# Recursion

There are three places recursion is commonly used: bindings, types, and modules.

Feature | Recursive | Non-recursive |
---|---|---|

Bindings | `let rec fn = ...` | `let fn = ...` |

Types | `type t = ...` | `type nonrec t = ...` |

Modules | `module rec A ...` | `module A ...` |

## Recursive Bindings

By default the name of a binding is not available for use on the right side of that binding. This applies to all `let`

bindings, including function definitions. This behavior is required for Binding Shadowing to work:

```
let x = 10;
/* If bindings were recursive by default this would form a cycle and break */
let x = x + 10;
```

The natural way to write a recursive function will have an error:

```
let infiniteRecursion = () => {
/* Error: Unbound value infiniteRecursion */
infiniteRecursion();
};
```

Opt-in to a recursive binding using the `rec`

keyword:

```
let rec infiniteRecursion = () => {
infiniteRecursion();
};
```

## Mutual Recursion

Mutually recursive functions use the `and`

keyword:

```
let rec function1 = () => {
function2();
}
and function2 = () => {
function3();
}
and function3 = () => {
function1();
};
```

- Note: The
`and`

keyword is not specific to recursion, it can be used without the`rec`

keyword. Doing so would cause all bindings to be created simultaneously but*not*visible to each other.

## Recursive Types

Types, unlike bindings, are recursive by default. This is because it is common for types to be recursive and uncommon for types to be shadowed. A recursive type could be used to define a binary tree:

```
type tree =
| Leaf
| Node(tree, tree);
```

Opt-out of recursive types using the `nonrec`

keyword:

```
type t = string;
type nonrec t = list(t);
/* t is now list(string) */
let x: t = ["hello", "world"];
```

## Mutually Recursive Types

Types can be mutually recursive just like bindings using the `and`

keyword:

```
type node = {
value: string,
edges: list(edge),
}
and edge = {
weight: int,
next: node,
};
```

## Mutually Recursive Modules

Sometimes functions will be organized across modules and both modules need functions from each other. Use the `module rec`

and `and`

keywords for this kind of mutual recursion.

*Note: Recursive modules require an explicit module type annotation.*

```
module type X = {
let x: unit => int;
let y: unit => int;
};
module rec A: X = {
let x = () => 1;
let y = () => B.y() + 1;
}
and B: X = {
let x = () => A.x() + 2;
let y = () => 2;
};
```