105 lines
4.2 KiB
Nix
105 lines
4.2 KiB
Nix
{ ... }:
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rec {
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# Compute the fixed point of the given function `f`, which is usually an
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# attribute set that expects its final, non-recursive representation as an
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# argument:
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#
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# f = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }
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#
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# Nix evaluates this recursion until all references to `self` have been
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# resolved. At that point, the final result is returned and `f x = x` holds:
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#
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# nix-repl> fix f
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# { bar = "bar"; foo = "foo"; foobar = "foobar"; }
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#
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# Type: fix :: (a -> a) -> a
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#
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# See https://en.wikipedia.org/wiki/Fixed-point_combinator for further
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# details.
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fix = f: let x = f x; in x;
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# A variant of `fix` that records the original recursive attribute set in the
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# result. This is useful in combination with the `extends` function to
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# implement deep overriding. See pkgs/development/haskell-modules/default.nix
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# for a concrete example.
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fix' = f: let x = f x // { __unfix__ = f; }; in x;
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# Return the fixpoint that `f` converges to when called recursively, starting
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# with the input `x`.
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#
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# nix-repl> converge (x: x / 2) 16
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# 0
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converge = f: x:
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let
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x' = f x;
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in
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if x' == x
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then x
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else converge f x';
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# Modify the contents of an explicitly recursive attribute set in a way that
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# honors `self`-references. This is accomplished with a function
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#
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# g = self: super: { foo = super.foo + " + "; }
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#
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# that has access to the unmodified input (`super`) as well as the final
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# non-recursive representation of the attribute set (`self`). `extends`
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# differs from the native `//` operator insofar as that it's applied *before*
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# references to `self` are resolved:
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#
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# nix-repl> fix (extends g f)
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# { bar = "bar"; foo = "foo + "; foobar = "foo + bar"; }
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#
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# The name of the function is inspired by object-oriented inheritance, i.e.
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# think of it as an infix operator `g extends f` that mimics the syntax from
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# Java. It may seem counter-intuitive to have the "base class" as the second
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# argument, but it's nice this way if several uses of `extends` are cascaded.
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#
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# To get a better understanding how `extends` turns a function with a fix
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# point (the package set we start with) into a new function with a different fix
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# point (the desired packages set) lets just see, how `extends g f`
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# unfolds with `g` and `f` defined above:
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#
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# extends g f = self: let super = f self; in super // g self super;
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# = self: let super = { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }; in super // g self super
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# = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; } // g self { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; }
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# = self: { foo = "foo"; bar = "bar"; foobar = self.foo + self.bar; } // { foo = "foo" + " + "; }
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# = self: { foo = "foo + "; bar = "bar"; foobar = self.foo + self.bar; }
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#
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extends = f: rattrs: self: let super = rattrs self; in super // f self super;
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# Compose two extending functions of the type expected by 'extends'
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# into one where changes made in the first are available in the
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# 'super' of the second
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composeExtensions =
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f: g: self: super:
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let fApplied = f self super;
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super' = super // fApplied;
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in fApplied // g self super';
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# Create an overridable, recursive attribute set. For example:
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#
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# nix-repl> obj = makeExtensible (self: { })
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#
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# nix-repl> obj
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# { __unfix__ = «lambda»; extend = «lambda»; }
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#
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# nix-repl> obj = obj.extend (self: super: { foo = "foo"; })
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#
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# nix-repl> obj
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# { __unfix__ = «lambda»; extend = «lambda»; foo = "foo"; }
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#
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# nix-repl> obj = obj.extend (self: super: { foo = super.foo + " + "; bar = "bar"; foobar = self.foo + self.bar; })
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#
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# nix-repl> obj
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# { __unfix__ = «lambda»; bar = "bar"; extend = «lambda»; foo = "foo + "; foobar = "foo + bar"; }
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makeExtensible = makeExtensibleWithCustomName "extend";
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# Same as `makeExtensible` but the name of the extending attribute is
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# customized.
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makeExtensibleWithCustomName = extenderName: rattrs:
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fix' rattrs // {
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${extenderName} = f: makeExtensibleWithCustomName extenderName (extends f rattrs);
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};
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}
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