## Generate sequences

There are multiple ways to create a sequence.

You can use functions from the Seq module:

```
// Create an empty generic sequence
let emptySeq = Seq.empty
// Create an empty int sequence
let emptyIntSeq = Seq.empty<int>
// Create a sequence with one element
let singletonSeq = Seq.singleton 10
// Create a sequence of n elements with the specified init function
let initSeq = Seq.init 10 (fun c -> c * 2)
// Combine two sequence to create a new one
let combinedSeq = emptySeq |> Seq.append singletonSeq
// Create an infinite sequence using unfold with generator based on state
let naturals = Seq.unfold (fun state -> Some(state, state + 1)) 0
```

You can also use sequence expression:

```
// Create a sequence with element from 0 to 10
let intSeq = seq { 0..10 }
// Create a sequence with an increment of 5 from 0 to 50
let intIncrementSeq = seq{ 0..5..50 }
// Create a sequence of strings, yield allow to define each element of the sequence
let stringSeq = seq {
yield "Hello"
yield "World"
}
// Create a sequence from multiple sequence, yield! allow to flatten sequences
let flattenSeq = seq {
yield! seq { 0..10 }
yield! seq { 11..20 }
}
```

## Infinite repeating sequences

```
let data = [1; 2; 3; 4; 5;]
let repeating = seq {while true do yield! data}
```

Repeating sequences can be created using a `seq {}`

computation expression

## Introduction to sequences

A sequence is a series of elements that can be enumerated. It is an alias of System.Collections.Generic.IEnumerable and lazy. It stores a series of elements of the same type (can be any value or object, even another sequence). Functions from the Seq.module can be used to operate on it.

Here is a simple example of a sequence enumeration:

```
let mySeq = { 0..20 } // Create a sequence of int from 0 to 20
mySeq
|> Seq.iter (printf "%i ") // Enumerate each element of the sequence and print it
```

Output:

```
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
```

## Seq.filter

Suppose that we have a sequence of integers and we want to create a sequence that contains only the even integers. We can obtain the latter by using the `filter`

function of the Seq module. The `filter`

function has the type signature `('a -> bool) -> seq<'a> -> seq<'a>`

; this indicates that it accepts a function that returns true or false (sometimes called a predicate) for a given input of type `'a`

and a sequence that comprises values of type `'a`

to yield a sequence that comprises values of type `'a`

.

```
// Function that tests if an integer is even
let isEven x = (x % 2) = 0
// Generates an infinite sequence that contains the natural numbers
let naturals = Seq.unfold (fun state -> Some(state, state + 1)) 0
// Can be used to filter the naturals sequence to get only the even numbers
let evens = Seq.filter isEven naturals
```

## Seq.map

```
let seq = seq {0..10}
s |> Seq.map (fun x -> x * 2)
> val it : seq<int> = seq [2; 4; 6; 8; ...]
```

Apply a function to every element of a sequence using Seq.map