2 Matching Annotations
1. Feb 2021
2. toraritte.github.io toraritte.github.io
1. 17.3. Fixed point

QUESTION: What is a fixed-point of a function?

ANSWER: See this video) at least, and the Fixed-point (mathematics)) wikipedia article:

In mathematics, a fixed point (sometimes shortened to fixpoint, also known as an invariant point) of a function is an element of the function's domain that is mapped to itself by the function. That is to say, c is a fixed point of the function `f` if `f(c) = c`. This means

``````f(f(...f(c)...)) = f n(c) = c
``````

an important terminating consideration when recursively computing f. A set of fixed points is sometimes called a fixed set.

For example, if f is defined on the real numbers by `f(x)=x^{2}-3x+4,}`, then 2 is a fixed point of `f`, because `f(2) = 2`.

There is also the wiki article fixed-point combinator that actually plays a role here, but read through the articles in this order.

Then dissect the Stackoverflow thread What is a Y combinator?, and pay attention to the comments! For example:

According to Mike Vanier's description, your definition for Y is actually not a combinator because it's recursive. Under "Eliminating (most) explicit recursion (lazy version)" he has the lazy scheme equivalent of your C# code but explains in point 2: "It is not a combinator, because the Y in the body of the definition is a free variable which is only bound once the definition is complete..." I think the cool thing about Y-combinators is that they produce recursion by evaluating the fixed-point of a function. In this way, they don't need explicit recursion. – GrantJ Jul 18 '11 at 0:02

(wut?)

Other resources in no particular order:

QUESTION: How the hell did they come up with the idea of using this with Nix and package management? (..and who? I remember a video saved somewhere, but maybe that was about overlays)

QUESTION: ... and how does it work in this context?

ANSWER: Well, not an answer yet, but this may be something in the right direction:

http://blog.tpleyer.de/posts/2020-01-29-Nix-overlay-evaluation-example.html

#### URL

3. Oct 2019
4. nixos.org nixos.org
1. fixed-point

"fixed-point", "fix point" seems to be most important concept in Nix, because `override`s, `overridePackages`, overlays are built using it.