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Diffstat (limited to 'nixpkgs/lib/fixed-points.nix')
-rw-r--r-- | nixpkgs/lib/fixed-points.nix | 104 |
1 files changed, 104 insertions, 0 deletions
diff --git a/nixpkgs/lib/fixed-points.nix b/nixpkgs/lib/fixed-points.nix new file mode 100644 index 00000000000..968930526a6 --- /dev/null +++ b/nixpkgs/lib/fixed-points.nix @@ -0,0 +1,104 @@ +{ ... }: +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: 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); + }; +} |