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author | Robert Hensing <robert@roberthensing.nl> | 2023-07-08 18:43:36 +0200 |
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committer | Robert Hensing <robert@roberthensing.nl> | 2023-07-08 18:46:08 +0200 |
commit | aa1beb0ab589b017a80927282d3ab60553071f71 (patch) | |
tree | 6e13b0aa60eac6bf99ca7c4991f137ffc10130e4 /lib/fixed-points.nix | |
parent | e08fab0406465bc1ba9f4d2895159c89e952ad71 (diff) | |
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doc: Render lib.fixedPoints
Diffstat (limited to 'lib/fixed-points.nix')
-rw-r--r-- | lib/fixed-points.nix | 196 |
1 files changed, 115 insertions, 81 deletions
diff --git a/lib/fixed-points.nix b/lib/fixed-points.nix index 926428293c1..a63f349b713 100644 --- a/lib/fixed-points.nix +++ b/lib/fixed-points.nix @@ -1,34 +1,49 @@ { 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. + /* + 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. + /* + A variant of `fix` that records the original recursive attribute set in the + result, in an attribute named `__unfix__`. + + This is useful in combination with the `extends` function to + implement deep overriding. + */ 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 + /* + Return the fixpoint that `f` converges to when called iteratively, starting + with the input `x`. + + ``` + nix-repl> converge (x: x / 2) 16 + 0 + ``` + + Type: (a -> a) -> a -> a + */ converge = f: x: let x' = f x; @@ -37,75 +52,94 @@ rec { 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; } - # + /* + Modify the contents of an explicitly recursive attribute set in a way that + honors `self`-references. This is accomplished with a function + + ```nix + 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 + /* + 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 + /* + 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"; } + /* + 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. + /* + 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); |