View Source Quark.FixedPoint (Quark v2.3.3-doma)
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)
362880The 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
1Link 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
Examples
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = turing(fac)
...> factorial.(9)
362880The famous Y-combinator. The resulting function will always be curried.
examples
Examples
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = y(fac)
...> factorial.(9)
362880A normal order fixed point.
examples
Examples
iex> fac = fn fac ->
...> fn
...> 0 -> 0
...> 1 -> 1
...> n -> n * fac.(n - 1)
...> end
...> end
...> factorial = z(fac)
...> factorial.(9)
362880