Compute the fixed point of the given function `f`, which is usually an
attribute set that expects its final, non-recursive representation as an
argument:
`fix f` computes the fixed point of the given function `f`. In other words, the return value is `x` in `x = f x`.
`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.
**Relation to syntactic recursion**
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-repl> rec {
foo = "foo";
bar = "bar";
foobar = foo + bar;
}
{ bar = "bar"; foo = "foo"; foobar = "foobar"; }
```
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-repl> let self = {
foo = "foo";
bar = "bar";
foobar = self.foo + self.bar;
}; in self
{ bar = "bar"; foo = "foo"; foobar = "foobar"; }
```
f = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }
But in general you can get more reuse out of `let` bindings by refactoring them to a function.
```nix
nix-repl> f = self: {
foo = "foo";
bar = "bar";
foobar = self.foo + self.bar;
}
```
Nix evaluates this recursion until all references to `self` have been
resolved. At that point, the final result is returned and `f x = x` holds:
This is where `fix` comes in, it contains the syntactic that's not in `f` anymore.
```nix
nix-repl> fix = f:
let self = f self; in self;
```
By applying `fix` we get the final result.
```nix
nix-repl> fix f
{ bar = "bar"; foo = "foo"; foobar = "foobar"; }
```
Such a refactored `f` using `fix` is not useful by itself.
See [`extends`](#function-library-lib.fixedPoints.extends) for an example use case.
There `self` is also often called `final`.
Type: fix :: (a -> a) -> a
See https://en.wikipedia.org/wiki/Fixed-point_combinator for further
