## for

`for`

sequence expression is designed to look just like its more famous cousin, the imperative for-loop. It "loops" through a sequence and evaluates the body of each iteration into the sequence it is generating. Just like everything sequence related, it is NOT mutable.

```
> let oneToTen = seq { for x in 1..10 -> x }
val oneToTen: seq<int> = seq [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
// Or, equivalently:
> let oneToTen = seq { for x in 1..10 do yield x }
val oneToTen: seq<int> = seq [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]
// Just like Seq.map: applies a mapping function to each item in a sequence to build a new sequence
> let map mapping seq1 = seq { for x in seq1 do yield mapping x }
> map (fun x -> x * x) [1..10]
val map: ('a -> 'b) -> seq<'a> -> seq<'b>
val it: seq<int> = seq [1; 4; 9; 16; 25; 36; 49; 64; 81; 100]
// An infinite sequence of consecutive integers starting at 0
> let naturals =
let numbersFrom n = seq { yield n; yield! numbersFrom (n + 1) }
numbersFrom 0
// Just like Seq.filter: returns a sequence consisting only of items from the input sequence that satisfy the predicate
> let filter predicate seq1 = seq { for x in seq1 do if predicate x then yield x }
> let evenNaturals = naturals |> filter (fun x -> x % 2 = 0)
val naturals: seq<int> = seq [1; 2; 3; ...]
val filter: ('a -> bool) -> seq<'a> -> seq<'a>
val evenNaturals: seq<int> = seq [2; 4; 6; ...]
// Just like Seq.concat: concatenates a collection of sequences together
> let concat seqSeq = seq { for seq in seqSeq do yield! seq }
> concat [[1;2;3];[10;20;30]]
val concat: seq<#seq<'b>> -> seq<'b>
val it: seq<int> = seq [1; 2; 3; 10; 20; 30]
```

## yield and yield!

In sequence workflows, `yield`

adds a single item into the sequence being built. (In monadic terminology, it is `return`

.)

```
> seq { yield 1; yield 2; yield 3 }
val it: seq<int> = seq [1; 2; 3]
> let homogenousTup2ToSeq (a, b) = seq { yield a; yield b }
> tup2Seq ("foo", "bar")
val homogenousTup2ToSeq: 'a * 'a -> seq<'a>
val it: seq<string> = seq ["foo"; "bar"]
```

`yield!`

(pronounced *yield bang*) inserts all the items of another sequence into this sequence being built. Or, in other words, it appends a sequence. (In relation to monads, it is `bind`

.)

```
> seq { yield 1; yield! [10;11;12]; yield 20 }
val it: seq<int> = seq [1; 10; 11; 12; 20]
// Creates a sequence containing the items of seq1 and seq2 in order
> let concat seq1 seq2 = seq { yield! seq1; yield! seq2 }
> concat ['a'..'c'] ['x'..'z']
val concat: seq<'a> -> seq<'a> -> seq<'a>
val it: seq<int> = seq ['a'; 'b'; 'c'; 'x'; 'y'; 'z']
```

Sequences created by sequence workflows are also lazy, meaning that items of the sequence don't actually get evaluated until they're needed. A few ways to force items include calling `Seq.take`

(pulls the first n items into a sequence), `Seq.iter`

(applies a function to each item for executing side effects), or `Seq.toList`

(converts a sequence to a list). Combining this with recursion is where `yield!`

really starts to shine.

```
> let rec numbersFrom n = seq { yield n; yield! numbersFrom (n + 1) }
> let naturals = numbersFrom 0
val numbersFrom: int -> seq<int>
val naturals: seq<int> = seq [0; 1; 2; ...]
// Just like Seq.map: applies a mapping function to each item in a sequence to build a new sequence
> let rec map f seq1 =
if Seq.isEmpty seq1 then Seq.empty
else seq { yield f (Seq.head seq1); yield! map f (Seq.tail seq1) }
> map (fun x -> x * x) [1..10]
val map: ('a -> 'b) -> seq<'a> -> 'b
val it: seq<int> = seq [1; 4; 9; 16; 25; 36; 49; 64; 81; 100]
```