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lib.fix: Improve doc more

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Done together in and after the docs team meeting

Co-Authored-By: Robert Hensing <robert@roberthensing.nl>
This commit is contained in:
Silvan Mosberger 2023-10-12 17:37:41 +02:00
parent 1f8b5c039e
commit b82c1c7b5c
1 changed files with 24 additions and 14 deletions
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38
lib/fixed-points.nix
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@ -3,12 +3,16 @@ rec {
/* /*
`fix f` computes the fixed point of the given function `f`. In other words, the return value is `x` in `x = f x`. `fix f` computes the fixed point of the given function `f`. In other words, the return value is `x` in `x = f x`.
`f` is usually returns an attribute set that expects its final, non-recursive representation as an argument.
`f` must be a lazy function. `f` must be a lazy function.
This means that `x` must be a value that can be partially evaluated,
such as an attribute set, a list, or a function.
This way, `f` can use one part of `x` to compute another part.
**How it works** **Relation to syntactic recursion**
For context, Nix lets you define attribute set values in terms of other attributes using the `rec { }` attribute set literal syntax. This section explains `fix` by refactoring from syntactic recursion to a call of `fix` instead.
For context, Nix lets you define attributes in terms of other attributes syntactically using the [`rec { }` syntax](https://nixos.org/manual/nix/stable/language/constructs.html#recursive-sets).
```nix ```nix
nix-repl> rec { nix-repl> rec {
@ -19,7 +23,8 @@ rec {
{ bar = "bar"; foo = "foo"; foobar = "foobar"; } { bar = "bar"; foo = "foo"; foobar = "foobar"; }
``` ```
This is convenient when constructing a value to pass to a function for example, but a similar effect can be achieved with a `let` binding: This is convenient when constructing a value to pass to a function for example,
but an equivalent effect can be achieved with the `let` binding syntax:
```nix ```nix
nix-repl> let self = { nix-repl> let self = {
@ -30,7 +35,7 @@ rec {
{ bar = "bar"; foo = "foo"; foobar = "foobar"; } { bar = "bar"; foo = "foo"; foobar = "foobar"; }
``` ```
`let` bindings are nice, but as it is with `let` bindings in general, we may get more reuse out of the code by defining a function. But in general you can get more reuse out of `let` bindings by refactoring them to a function.
```nix ```nix
nix-repl> f = self: { nix-repl> f = self: {
@ -40,27 +45,32 @@ rec {
} }
``` ```
This is where `fix` comes in. Note that the body of the `fix` function This is where `fix` comes in, it contains the syntactic that's not in `f` anymore.
looks a lot like our earlier `let` binding, and that's no coincidence.
Fix is no more than such a recursive `let` binding, but with everything
except the recursion factored out into a function parameter `f`.
```nix ```nix
fix = f: nix-repl> fix = f:
let self = f self; in self; let self = f self; in self;
``` ```
So applying `fix` is another way to express our earlier examples. By applying `fix` we get the final result.
``` ```nix
nix-repl> fix f nix-repl> fix f
{ bar = "bar"; foo = "foo"; foobar = "foobar"; } { bar = "bar"; foo = "foo"; foobar = "foobar"; }
``` ```
This example did not _need_ `fix`, and arguably it shouldn't be used in such an example. Such a refactored `f` using `fix` is not useful by itself.
However, `fix` is useful when your `f` is a parameter, or when it is constructed from higher order functions. See [`extends`](#function-library-lib.fixedPoints.extends) for an example use case.
There `self` is also often called `final`.
Type: fix :: (a -> a) -> a Type: fix :: (a -> a) -> a
Example:
fix (self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; })
=> { bar = "bar"; foo = "foo"; foobar = "foobar"; }
fix (self: [ 1 2 (elemAt self 0 + elemAt self 1) ])
=> [ 1 2 3 ]
*/ */
fix = f: let x = f x; in x; fix = f: let x = f x; in x;