lib: Move fixed-point combinators out of trivial

Trivia != prelude. This is a better organized and less likely to
scare off new contributors.

lib/fixed-points.nix

@@ -0,0 +1,78 @@
+rec {
+  # 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:
+  #
+  #     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:
+  #
+  #     nix-repl> fix f
+  #     { bar = "bar"; foo = "foo"; foobar = "foobar"; }
+  #
+  #  Type: fix :: (a -> a) -> a
+  #
+  # See https://en.wikipedia.org/wiki/Fixed-point_combinator for further
+  # details.
+  fix = f: let x = f x; in x;
+
+  # A variant of `fix` that records the original recursive attribute set in the
+  # result. This is useful in combination with the `extends` function to
+  # implement deep overriding. See pkgs/development/haskell-modules/default.nix
+  # for a concrete example.
+  fix' = f: let x = f x // { __unfix__ = f; }; in x;
+
+  # Modify the contents of an explicitly recursive attribute set in a way that
+  # honors `self`-references. This is accomplished with a function
+  #
+  #     g = self: super: { foo = super.foo + " + "; }
+  #
+  # that has access to the unmodified input (`super`) as well as the final
+  # non-recursive representation of the attribute set (`self`). `extends`
+  # differs from the native `//` operator insofar as that it's applied *before*
+  # references to `self` are resolved:
+  #
+  #     nix-repl> fix (extends g f)
+  #     { bar = "bar"; foo = "foo + "; foobar = "foo + bar"; }
+  #
+  # The name of the function is inspired by object-oriented inheritance, i.e.
+  # think of it as an infix operator `g extends f` that mimics the syntax from
+  # Java. It may seem counter-intuitive to have the "base class" as the second
+  # argument, but it's nice this way if several uses of `extends` are cascaded.
+  extends = f: rattrs: self: let super = rattrs self; in super // f self super;
+
+  # Compose two extending functions of the type expected by 'extends'
+  # into one where changes made in the first are available in the
+  # 'super' of the second
+  composeExtensions =
+    f: g: self: super:
+      let fApplied = f self super;
+          super' = super // fApplied;
+      in fApplied // g self super';
+
+  # Create an overridable, recursive attribute set. For example:
+  #
+  #     nix-repl> obj = makeExtensible (self: { })
+  #
+  #     nix-repl> obj
+  #     { __unfix__ = «lambda»; extend = «lambda»; }
+  #
+  #     nix-repl> obj = obj.extend (self: super: { foo = "foo"; })
+  #
+  #     nix-repl> obj
+  #     { __unfix__ = «lambda»; extend = «lambda»; foo = "foo"; }
+  #
+  #     nix-repl> obj = obj.extend (self: super: { foo = super.foo + " + "; bar = "bar"; foobar = self.foo + self.bar; })
+  #
+  #     nix-repl> obj
+  #     { __unfix__ = «lambda»; bar = "bar"; extend = «lambda»; foo = "foo + "; foobar = "foo + bar"; }
+  makeExtensible = makeExtensibleWithCustomName "extend";
+
+  # Same as `makeExtensible` but the name of the extending attribute is
+  # customized.
+  makeExtensibleWithCustomName = extenderName: rattrs:
+    fix' rattrs // {
+      ${extenderName} = f: makeExtensibleWithCustomName extenderName (extends f rattrs);
+   };
+}