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{ lib, ... }:
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;
# Return the fixpoint that `f` converges to when called recursively, starting
# with the input `x`.
#
# nix-repl> converge (x: x / 2) 16
# 0
converge = f: x:
let
x' = f x;
in
if x' == x
then x
else converge f 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.
#
# To get a better understanding how `extends` turns a function with a fix
# point (the package set we start with) into a new function with a different fix
# point (the desired packages set) lets just see, how `extends g f`
# unfolds with `g` and `f` defined above:
#
# extends g f = self: let super = f self; in super // g self super;
# = self: let super = { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }; in super // g self super
# = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; } // g self { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }
# = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; } // { foo = "foo" + " + "; }
# = self: { foo = "foo + "; bar = "bar"; foobar = self.foo + self.bar; }
#
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: final: prev:
let fApplied = f final prev;
prev' = prev // fApplied;
in fApplied // g final prev';
# Compose several extending functions of the type expected by 'extends' into
# one where changes made in preceding functions are made available to
# subsequent ones.
#
# composeManyExtensions : [packageSet -> packageSet -> packageSet] -> packageSet -> packageSet -> packageSet
# ^final ^prev ^overrides ^final ^prev ^overrides
composeManyExtensions =
lib.foldr (x: y: composeExtensions x y) (final: prev: {});
# 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' (self: (rattrs self) // {
${extenderName} = f: makeExtensibleWithCustomName extenderName (extends f rattrs);
});
}
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