Lists

Syntax#

[] // an empty list.

head::tail // a construction cell holding an element, head, and a list, tail. :: is called the Cons operator.

let list1 = [ 1; 2; 3 ] // Note the usage of a semicolon.

let list2 = 0 :: list1 // result is [ 0; 1; 2; 3 ]

let list3 = list1 @ list2 // result is [ 1; 2; 3; 0; 1; 2; 3 ]. @ is the append operator.

let list4 = [ 1..3 ] // result is [ 1; 2; 3 ]

let list5 = [ 1..2..10 ] // result is [ 1; 3; 5; 7; 9 ]

let list6 = [ for i in 1..10 do if i % 2 = 1 then yield i ] // result is [ 1; 3; 5; 7; 9 ]

Basic List Usage

let list1 = [ 1; 2 ]
let list2 = [ 1 .. 100 ]

// Accessing an element
printfn "%A" list1.[0]

// Pattern matching
let rec patternMatch aList = 
    match aList with
    | [] -> printfn "This is an empty list"
    | head::tail -> printfn "This list consists of a head element %A and a tail list %A" head tail
                    patternMatch tail

patternMatch list1

// Mapping elements
let square x = x*x
let list2squared = list2
                   |> List.map square
printfn "%A" list2squared

Calculating the total sum of numbers in a list

By recursion

let rec sumTotal list = 
    match list with
    | [] -> 0 // empty list -> return 0
    | head :: tail -> head + sumTotal tail

The above example says: “Look at the list, is it empty? return 0. Otherwise it is a non-empty list. So it could be [1], [1; 2], [1; 2; 3] etc. If listis [1] then bind the variable head to 1 and tail to [] then execute head + sumTotal tail.

Example execution:

sumTotal [1; 2; 3]
// head -> 1, tail -> [2; 3]
1 + sumTotal [2; 3]
1 + (2 + sumTotal [3])
1 + (2 + (3 + sumTotal [])) // sumTotal [] is defined to be 0, recursion stops here
1 + (2 + (3 + 0)))
1 + (2 + 3)
1 + 5 
6

A more general way to encapsulate the above pattern is by using functional folds! sumTotal becomes this:

let sumTotal list = List.fold (+) 0 list

Creating lists

A way to create a list is to place elements in two square brackets, separated by semicolons. The elements must have the same type.

Example:

> let integers = [1; 2; 45; -1];;
val integers : int list = [1; 2; 45; -1]


> let floats = [10.7; 2.0; 45.3; -1.05];;
val floats : float list = [10.7; 2.0; 45.3; -1.05]

When a list has no element, it is empty. An empty list can be declared as follows:

> let emptyList = [];;
val emptyList : 'a list

Other example

To create a list of byte, simply to cast the integers:

> let bytes = [byte(55); byte(10); byte(100)];;
val bytes : byte list = [55uy; 10uy; 100uy]

It is also possible to define lists of functions, of elements of a type defined previously, of objects of a class, etc.

Example

> type number = | Real of float | Integer of int;;

type number =
  | Real of float
  | Integer of int

> let numbers = [Integer(45); Real(0.0); Integer(127)];;
val numbers : number list = [Integer 45; Real 0.0; Integer 127]

Ranges

For certain types of elements (int, float, char,…), it is possible to define a list by the start element and the end element, using the following template:

[start..end]

Examples:

> let c=['a' .. 'f'];;
val c : char list = ['a'; 'b'; 'c'; 'd'; 'e'; 'f']

let f=[45 .. 60];;
val f : int list =
  [45; 46; 47; 48; 49; 50; 51; 52; 53; 54; 55; 56; 57; 58; 59; 60]

You can also specify a step for certain types, with the following model:

[start..step..end]

Examples:

> let i=[4 .. 2 .. 11];;
val i : int list = [4; 6; 8; 10]

> let r=[0.2 .. 0.05 .. 0.28];;
val r : float list = [0.2; 0.25]

Generator

Another way to create a list is to generate it automatically by using generator.

We can use one of the following models:

[for <identifier> in range -> expr]

[for <identifier> in range do ... yield expr]

Examples

> let oddNumbers = [for i in 0..10 -> 2 * i + 1];; // odd numbers from 1 to 21
val oddNumbers : int list = [1; 3; 5; 7; 9; 11; 13; 15; 17; 19; 21]

> let multiples3Sqrt = [for i in 1..27 do if i % 3 = 0 then yield sqrt(float(i))];; //sqrt of multiples of 3 from 3 to 27
val multiples3Sqrt : float list =
  [1.732050808; 2.449489743; 3.0; 3.464101615; 3.872983346; 4.242640687;    4.582575695; 4.898979486; 5.196152423]

Operators

Some operators may be used to construct lists:

Cons operator ::

This operator :: is used to add a head element to a list:

> let l=12::[] ;;
val l : int list = [12]

> let l1=7::[14; 78; 0] ;;
val l1 : int list = [7; 14; 78; 0]

> let l2 = 2::3::5::7::11::[13;17] ;;
val l2 : int list = [2; 3; 5; 7; 11; 13; 17]

Concatenation

The concatenation of lists is carried out with the operator @.

> let l1 = [12.5;89.2];;
val l1 : float list = [12.5; 89.2]

> let l2 = [1.8;7.2] @ l1;;
val l2 : float list = [1.8; 7.2; 12.5; 89.2]