputs) ||> List.mapFold (fun acc charge ->
         match charge with
         | In i -> In (i*2), acc + i
         | Out o -> Out (o*2), acc - o)

Combines map and foldBack. Builds a new list whose elements are the results of applying the given function to each of the elements of the input list. The function is also used to accumulate a final value.

mapping : 'T -> 'State -> 'Result * 'State

The function to transform elements from the input list and accumulate the final value.

list : 'T list

The input list.

state : 'State

The initial state.

Returns: 'Result list * 'State

The list of transformed elements, and the final accumulated value.

Example

Accumulate the charges from back to front, and double them as well

 type Charge =
     | In of int
     | Out of int

 let charges = [ In 1; Out 2; In 3 ]

 let newCharges, balance =
     (charges, 0) ||> List.mapFoldBack (fun charge acc ->
         match charge with
         | In i -> In (i*2), acc + i
         | Out o -> Out (o*2), acc - o)

Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection. The integer index passed to the function indicates the index (from 0) of element being transformed.

mapping : int -> 'T -> 'U

The function to transform elements and their indices.

list : 'T list

The input list.

Returns: 'U list

The list of transformed elements.

Example

 let inputs = [ 10; 10; 10 ]

 inputs |> List.mapi (fun i x -> i + x)

Like mapi, but mapping corresponding elements from two lists of equal length.

mapping : int -> 'T1 -> 'T2 -> 'U

The function to transform pairs of elements from the two lists and their index.

list1 : 'T1 list

The first input list.

list2 : 'T2 list

The second input list.

Returns: 'U list

The list of transformed elements.

Example

 let inputs1 = ["a"; "bad"; "good"]
 let inputs2 = [0; 2; 1]

 (inputs1, inputs2) ||> List.mapi2 (fun i x y -> i, x[y])

Return the greatest of all elements of the list, compared via Operators.max.

Raises ArgumentException if list is empty

list : 'T list

The input list.

Returns: 'T

The maximum element.

Example

 let inputs = [ 10; 12; 11 ]

 inputs |> List.max

Example

 let inputs = [ ]

 inputs |> List.max

Returns the greatest of all elements of the list, compared via Operators.max on the function result.

Raises ArgumentException if list is empty.

projection : 'T -> 'U

The function to transform the list elements into the type to be compared.

list : 'T list

The input list.

Returns: 'T

The maximum element.

Example

 let inputs = ["aaa"; "b"; "cccc"]

 inputs |> List.maxBy (fun s -> s.Length)

Example

 let inputs = []

 inputs |> List.maxBy (fun (s: string) -> s.Length)

Returns the lowest of all elements of the list, compared via Operators.min.

Raises ArgumentException if list is empty

list : 'T list

The input list.

Returns: 'T

The minimum value.

Example

 let inputs = [10; 12; 11]

 inputs |> List.min

Example

 let inputs = []

 inputs |> List.min

Returns the lowest of all elements of the list, compared via Operators.min on the function result

Raises ArgumentException if list is empty.

projection : 'T -> 'U

The function to transform list elements into the type to be compared.

list : 'T list

The input list.

Returns: 'T

The minimum value.

Example

 let inputs = ["aaa"; "b"; "cccc"]

 inputs |> List.minBy (fun s -> s.Length)

Example

 let inputs = []

 inputs |> List.minBy (fun (s: string) -> s.Length)

Builds a list from the given array.

array : 'T[]

The input array.

Returns: 'T list

The list of elements from the array.

Example

 let inputs = [| 1; 2; 5 |]

 inputs |> List.ofArray

Builds a new list from the given enumerable object.

source : seq<'T>

The input sequence.

Returns: 'T list

The list of elements from the sequence.

Example

 let inputs = seq { 1; 2; 5 }

 inputs |> List.ofSeq

Returns a list of each element in the input list and its predecessor, with the exception of the first element which is only returned as the predecessor of the second element.

list : 'T list

The input list.

Returns: ('T * 'T) list

The result list.

Example

 let inputs = [1; 2; 3; 4]

 inputs |> List.pairwise

Splits the collection into two collections, containing the elements for which the given predicate returns True and False respectively. Element order is preserved in both of the created lists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T list * 'T list

A list containing the elements for which the predicate evaluated to true and a list containing the elements for which the predicate evaluated to false.

Example

 let inputs = [1; 2; 3; 4]

 let evens, odds = inputs |> List.partition (fun x -> x % 2 = 0)

Returns a list with all elements permuted according to the specified permutation.

indexMap : int -> int

The function to map input indices to output indices.

list : 'T list

The input list.

Returns: 'T list

The permuted list.

Example

 let inputs = [1; 2; 3; 4]

 inputs |> List.permute (fun x -> (x + 1) % 4)

Applies the given function to successive elements, returning the first result where function returns Some(x) for some x. If no such element exists then raise KeyNotFoundException

chooser : 'T -> 'U option

The function to generate options from the elements.

list : 'T list

The input list.

Returns: 'U

The first resulting value.

Example

 let input = [1; 2; 3]

 input |> List.pick (fun n -> if n % 2 = 0 then Some (string n) else None)

Example

 let input = [1; 2; 3]

 input |> List.pick (fun n -> if n > 3 = 0 then Some (string n) else None)

Apply a function to each element of the collection, threading an accumulator argument through the computation. Apply the function to the first two elements of the list. Then feed this result into the function along with the third element and so on. Return the final result. If the input function is f and the elements are i0...iN then computes f (... (f i0 i1) i2 ...) iN.

Raises ArgumentException if list is empty

reduction : 'T -> 'T -> 'T

The function to reduce two list elements to a single element.

list : 'T list

The input list.

Returns: 'T

The final reduced value.

Example

 let inputs = [1; 3; 4; 2]

 inputs |> List.reduce (fun a b -> a * 10 + b)

Applies a function to each element of the collection, starting from the end, threading an accumulator argument through the computation. If the input function is f and the elements are i0...iN then computes f i0 (...(f iN-1 iN)).

reduction : 'T -> 'T -> 'T

A function that takes in the next-to-last element of the list and the current accumulated result to produce the next accumulated result.

list : 'T list

The input list.

Returns: 'T

The final result of the reductions.

Example

 let inputs = [1; 3; 4; 2]

 inputs |> List.reduceBack (fun a b -> a + b * 10)

Return a new list with the item at a given index removed.

index : int

The index of the item to be removed.

source : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = [ 0; 1; 2 ]

 inputs |> List.removeAt 1

Return a new list with the number of items starting at a given index removed.

index : int

The index of the item to be removed.

count : int

The number of items to remove.

source : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = [ 0; 1; 2; 3 ]

 inputs |> List.removeManyAt 1 2

Creates a list by replicating the given initial value.

count : int

The number of elements to replicate.

initial : 'T

The value to replicate

Returns: 'T list

The generated list.

Example

 List.replicate 3 "a"

Returns a new list with the elements in reverse order.

list : 'T list

The input list.

Returns: 'T list

The reversed list.

Example

 let inputs = [ 0; 1; 2 ]

 inputs |> List.rev

Applies a function to each element of the collection, threading an accumulator argument through the computation. Take the second argument, and apply the function to it and the first element of the list. Then feed this result into the function along with the second element and so on. Returns the list of intermediate results and the final result.

folder : 'State -> 'T -> 'State

The function to update the state given the input elements.

state : 'State

The initial state.

list : 'T list

The input list.

Returns: 'State list

The list of states.

Example

Apply a list charges and collect the running balances as each is applied:

 type Charge =
     | In of int
     | Out of int

 let inputs = [In 1; Out 2; In 3]

 (0, inputs) ||> List.scan (fun acc charge ->
     match charge with
     | In i -> acc + i
     | Out o -> acc - o)

Like foldBack, but returns both the intermediary and final results

folder : 'T -> 'State -> 'State

The function to update the state given the input elements.

list : 'T list

The input list.

state : 'State

The initial state.

Returns: 'State list

The list of states.

Example

Apply a list charges from back to front, and collect the running balances as each is applied:

 type Charge =
     | In of int
     | Out of int

 let inputs = [ In 1; Out 2; In 3 ]

 (inputs, 0) ||> List.scanBack (fun charge acc ->
     match charge with
     | In i -> acc + i
     | Out o -> acc - o)

Returns a list that contains one item only.

value : 'T

The input item.

Returns: 'T list

The result list of one item.

Example

 List.singleton 7

Returns the list after removing the first N elements.

count : int

The number of elements to skip. If the number is 0 or negative the input list is returned.

list : 'T list

The input list.

Returns: 'T list

The list after removing the first N elements.

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.skip 2

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.skip 5

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.skip -1

Bypasses elements in a list while the given predicate returns True, and then returns the remaining elements of the list.

predicate : 'T -> bool

A function that evaluates an element of the list to a boolean value.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = ["a"; "bbb"; "cc"; "d"]

 inputs |> List.skipWhile (fun x -> x.Length < 3)

Sorts the given list using Operators.compare.

This is a stable sort, i.e. the original order of equal elements is preserved.

list : 'T list

The input list.

Returns: 'T list

The sorted list.

Example

 let input = [8; 4; 3; 1; 6; 1]

 List.sort input

Sorts the given list using keys given by the given projection. Keys are compared using Operators.compare.

This is a stable sort, i.e. the original order of equal elements is preserved.

projection : 'T -> 'Key

The function to transform the list elements into the type to be compared.

list : 'T list

The input list.

Returns: 'T list

The sorted list.

Example

 let input = [ "a"; "bbb"; "cccc"; "dd" ]

 input |> List.sortBy (fun s -> s.Length)

Sorts the given list in descending order using keys given by the given projection. Keys are compared using Operators.compare.

This is a stable sort, i.e. the original order of equal elements is preserved.

projection : 'T -> 'Key

The function to transform the list elements into the type to be compared.

list : 'T list

The input list.

Returns: 'T list

The sorted list.

Example

 let input = ["a"; "bbb"; "cccc"; "dd"]

 input |> List.sortByDescending (fun s -> s.Length)

Sorts the given list in descending order using Operators.compare.

This is a stable sort, i.e. the original order of equal elements is preserved.

list : 'T list

The input list.

Returns: 'T list

The sorted list.

Example

 let input = [8; 4; 3; 1; 6; 1]

 input |> List.sortDescending

Sorts the given list using the given comparison function.

This is a stable sort, i.e. the original order of equal elements is preserved.

comparer : 'T -> 'T -> int

The function to compare the list elements.

list : 'T list

The input list.

Returns: 'T list

The sorted list.

Example

Sort a list of pairs using a comparison function that compares string lengths then index numbers:

 let compareEntries (n1: int, s1: string) (n2: int, s2: string) =
     let c = compare s1.Length s2.Length
     if c <> 0 then c else
     compare n1 n2

 let input = [ (0,"aa"); (1,"bbb"); (2,"cc"); (3,"dd") ]

 input |> List.sortWith compareEntries

Splits a list into two lists, at the given index.

index : int

The index at which the list is split.

list : 'T list

The input list.

Returns: 'T list * 'T list

The two split lists.

Example

 let input = [8; 4; 3; 1; 6; 1]

 let front, back = input |> List.splitAt 3

Splits the input list into at most count chunks.

count : int

The maximum number of chunks.

list : 'T list

The input list.

Returns: 'T list list

The list split into chunks.

Example

 [1..10] |> List.splitInto 2

Example

 [1..10] |> List.splitInto 4

Returns the sum of the elements in the list.

list : ^T list

The input list.

Returns: ^T

The resulting sum.

Example

 let input = [ 1; 5; 3; 2 ]

 input |> List.sum

Returns the sum of the results generated by applying the function to each element of the list.

projection : 'T -> ^U

The function to transform the list elements into the type to be summed.

list : 'T list

The input list.

Returns: ^U

The resulting sum.

Example

 let input = [ "aa"; "bbb"; "cc" ]

 input |> List.sumBy (fun s -> s.Length)

Returns the list after removing the first element.

list : 'T list

The input list.

Returns: 'T list

The list after removing the first element.

Example

 let inputs = ["a"; "bb"; "ccc"]

 inputs |> List.tail

Returns the first N elements of the list.

Throws InvalidOperationException if the count exceeds the number of elements in the list. List.truncate returns as many items as the list contains instead of throwing an exception.

count : int

The number of items to take.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.take 2

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.take 6

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.take 0

Returns a list that contains all elements of the original list while the given predicate returns True, and then returns no further elements.

predicate : 'T -> bool

A function that evaluates to false when no more items should be returned.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = ["a"; "bb"; "ccc"; "d"]

 inputs |> List.takeWhile (fun x -> x.Length < 3)

Builds an array from the given list.

list : 'T list

The input list.

Returns: 'T[]

The array containing the elements of the list.

Example

 let inputs = [ 1; 2; 5 ]

 inputs |> List.toArray

Views the given list as a sequence.

list : 'T list

The input list.

Returns: seq<'T>

The sequence of elements in the list.

Example

 let inputs = [ 1; 2; 5 ]

 inputs |> List.toSeq

Returns the transpose of the given sequence of lists.

lists : seq<'T list>

The input sequence of list.

Returns: 'T list list

The transposed list.

Example

 let inputs =
     [ [ 10; 20; 30 ]
       [ 11; 21; 31 ] ]

 inputs |> List.transpose

Returns at most N elements in a new list.

count : int

The maximum number of items to return.

list : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.truncate 2

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.truncate 6

Example

 let inputs = ["a"; "b"; "c"; "d"]

 inputs |> List.truncate 0

Returns the only element of the list or None if it is empty or contains more than one element.

list : 'T list

The input list.

Returns: 'T option

The only element of the list or None.

Example

 [1] |> List.tryExactlyOne               // evaluates Some 1
 [1;2] |> List.tryExactlyOne             // evaluates None
 ([] : int list) |> List.tryExactlyOne   // evaluates None

Returns the first element for which the given function returns True. Return None if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T option

The first element for which the predicate returns true, or None if every element evaluates to false.

Example

Try to find the first even number:

 let inputs = [1; 2; 3]

 inputs |> List.tryFind (fun elm -> elm % 2 = 0)

Example

Try to find the first even number:

 let inputs = [1; 5; 3]

 inputs |> List.tryFind (fun elm -> elm % 2 = 0)

Returns the last element for which the given function returns True. Return None if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T option

The last element for which the predicate returns true, or None if every element evaluates to false.

Example

Try to find the first even number from the back:

 let inputs = [1; 2; 3; 4; 5]

 inputs |> List.tryFindBack (fun elm -> elm % 2 = 0)

Example

Try to find the first even number from the back:

 let inputs = [1; 5; 3]

 inputs |> List.tryFindBack (fun elm -> elm % 2 = 0)

Returns the index of the first element in the list that satisfies the given predicate. Return None if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: int option

The index of the first element for which the predicate returns true, or None if every element evaluates to false.

Example

Try to find the index of the first even number:

 let inputs = [1; 2; 3; 4; 5]

 inputs |> List.tryFindIndex (fun elm -> elm % 2 = 0)

Example

Try to find the index of the first even number:

 let inputs = [1; 3; 5; 7]

 inputs |> List.tryFindIndex (fun elm -> elm % 2 = 0)

Returns the index of the last element in the list that satisfies the given predicate. Return None if no such element exists.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: int option

The index of the last element for which the predicate returns true, or None if every element evaluates to false.

Example

Try to find the index of the first even number from the back:

 let inputs = [1; 2; 3; 4; 5]

 inputs |> List.tryFindIndexBack (fun elm -> elm % 2 = 0)

Example

Try to find the index of the first even number from the back:

 let inputs = [1; 3; 5; 7]

 inputs |> List.tryFindIndexBack (fun elm -> elm % 2 = 0)

Returns the first element of the list, or None if the list is empty.

list : 'T list

The input list.

Returns: 'T option

The first element of the list or None.

Example

 let inputs = [ "banana"; "pear" ]

 inputs |> List.tryHead

Example

 let inputs : int list = []

 inputs |> List.tryHead

Tries to find the nth element in the list. Returns None if index is negative or the list does not contain enough elements.

index : int

The index to retrieve.

list : 'T list

The input list.

Returns: 'T option

The value at the given index or None.

Example

 let inputs = ["a"; "b"; "c"]

 inputs |> List.tryItem 1

Example

 let inputs = ["a"; "b"; "c"]

 inputs |> List.tryItem 4

Returns the last element of the list. Return None if no such element exists.

list : 'T list

The input list.

Returns: 'T option

The last element of the list or None.

Example

 [ "pear"; "banana" ] |> List.tryLast

Example

 [ ] |> List.tryLast

Applies the given function to successive elements, returning Some(x) the first result where function returns Some(x) for some x. If no such element exists then return None.

chooser : 'T -> 'U option

The function to generate options from the elements.

list : 'T list

The input list.

Returns: 'U option

The first resulting value or None.

Example

 let input = [1; 2; 3]

 input |> List.tryPick (fun n -> if n % 2 = 0 then Some (string n) else None)

Example

 let input = [1; 2; 3]

 input |> List.tryPick (fun n -> if n > 3 = 0 then Some (string n) else None)

Returns a list that contains the elements generated by the given computation. The generator is repeatedly called to build the list until it returns `None`. The given initial state argument is passed to the element generator.

generator : 'State -> ('T * 'State) option

A function that takes in the current state and returns an option tuple of the next element of the list and the next state value.

state : 'State

The initial state value.

Returns: 'T list

The result list.

Example

 1 |> List.unfold (fun state -> if state > 100 then None else Some (state, state * 2))

Splits a list of pairs into two lists.

list : ('T1 * 'T2) list

The input list.

Returns: 'T1 list * 'T2 list

Two lists of split elements.

Example

 let inputs = [(1, "one"); (2, "two")]

 let numbers, names = inputs |> List.unzip

Splits a list of triples into three lists.

list : ('T1 * 'T2 * 'T3) list

The input list.

Returns: 'T1 list * 'T2 list * 'T3 list

Three lists of split elements.

Example

 let inputs = [(1, "one", "I"); (2, "two", "II")]

 let numbers, names, roman = inputs |> List.unzip3

Return a new list with the item at a given index set to the new value.

index : int

The index of the item to be replaced.

value : 'T

The new value.

source : 'T list

The input list.

Returns: 'T list

The result list.

Example

 let inputs = [ 0; 1; 2 ]

 inputs |> List.updateAt 1 9

Returns a new list containing only the elements of the list for which the given predicate returns "true"

This is identical to List.filter.

predicate : 'T -> bool

The function to test the input elements.

list : 'T list

The input list.

Returns: 'T list

A list containing only the elements that satisfy the predicate.

Example

Select only the even numbers:

 let inputs = [1; 2; 3; 4]

 inputs |> List.where (fun elm -> elm % 2 = 0)