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{ ... }:
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: f: makeExtensibleWithInterface
(fixedPoint: extend: fixedPoint // { ${extenderName} = ext: extend (_: ext); })
(_: f);
# A version of `makeExtensible` that allows the function being fixed
# to return a different interface than the interface returned to the
# user. Along with `self` and `super` views of the internal
# interface, a `self` view of the output interface is also
# provided. `extend` is not added to the output by default. This is
# the job of the interface.
#
# nix-repl> foo = {a, b}: {c = a + b;}
#
# nix-repl> interface = {args, val, ...}: extend: val // {inherit extend;}
#
# nix-repl> obj = makeExtensibleWithInterface interface (output: self: { args = {a = 1; b = 2;}; val = foo self.args; })
#
# nix-repl> obj.c
# 3
#
# nix-repl> obj = obj.extend (output: self: super: { args = super.args // { b = output.d; }; })
#
# nix-repl> obj = obj.extend (output: self: super: { val = super.val // { d = 10; }; })
#
# nix-repl> { inherit (obj) c d; }
# { c = 11; d = 10; }
makeExtensibleWithInterface = interface: f: let i = interface
(fix' (f i))
(fext: makeExtensibleWithInterface interface (i': (extends (fext i') (f i'))));
in i;
}
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