lib.fixedPoints.fix

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.

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-repl> let self = {
  foo = "foo";
  bar = "bar";
  foobar = self.foo + self.bar;
}; in self
{ bar = "bar"; foo = "foo"; foobar = "foobar"; }

But in general you can get more reuse out of let bindings by refactoring them to a function.

nix-repl> f = self: {
  foo = "foo";
  bar = "bar";
  foobar = self.foo + self.bar;
}

This is where fix comes in, it contains the syntactic recursion that's not in f anymore.

nix-repl> fix = f:
  let self = f self; in self;

By applying fix we get the final result.

nix-repl> fix f
{ bar = "bar"; foo = "foo"; foobar = "foobar"; }

Such a refactored f using fix is not useful by itself. See extends for an example use case. There self is also often called final.

Inputs

f

1. Function argument

Type

fix :: (a -> a) -> a

Examples

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 ]

Noogle detected

• lib.fix

fix =
    f:
    let
      x = f x;
    in
    x;