# Quark.FixedPoint (Quark v2.3.2) View Source

Fixed point combinators generalize the idea of a recursive function. This can be used to great effect, simplifying many definitions.

For example, here is the factorial function written in terms of `y/1`

:

```
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = y(fac)
...> factorial.(9)
362880
```

The resulting function will always be curried

```
iex> import Quark.SKI, only: [s: 3]
...> one_run = y(&s/3)
...> {_, arity} = :erlang.fun_info(one_run, :arity)
...> arity
1
```

# Link to this section Summary

## Functions

Alan Turing's fix-point combinator. This is the call-by-value formulation.

The famous Y-combinator. The resulting function will always be curried.

A normal order fixed point.

# Link to this section Functions

See `Quark.FixedPoint.y/0`

.

See `Quark.FixedPoint.y/1`

.

Alan Turing's fix-point combinator. This is the call-by-value formulation.

## Examples

```
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = turing(fac)
...> factorial.(9)
362880
```

## Specs

The famous Y-combinator. The resulting function will always be curried.

## Examples

```
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = y(fac)
...> factorial.(9)
362880
```

## Specs

A normal order fixed point.

## Examples

```
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = z(fac)
...> factorial.(9)
362880
```