F# - Lists

In F#, a list is an ordered, immutable series of elements of the same type. It is to some extent equivalent to a linked list data structure.

The F# module, Microsoft.FSharp.Collections.List, has the common operations on lists. However F# imports this module automatically and makes it accessible to every F# application.

Creating and Initializing a List

Following are the various ways of creating lists −

• Using list literals.

• Using cons (::) operator.

• Using the List.init method of List module.

• Using some syntactic constructs called List Comprehensions.

List Literals

In this method, you just specify a semicolon-delimited sequence of values in square brackets. For example −

let list1 = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]

The cons (::) Operator

With this method, you can add some values by prepending or cons-ing it to an existing list using the :: operator. For example −

let list2 = 1::2::3::4::5::6::7::8::9::10::[];;

[] denotes an empty list.

List init Method

The List.init method of the List module is often used for creating lists. This method has the type −

val init : int -> (int -> 'T) -> 'T list

The first argument is the desired length of the new list, and the second argument is an initializer function, which generates items in the list.

For example,

let list5 = List.init 5 (fun index -> (index, index * index, index * index * index))

Here, the index function generates the list.

List Comprehensions

List comprehensions are special syntactic constructs used for generating lists.

F# list comprehension syntax comes in two forms − ranges and generators.

Ranges have the constructs − [start .. end] and [start .. step .. end]

For example,

let list3 = [1 .. 10]

Generators have the construct − [for x in collection do ... yield expr]

For example,

let list6 = [ for a in 1 .. 10 do yield (a * a) ]

As the yield keyword pushes a single value into a list, the keyword, yield!, pushes a collection of values into the list.

The following function demonstrates the above methods −

Example

(* using list literals *)
let list1 = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
printfn "The list: %A" list1

(*using cons operator *)
let list2 = 1 :: 2 :: 3 :: []
printfn "The list: %A" list2

(* using range constructs*)
let list3 = [1 .. 10]
printfn "The list: %A" list3

(* using range constructs *)
let list4 = ['a' .. 'm']
printfn "The list: %A" list4

(* using init method *)
let list5 = List.init 5 (fun index -> (index, index * index, index * index * index))
printfn "The list: %A" list5

(* using yield operator *)
let list6 = [ for a in 1 .. 10 do yield (a * a) ]
printfn "The list: %A" list6

(* using yield operator *)
let list7 = [ for a in 1 .. 100 do if a % 3 = 0 && a % 5 = 0 then yield a]
printfn "The list: %A" list7

(* using yield! operator *)
let list8 = [for a in 1 .. 3 do yield! [ a .. a + 3 ] ]
printfn "The list: %A" list8

When you compile and execute the program, it yields the following output −

The list: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
The list: [1; 2; 3]
The list: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
The list: ['a'; 'b'; 'c'; 'd'; 'e'; 'f'; 'g'; 'h'; 'i'; 'j'; 'k'; 'l'; 'm']
The list: [(0, 0, 0); (1, 1, 1); (2, 4, 8); (3, 9, 27); (4, 16, 64)]
The list: [1; 4; 9; 16; 25; 36; 49; 64; 81; 100]
The list: [15; 30; 45; 60; 75; 90]
The list: [1; 2; 3; 4; 2; 3; 4; 5; 3; 4; 5; 6]

Properties of List Data Type

The following table shows various properties of list data type −

The following example shows the use of these properties −

Example

let list1 = [ 2; 4; 6; 8; 10; 12; 14; 16 ]

// Use of Properties
printfn "list1.IsEmpty is %b" (list1.IsEmpty)
printfn "list1.Length is %d" (list1.Length)
printfn "list1.Head is %d" (list1.Head)
printfn "list1.Tail.Head is %d" (list1.Tail.Head)
printfn "list1.Tail.Tail.Head is %d" (list1.Tail.Tail.Head)
printfn "list1.Item(1) is %d" (list1.Item(1))

When you compile and execute the program, it yields the following output −

list1.IsEmpty is false
list1.Length is 8
list1.Head is 2
list1.Tail.Head is 4
list1.Tail.Tail.Head is 6
list1.Item(1) is 4

Basic Operators on List

The following table shows the basic operations on list data type −

The following examples demonstrate the uses of the above functionalities −

Example 1

This program shows reversing a list recursively −

let list1 = [ 2; 4; 6; 8; 10; 12; 14; 16 ]
printfn "The original list: %A" list1

let reverse lt =
   let rec loop acc = function
      | [] -> acc
      | hd :: tl -> loop (hd :: acc) tl
   loop [] lt

printfn "The reversed list: %A" (reverse list1)

When you compile and execute the program, it yields the following output −

The original list: [2; 4; 6; 8; 10; 12; 14; 16]
The reversed list: [16; 14; 12; 10; 8; 6; 4; 2]

However, you can use the rev function of the module for the same purpose −

let list1 = [ 2; 4; 6; 8; 10; 12; 14; 16 ]
printfn "The original list: %A" list1
printfn "The reversed list: %A" (List.rev list1)

When you compile and execute the program, it yields the following output −

The original list: [2; 4; 6; 8; 10; 12; 14; 16]
The reversed list: [16; 14; 12; 10; 8; 6; 4; 2]

Example 2

This program shows filtering a list using the List.filter method −

let list1 = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
printfn "The list: %A" list1
let list2 = list1 |> List.filter (fun x -> x % 2 = 0);;
printfn "The Filtered list: %A" list2

When you compile and execute the program, it yields the following output −

The list: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
The Filtered list: [2; 4; 6; 8; 10]

Example 3

The List.map method maps a list from one type to another −

let list1 = [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
printfn "The list: %A" list1
let list2 = list1 |> List.map (fun x -> (x * x).ToString());;
printfn "The Mapped list: %A" list2

When you compile and execute the program, it yields the following output −

The list: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
The Mapped list: ["1"; "4"; "9"; "16"; "25"; "36"; "49"; "64"; "81"; "100"]

Example 4

The List.append method and the @ operator appends one list to another −

let list1 = [1; 2; 3; 4; 5 ]
let list2 = [6; 7; 8; 9; 10]
let list3 = List.append list1 list2

printfn "The first list: %A" list1
printfn "The second list: %A" list2
printfn "The appened list: %A" list3

let lt1 = ['a'; 'b';'c' ]
let lt2 = ['e'; 'f';'g' ]
let lt3 = lt1 @ lt2

printfn "The first list: %A" lt1
printfn "The second list: %A" lt2
printfn "The appened list: %A" lt3

When you compile and execute the program, it yields the following output −

The first list: [1; 2; 3; 4; 5]
The second list: [6; 7; 8; 9; 10]
The appened list: [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
The first list: ['a'; 'b'; 'c']
The second list: ['e'; 'f'; 'g']
The appened list: ['a'; 'b'; 'c'; 'e'; 'f'; 'g']

Example 5

The List.sort method sorts a list. The List.sum method gives the sum of elements in the list and the List.average method gives the average of elements in the list −

let list1 = [9.0; 0.0; 2.0; -4.5; 11.2; 8.0; -10.0]
printfn "The list: %A" list1

let list2 = List.sort list1
printfn "The sorted list: %A" list2

let s = List.sum list1
let avg = List.average list1
printfn "The sum: %f" s
printfn "The average: %f" avg

When you compile and execute the program, it yields the following output −

The list: [9.0; 0.0; 2.0; -4.5; 11.2; 8.0; -10.0]
The sorted list: [-10.0; -4.5; 0.0; 2.0; 8.0; 9.0; 11.2]
The sum: 15.700000
The average: 2.242857

A "fold" operation applies a function to each element in a list, aggregates the result of the function in an accumulator variable, and returns the accumulator as the result of the fold operation.

Example 6

The List.fold method applies a function to each element from left to right, while List.foldBack applies a function to each element from right to left.

let sumList list = List.fold (fun acc elem -> acc + elem) 0 list
printfn "Sum of the elements of list %A is %d." [ 1 .. 10 ] (sumList [ 1 .. 10 ])

When you compile and execute the program, it yields the following output −

Sum of the elements of list [1; 2; 3; 4; 5; 6; 7; 8; 9; 10] is 55.