fix-extends monoid

default.nix

{
  # Like `extends` from the "fix-extends" idiom, but with the type:
  #
  #      ({..} -> {..} -> {..})
  #   -> ({..} -> {..} -> {..})
  #   -> ({..} -> {..} -> {..})
  #
  # instead of
  #
  #      ({..} -> {..} -> {..})
  #   -> ({..} -> {..})
  #   -> ({..} -> {..} -> {..})
  #
  # Since both parameters have the same type, this could be a monoid, and in
  # fact it is! Given the following identity value:
  #
  #   id = _: _: {};
  #
  # extendsMonoid f id =
  #   self: super0: let super1 = id self super0; in super1 // f self (super0 // super1);
  #   self: super0: let super1 = {};             in super1 // f self (super0 // super1);
  #   self: super0:                              in {}     // f self (super0 // {});
  #   self: super0:                              in           f self super0;
  #   self: super0:                              in           f self super0;
  #                                                           f;
  #
  #
  # extendsMonoid id f =
  #   self: super0: let super1 = f self super0; in super1 // id self (super0 // super1);
  #   self: super0: let super1 = f self super0; in super1 // {};
  #   self: super0: let super1 = f self super0; in super1;
  #   self: super0:              f self super0;
  #                              f;
  #
  # extendsMonoid f0 (extendsMonoid f1 f2) =
  #
  #   self: super0: let super1 = (extendsMonoid f1 f2) self super0;
  #     in super1 // f0 self (super0 // super1);
  #
  #   self: super0: let super1 = (self': super': let super2 = f2 self' super';
  #                                 in super2 // f1 self' (super' // super2))
  #                              self super0;
  #     in super1 // f0 self (super0 // super1);
  #
  #   self: super0: let super1 = let super2 = f2 self super0;
  #                                 in super2 // f1 self (super0 // super2)
  #     in super1 // f0 self (super0 // super1);
  #
  #   self: super0: let super2 = f2 self super0;
  #                     super1 = super2 // f1 self (super0 // super2)
  #     in super1 // f0 self (super0 // super1);
  #
  #   self: super0: let super2 = f2 self super0;
  #     in let super1 = super2 // f1 self (super0 // super2)
  #          in super1 // f0 self (super0 // super1);
  #
  #   self: super0: let super2 = f2 self super0;
  #     in let super1 = f1 self (super0 // super2)
  #          in (super2 // super1) // f0 self (super0 // (super2 // super1));
  #
  #   self: super0: let super2 = f2 self super0;
  #     in super2 // let super1 = f1 self (super0 // super2)
  #          in super1 // f0 self ((super0 // super2) // super1);
  #
  #   self: super0: let super2 = f2 self super0;
  #     in super2 // (self': super': let super1 = f1 self' super'
  #                     in super1 // f0 self' (super' // super1))
  #                  self' (super0 // super2);
  #
  #   self: super0: let super2 = f2 self super0;
  #     in super2 // (extendsMonoid f0 f1) self' (super0 // super2);
  #
  #   extendsMonoid (extendsMonoid f0 f1) f2;
  extendsMonoid = f0: f1: self: super0: let super1 = f1 self super0; in super1 // f0 self (super0 // super1);
}