lib/network: init

lib/default.nix

@@ -7,6 +7,7 @@ let
       callLibs = file: import file { inherit inputs lib self; };
     in
     {
+      network = callLibs ./network;
       path = callLibs ./path.nix;
     }
   );

lib/network/default.nix

@@ -0,0 +1,334 @@
+# Portions of this file are sourced from
+# https://gist.github.com/duairc/5c9bb3c922e5d501a1edb9e7b3b845ba
+{ lib, ... }:
+let
+  inherit (import ./internal.nix { inherit lib; }) typechecks builders implementations;
+in
+{
+  ip = {
+    # add :: (ip | mac | integer) -> ip -> ip
+    #
+    # Examples:
+    #
+    # Adding integer to IPv4:
+    # > net.ip.add 100 "10.0.0.1"
+    # "10.0.0.101"
+    #
+    # Adding IPv4 to IPv4:
+    # > net.ip.add "127.0.0.1" "10.0.0.1"
+    # "137.0.0.2"
+    #
+    # Adding IPv6 to IPv4:
+    # > net.ip.add "::cafe:beef" "10.0.0.1"
+    # "212.254.186.191"
+    #
+    # Adding MAC to IPv4 (overflows):
+    # > net.ip.add "fe:ed:fa:ce:f0:0d" "10.0.0.1"
+    # "4.206.240.14"
+    #
+    # Adding integer to IPv6:
+    # > net.ip.add 100 "dead:cafe:beef::"
+    # "dead:cafe:beef::64"
+    #
+    # Adding IPv4 to to IPv6:
+    # > net.ip.add "127.0.0.1" "dead:cafe:beef::"
+    # "dead:cafe:beef::7f00:1"
+    #
+    # Adding MAC to IPv6:
+    # > net.ip.add "fe:ed:fa:ce:f0:0d" "dead:cafe:beef::"
+    # "dead:cafe:beef::feed:face:f00d"
+    add =
+      delta: ip:
+      let
+        function = "net.ip.add";
+        delta' = typechecks.numeric function "delta" delta;
+        ip' = typechecks.ip function "ip" ip;
+      in
+      builders.ip (implementations.ip.add delta' ip');
+
+    # diff :: ip -> ip -> (integer | ipv6)
+    #
+    # net.ip.diff is the reverse of net.ip.add:
+    #
+    # net.ip.diff (net.ip.add a b) a = b
+    # net.ip.diff (net.ip.add a b) b = a
+    #
+    # The difference between net.ip.diff and net.ip.subtract is that
+    # net.ip.diff will try its best to return an integer (falling back
+    # to an IPv6 if the result is too big to fit in an integer). This is
+    # useful if you have two hosts that you know are on the same network
+    # and you just want to calculate the offset between them — a result
+    # like "0.0.0.10" is not very useful (which is what you would get
+    # from net.ip.subtract).
+    diff =
+      minuend: subtrahend:
+      let
+        function = "net.ip.diff";
+        minuend' = typechecks.ip function "minuend" minuend;
+        subtrahend' = typechecks.ip function "subtrahend" subtrahend;
+        result = implementations.ip.diff minuend' subtrahend';
+      in
+      if result ? ipv6 then builders.ipv6 result else result;
+
+    # subtract :: (ip | mac | integer) -> ip -> ip
+    #
+    # net.ip.subtract is also the reverse of net.ip.add:
+    #
+    # net.ip.subtract a (net.ip.add a b) = b
+    # net.ip.subtract b (net.ip.add a b) = a
+    #
+    # The difference between net.ip.subtract and net.ip.diff is that
+    # net.ip.subtract will always return the same type as its "ip"
+    # parameter. Its implementation takes the "delta" parameter,
+    # coerces it to be the same type as the "ip" paramter, negates it
+    # (using two's complement), and then adds it to "ip".
+    subtract =
+      delta: ip:
+      let
+        function = "net.ip.subtract";
+        delta' = typechecks.numeric function "delta" delta;
+        ip' = typechecks.ip function "ip" ip;
+      in
+      builders.ip (implementations.ip.subtract delta' ip');
+  };
+
+  mac = {
+    # add :: (ip | mac | integer) -> mac -> mac
+    #
+    # Examples:
+    #
+    # Adding integer to MAC:
+    # > net.mac.add 100 "fe:ed:fa:ce:f0:0d"
+    # "fe:ed:fa:ce:f0:71"
+    #
+    # Adding IPv4 to MAC:
+    # > net.mac.add "127.0.0.1" "fe:ed:fa:ce:f0:0d"
+    # "fe:ee:79:ce:f0:0e"
+    #
+    # Adding IPv6 to MAC:
+    # > net.mac.add "::cafe:beef" "fe:ed:fa:ce:f0:0d"
+    # "fe:ee:c5:cd:aa:cb
+    #
+    # Adding MAC to MAC:
+    # > net.mac.add "fe:ed:fa:00:00:00" "00:00:00:ce:f0:0d"
+    # "fe:ed:fa:ce:f0:0d"
+    add =
+      delta: mac:
+      let
+        function = "net.mac.add";
+        delta' = typechecks.numeric function "delta" delta;
+        mac' = typechecks.mac function "mac" mac;
+      in
+      builders.mac (implementations.mac.add delta' mac');
+
+    # diff :: mac -> mac -> integer
+    #
+    # net.mac.diff is the reverse of net.mac.add:
+    #
+    # net.mac.diff (net.mac.add a b) a = b
+    # net.mac.diff (net.mac.add a b) b = a
+    #
+    # The difference between net.mac.diff and net.mac.subtract is that
+    # net.mac.diff will always return an integer.
+    diff =
+      minuend: subtrahend:
+      let
+        function = "net.mac.diff";
+        minuend' = typechecks.mac function "minuend" minuend;
+        subtrahend' = typechecks.mac function "subtrahend" subtrahend;
+      in
+      implementations.mac.diff minuend' subtrahend';
+
+    # subtract :: (ip | mac | integer) -> mac -> mac
+    #
+    # net.mac.subtract is also the reverse of net.ip.add:
+    #
+    # net.mac.subtract a (net.mac.add a b) = b
+    # net.mac.subtract b (net.mac.add a b) = a
+    #
+    # The difference between net.mac.subtract and net.mac.diff is that
+    # net.mac.subtract will always return a MAC address.
+    subtract =
+      delta: mac:
+      let
+        function = "net.mac.subtract";
+        delta' = typechecks.numeric function "delta" delta;
+        mac' = typechecks.mac function "mac" mac;
+      in
+      builders.mac (implementations.mac.subtract delta' mac');
+  };
+
+  cidr = {
+    # add :: (ip | mac | integer) -> cidr -> cidr
+    #
+    # > net.cidr.add 2 "127.0.0.0/8"
+    # "129.0.0.0/8"
+    #
+    # > net.cidr.add (-2) "127.0.0.0/8"
+    # "125.0.0.0/8"
+    add =
+      delta: cidr:
+      let
+        function = "net.cidr.add";
+        delta' = typechecks.numeric function "delta" delta;
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      builders.cidr (implementations.cidr.add delta' cidr');
+
+    # child :: cidr -> cidr -> bool
+    #
+    # > net.cidr.child "10.10.10.0/24" "10.0.0.0/8"
+    # true
+    #
+    # > net.cidr.child "127.0.0.0/8" "10.0.0.0/8"
+    # false
+    child =
+      subcidr: cidr:
+      let
+        function = "net.cidr.child";
+        subcidr' = typechecks.cidr function "subcidr" subcidr;
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      implementations.cidr.child subcidr' cidr';
+
+    # contains :: ip -> cidr -> bool
+    #
+    # > net.cidr.contains "127.0.0.1" "127.0.0.0/8"
+    # true
+    #
+    # > net.cidr.contains "127.0.0.1" "192.168.0.0/16"
+    # false
+    contains =
+      ip: cidr:
+      let
+        function = "net.cidr.contains";
+        ip' = typechecks.ip function "ip" ip;
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      implementations.cidr.contains ip' cidr';
+
+    # capacity :: cidr -> integer
+    #
+    # > net.cidr.capacity "172.16.0.0/12"
+    # 1048576
+    #
+    # > net.cidr.capacity "dead:cafe:beef::/96"
+    # 4294967296
+    #
+    # > net.cidr.capacity "dead:cafe:beef::/48" (saturates to maxBound)
+    # 9223372036854775807
+    capacity =
+      cidr:
+      let
+        function = "net.cidr.capacity";
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      implementations.cidr.capacity cidr';
+
+    # host :: (ip | mac | integer) -> cidr -> ip
+    #
+    # > net.cidr.host 10000 "10.0.0.0/8"
+    # 10.0.39.16
+    #
+    # > net.cidr.host 10000 "dead:cafe:beef::/64"
+    # "dead:cafe:beef::2710"
+    #
+    # net.cidr.host "127.0.0.1" "dead:cafe:beef::/48"
+    # > "dead:cafe:beef::7f00:1"
+    #
+    # Inpsired by:
+    # https://www.terraform.io/docs/configuration/functions/cidrhost.html
+    host =
+      hostnum: cidr:
+      let
+        function = "net.cidr.host";
+        hostnum' = typechecks.numeric function "hostnum" hostnum;
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      builders.ip (implementations.cidr.host hostnum' cidr');
+
+    # length :: cidr -> integer
+    #
+    # > net.cidr.length "127.0.0.0/8"
+    # 8
+    #
+    # > net.cidr.length "dead:cafe:beef::/48"
+    # 48
+    length =
+      cidr:
+      let
+        function = "net.cidr.length";
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      implementations.cidr.length cidr';
+
+    # make :: integer -> ip -> cidr
+    #
+    # > net.cidr.make 24 "192.168.0.150"
+    # "192.168.0.0/24"
+    #
+    # > net.cidr.make 40 "dead:cafe:beef::feed:face:f00d"
+    # "dead:cafe:be00::/40"
+    make =
+      length: base:
+      let
+        function = "net.cidr.make";
+        length' = typechecks.int function "length" length;
+        base' = typechecks.ip function "base" base;
+      in
+      builders.cidr (implementations.cidr.make length' base');
+
+    # netmask :: cidr -> ip
+    #
+    # > net.cidr.netmask "192.168.0.0/24"
+    # "255.255.255.0"
+    #
+    # > net.cidr.netmask "dead:cafe:beef::/64"
+    # "ffff:ffff:ffff:ffff::"
+    netmask =
+      cidr:
+      let
+        function = "net.cidr.netmask";
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      builders.ip (implementations.cidr.netmask cidr');
+
+    # size :: cidr -> integer
+    #
+    # > net.cidr.size "127.0.0.0/8"
+    # 24
+    #
+    # > net.cidr.size "dead:cafe:beef::/48"
+    # 80
+    size =
+      cidr:
+      let
+        function = "net.cidr.size";
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      implementations.cidr.size cidr';
+
+    # subnet :: integer -> (ip | mac | integer) -> cidr -> cidr
+    #
+    # > net.cidr.subnet 4 2 "172.16.0.0/12"
+    # "172.18.0.0/16"
+    #
+    # > net.cidr.subnet 4 15 "10.1.2.0/24"
+    # "10.1.2.240/28"
+    #
+    # > net.cidr.subnet 16 162 "fd00:fd12:3456:7890::/56"
+    # "fd00:fd12:3456:7800:a200::/72"
+    #
+    # Inspired by:
+    # https://www.terraform.io/docs/configuration/functions/cidrsubnet.html
+    subnet =
+      length: netnum: cidr:
+      let
+        function = "net.cidr.subnet";
+        length' = typechecks.int function "length" length;
+        netnum' = typechecks.numeric function "netnum" netnum;
+        cidr' = typechecks.cidr function "cidr" cidr;
+      in
+      builders.cidr (implementations.cidr.subnet length' netnum' cidr');
+  };
+}

lib/network/internal.nix

@@ -0,0 +1,917 @@
+# Portions of this file are sourced from
+# https://gist.github.com/duairc/5c9bb3c922e5d501a1edb9e7b3b845ba
+{ ... }:
+let
+  list = {
+    cons = a: b: [ a ] ++ b;
+  };
+
+  bit = rec {
+    shift =
+      n: x:
+      if n < 0 then
+        x * math.pow 2 (-n)
+      else
+        let
+          safeDiv = n: d: if d == 0 then 0 else n / d;
+          d = math.pow 2 n;
+        in
+        if x < 0 then not (safeDiv (not x) d) else safeDiv x d;
+
+    left = n: shift (-n);
+
+    right = shift;
+
+    and = builtins.bitAnd;
+
+    or = builtins.bitOr;
+
+    xor = builtins.bitXor;
+
+    not = xor (-1);
+
+    mask = n: and (left n 1 - 1);
+  };
+
+  math = rec {
+    max = a: b: if a > b then a else b;
+
+    min = a: b: if a < b then a else b;
+
+    clamp =
+      a: b: c:
+      max a (min b c);
+
+    pow =
+      x: n:
+      if n == 0 then
+        1
+      else if bit.and n 1 != 0 then
+        x * pow (x * x) ((n - 1) / 2)
+      else
+        pow (x * x) (n / 2);
+  };
+
+  parsers =
+    let
+      # fmap :: (a -> b) -> parser a -> parser b
+      fmap = f: ma: bind ma (a: pure (f a));
+
+      # pure :: a -> parser a
+      pure = a: string: {
+        leftovers = string;
+        result = a;
+      };
+
+      # liftA2 :: (a -> b -> c) -> parser a -> parser b -> parser c
+      liftA2 =
+        f: ma: mb:
+        bind ma (a: bind mb (b: pure (f a b)));
+      liftA3 =
+        f: a: b:
+        ap (liftA2 f a b);
+      liftA4 =
+        f: a: b: c:
+        ap (liftA3 f a b c);
+      liftA5 =
+        f: a: b: c: d:
+        ap (liftA4 f a b c d);
+      liftA6 =
+        f: a: b: c: d: e:
+        ap (liftA5 f a b c d e);
+
+      # ap :: parser (a -> b) -> parser a -> parser b
+      ap = liftA2 (a: a);
+
+      # then_ :: parser a -> parser b -> parser b
+      then_ = liftA2 (_a: b: b);
+
+      # empty :: parser a
+      empty = _string: null;
+
+      # alt :: parser a -> parser a -> parser a
+      alt =
+        left: right: string:
+        let
+          result = left string;
+        in
+        if builtins.isNull result then right string else result;
+
+      # guard :: bool -> parser {}
+      guard = condition: if condition then pure { } else empty;
+
+      # mfilter :: (a -> bool) -> parser a -> parser a
+      mfilter = f: parser: bind parser (a: then_ (guard (f a)) (pure a));
+
+      # some :: parser a -> parser [a]
+      some = v: liftA2 list.cons v (many v);
+
+      # many :: parser a -> parser [a]
+      many = v: alt (some v) (pure [ ]);
+
+      # bind :: parser a -> (a -> parser b) -> parser b
+      bind =
+        parser: f: string:
+        let
+          a = parser string;
+        in
+        if builtins.isNull a then null else f a.result a.leftovers;
+
+      # run :: parser a -> string -> maybe a
+      run =
+        parser: string:
+        let
+          result = parser string;
+        in
+        if builtins.isNull result || result.leftovers != "" then null else result.result;
+
+      next =
+        string:
+        if string == "" then
+          null
+        else
+          {
+            leftovers = builtins.substring 1 (-1) string;
+            result = builtins.substring 0 1 string;
+          };
+
+      # Count how many characters were consumed by a parser
+      count =
+        parser: string:
+        let
+          result = parser string;
+        in
+        if builtins.isNull result then
+          null
+        else
+          result
+          // {
+            result = {
+              inherit (result) result;
+              count = with result; builtins.stringLength string - builtins.stringLength leftovers;
+            };
+          };
+
+      # Limit the parser to n characters at most
+      limit = n: parser: fmap (a: a.result) (mfilter (a: a.count <= n) (count parser));
+
+      # Ensure the parser consumes exactly n characters
+      exactly = n: parser: fmap (a: a.result) (mfilter (a: a.count == n) (count parser));
+
+      char = c: bind next (c': guard (c == c'));
+
+      string =
+        css:
+        if css == "" then
+          pure { }
+        else
+          let
+            c = builtins.substring 0 1 css;
+            cs = builtins.substring 1 (-1) css;
+          in
+          then_ (char c) (string cs);
+
+      digit = set: bind next (c: then_ (guard (builtins.hasAttr c set)) (pure (builtins.getAttr c set)));
+
+      decimalDigits = {
+        "0" = 0;
+        "1" = 1;
+        "2" = 2;
+        "3" = 3;
+        "4" = 4;
+        "5" = 5;
+        "6" = 6;
+        "7" = 7;
+        "8" = 8;
+        "9" = 9;
+      };
+
+      hexadecimalDigits = decimalDigits // {
+        "a" = 10;
+        "b" = 11;
+        "c" = 12;
+        "d" = 13;
+        "e" = 14;
+        "f" = 15;
+        "A" = 10;
+        "B" = 11;
+        "C" = 12;
+        "D" = 13;
+        "E" = 14;
+        "F" = 15;
+      };
+
+      fromDecimalDigits = builtins.foldl' (a: c: a * 10 + c) 0;
+      fromHexadecimalDigits = builtins.foldl' (a: bit.or (bit.left 4 a)) 0;
+
+      # disallow leading zeros
+      decimal = bind (digit decimalDigits) (
+        n:
+        if n == 0 then
+          pure 0
+        else
+          fmap (ns: fromDecimalDigits (list.cons n ns)) (many (digit decimalDigits))
+      );
+
+      hexadecimal = fmap fromHexadecimalDigits (some (digit hexadecimalDigits));
+
+      ipv4 =
+        let
+          dot = char ".";
+
+          octet = mfilter (n: n < 256) decimal;
+
+          octet' = then_ dot octet;
+
+          fromOctets = a: b: c: d: {
+            ipv4 = bit.or (bit.left 8 (bit.or (bit.left 8 (bit.or (bit.left 8 a) b)) c)) d;
+          };
+        in
+        liftA4 fromOctets octet octet' octet' octet';
+
+      # This is more or less a literal translation of
+      # https://hackage.haskell.org/package/ip/docs/src/Net.IPv6.html#parser
+      ipv6 =
+        let
+          colon = char ":";
+
+          hextet = limit 4 hexadecimal;
+
+          fromHextets =
+            hextets:
+            if builtins.length hextets != 8 then
+              empty
+            else
+              let
+                a = builtins.elemAt hextets 0;
+                b = builtins.elemAt hextets 1;
+                c = builtins.elemAt hextets 2;
+                d = builtins.elemAt hextets 3;
+                e = builtins.elemAt hextets 4;
+                f = builtins.elemAt hextets 5;
+                g = builtins.elemAt hextets 6;
+                h = builtins.elemAt hextets 7;
+              in
+              pure {
+                ipv6 = {
+                  a = bit.or (bit.left 16 a) b;
+                  b = bit.or (bit.left 16 c) d;
+                  c = bit.or (bit.left 16 e) f;
+                  d = bit.or (bit.left 16 g) h;
+                };
+              };
+
+          ipv4' = fmap (
+            address:
+            let
+              upper = bit.right 16 address.ipv4;
+              lower = bit.mask 16 address.ipv4;
+            in
+            [
+              upper
+              lower
+            ]
+          ) ipv4;
+
+          part =
+            n:
+            let
+              n' = n + 1;
+              hex = liftA2 list.cons hextet (then_ colon (alt (then_ colon (doubleColon n')) (part n')));
+            in
+            if n == 7 then
+              fmap (a: [ a ]) hextet
+            else if n == 6 then
+              alt ipv4' hex
+            else
+              hex;
+
+          doubleColon =
+            n:
+            bind (alt afterDoubleColon (pure [ ])) (
+              rest:
+              let
+                missing = 8 - n - builtins.length rest;
+              in
+              if missing < 0 then empty else pure (builtins.genList (_: 0) missing ++ rest)
+            );
+
+          afterDoubleColon = alt ipv4' (
+            liftA2 list.cons hextet (alt (then_ colon afterDoubleColon) (pure [ ]))
+          );
+        in
+        bind (alt (then_ (string "::") (doubleColon 0)) (part 0)) fromHextets;
+
+      cidrv4 = liftA2 (base: length: implementations.cidr.make length base) ipv4 (
+        then_ (char "/") (mfilter (n: n <= 32) decimal)
+      );
+
+      cidrv6 = liftA2 (base: length: implementations.cidr.make length base) ipv6 (
+        then_ (char "/") (mfilter (n: n <= 128) decimal)
+      );
+
+      mac =
+        let
+          colon = char ":";
+
+          octet = exactly 2 hexadecimal;
+
+          octet' = then_ colon octet;
+
+          fromOctets = a: b: c: d: e: f: {
+            mac = bit.or (bit.left 8 (
+              bit.or (bit.left 8 (bit.or (bit.left 8 (bit.or (bit.left 8 (bit.or (bit.left 8 a) b)) c)) d)) e
+            )) f;
+          };
+        in
+        liftA6 fromOctets octet octet' octet' octet' octet' octet';
+    in
+    {
+      ipv4 = run ipv4;
+      ipv6 = run ipv6;
+      ip = run (alt ipv4 ipv6);
+      cidrv4 = run cidrv4;
+      cidrv6 = run cidrv6;
+      cidr = run (alt cidrv4 cidrv6);
+      mac = run mac;
+      numeric = run (alt (alt ipv4 ipv6) mac);
+    };
+
+  builders =
+    let
+      ipv4 =
+        address:
+        let
+          abcd = address.ipv4;
+          abc = bit.right 8 abcd;
+          ab = bit.right 8 abc;
+          a = bit.right 8 ab;
+          b = bit.mask 8 ab;
+          c = bit.mask 8 abc;
+          d = bit.mask 8 abcd;
+        in
+        builtins.concatStringsSep "." (
+          map toString [
+            a
+            b
+            c
+            d
+          ]
+        );
+
+      # This is more or less a literal translation of
+      # https://hackage.haskell.org/package/ip/docs/src/Net.IPv6.html#encode
+      ipv6 =
+        address:
+        let
+          digits = "0123456789abcdef";
+
+          toHexString =
+            n:
+            let
+              rest = bit.right 4 n;
+              current = bit.mask 4 n;
+              prefix = if rest == 0 then "" else toHexString rest;
+            in
+            "${prefix}${builtins.substring current 1 digits}";
+        in
+        if (with address.ipv6; a == 0 && b == 0 && c == 0 && d > 65535) then
+          "::${ipv4 { ipv4 = address.ipv6.d; }}"
+        else if (with address.ipv6; a == 0 && b == 0 && c == 65535) then
+          "::ffff:${ipv4 { ipv4 = address.ipv6.d; }}"
+        else
+          let
+            a = bit.right 16 address.ipv6.a;
+            b = bit.mask 16 address.ipv6.a;
+            c = bit.right 16 address.ipv6.b;
+            d = bit.mask 16 address.ipv6.b;
+            e = bit.right 16 address.ipv6.c;
+            f = bit.mask 16 address.ipv6.c;
+            g = bit.right 16 address.ipv6.d;
+            h = bit.mask 16 address.ipv6.d;
+
+            hextets = [
+              a
+              b
+              c
+              d
+              e
+              f
+              g
+              h
+            ];
+
+            # calculate the position and size of the longest sequence of
+            # zeroes within the list of hextets
+            longest =
+              let
+                go =
+                  i: current: best:
+                  if i < builtins.length hextets then
+                    let
+                      n = builtins.elemAt hextets i;
+
+                      current' =
+                        if n == 0 then
+                          if builtins.isNull current then
+                            {
+                              size = 1;
+                              position = i;
+                            }
+                          else
+                            current
+                            // {
+                              size = current.size + 1;
+                            }
+                        else
+                          null;
+
+                      best' =
+                        if n == 0 then
+                          if builtins.isNull best then
+                            current'
+                          else if current'.size > best.size then
+                            current'
+                          else
+                            best
+                        else
+                          best;
+                    in
+                    go (i + 1) current' best'
+                  else
+                    best;
+              in
+              go 0 null null;
+
+            format = hextets: builtins.concatStringsSep ":" (map toHexString hextets);
+          in
+          if builtins.isNull longest then
+            format hextets
+          else
+            let
+              sublist =
+                i: length: xs:
+                map (builtins.elemAt xs) (builtins.genList (x: x + i) length);
+
+              end = longest.position + longest.size;
+
+              before = sublist 0 longest.position hextets;
+
+              after = sublist end (builtins.length hextets - end) hextets;
+            in
+            "${format before}::${format after}";
+
+      ip = address: if address ? ipv4 then ipv4 address else ipv6 address;
+
+      cidrv4 = cidr: "${ipv4 cidr.base}/${toString cidr.length}";
+
+      cidrv6 = cidr: "${ipv6 cidr.base}/${toString cidr.length}";
+
+      cidr = cidr: "${ip cidr.base}/${toString cidr.length}";
+
+      mac =
+        address:
+        let
+          digits = "0123456789abcdef";
+          octet =
+            n:
+            let
+              upper = bit.right 4 n;
+              lower = bit.mask 4 n;
+            in
+            "${builtins.substring upper 1 digits}${builtins.substring lower 1 digits}";
+        in
+        let
+          a = bit.mask 8 (bit.right 40 address.mac);
+          b = bit.mask 8 (bit.right 32 address.mac);
+          c = bit.mask 8 (bit.right 24 address.mac);
+          d = bit.mask 8 (bit.right 16 address.mac);
+          e = bit.mask 8 (bit.right 8 address.mac);
+          f = bit.mask 8 (bit.right 0 address.mac);
+        in
+        "${octet a}:${octet b}:${octet c}:${octet d}:${octet e}:${octet f}";
+    in
+    {
+      inherit
+        ipv4
+        ipv6
+        ip
+        cidrv4
+        cidrv6
+        cidr
+        mac
+        ;
+    };
+
+  arithmetic = rec {
+    # or :: (ip | mac | integer) -> (ip | mac | integer) -> (ip | mac | integer)
+    or =
+      a_: b:
+      let
+        a = coerce b a_;
+      in
+      if a ? ipv6 then
+        {
+          ipv6 = {
+            a = bit.or a.ipv6.a b.ipv6.a;
+            b = bit.or a.ipv6.b b.ipv6.b;
+            c = bit.or a.ipv6.c b.ipv6.c;
+            d = bit.or a.ipv6.d b.ipv6.d;
+          };
+        }
+      else if a ? ipv4 then
+        {
+          ipv4 = bit.or a.ipv4 b.ipv4;
+        }
+      else if a ? mac then
+        {
+          mac = bit.or a.mac b.mac;
+        }
+      else
+        bit.or a b;
+
+    # and :: (ip | mac | integer) -> (ip | mac | integer) -> (ip | mac | integer)
+    and =
+      a_: b:
+      let
+        a = coerce b a_;
+      in
+      if a ? ipv6 then
+        {
+          ipv6 = {
+            a = bit.and a.ipv6.a b.ipv6.a;
+            b = bit.and a.ipv6.b b.ipv6.b;
+            c = bit.and a.ipv6.c b.ipv6.c;
+            d = bit.and a.ipv6.d b.ipv6.d;
+          };
+        }
+      else if a ? ipv4 then
+        {
+          ipv4 = bit.and a.ipv4 b.ipv4;
+        }
+      else if a ? mac then
+        {
+          mac = bit.and a.mac b.mac;
+        }
+      else
+        bit.and a b;
+
+    # not :: (ip | mac | integer) -> (ip | mac | integer)
+    not =
+      a:
+      if a ? ipv6 then
+        {
+          ipv6 = {
+            a = bit.mask 32 (bit.not a.ipv6.a);
+            b = bit.mask 32 (bit.not a.ipv6.b);
+            c = bit.mask 32 (bit.not a.ipv6.c);
+            d = bit.mask 32 (bit.not a.ipv6.d);
+          };
+        }
+      else if a ? ipv4 then
+        {
+          ipv4 = bit.mask 32 (bit.not a.ipv4);
+        }
+      else if a ? mac then
+        {
+          mac = bit.mask 48 (bit.not a.mac);
+        }
+      else
+        bit.not a;
+
+    # add :: (ip | mac | integer) -> (ip | mac | integer) -> (ip | mac | integer)
+    add =
+      let
+        split = a: {
+          fst = bit.mask 32 (bit.right 32 a);
+          snd = bit.mask 32 a;
+        };
+      in
+      a_: b:
+      let
+        a = coerce b a_;
+      in
+      if a ? ipv6 then
+        let
+          a' = split (a.ipv6.a + b.ipv6.a + b'.fst);
+          b' = split (a.ipv6.b + b.ipv6.b + c'.fst);
+          c' = split (a.ipv6.c + b.ipv6.c + d'.fst);
+          d' = split (a.ipv6.d + b.ipv6.d);
+        in
+        {
+          ipv6 = {
+            a = a'.snd;
+            b = b'.snd;
+            c = c'.snd;
+            d = d'.snd;
+          };
+        }
+      else if a ? ipv4 then
+        {
+          ipv4 = bit.mask 32 (a.ipv4 + b.ipv4);
+        }
+      else if a ? mac then
+        {
+          mac = bit.mask 48 (a.mac + b.mac);
+        }
+      else
+        a + b;
+
+    # subtract :: (ip | mac | integer) -> (ip | mac | integer) -> (ip | mac | integer)
+    subtract = a: b: add (add 1 (not (coerce b a))) b;
+
+    # diff :: (ip | mac | integer) -> (ip | mac | integer) -> (ipv6 | integer)
+    diff =
+      a: b:
+      let
+        toIPv6 = coerce ({ ipv6.a = 0; });
+        result = (subtract b (toIPv6 a)).ipv6;
+        max32 = bit.left 32 1 - 1;
+      in
+      if
+        result.a == 0 && result.b == 0 && bit.right 31 result.c == 0
+        || result.a == max32 && result.b == max32 && bit.right 31 result.c == 1
+      then
+        bit.or (bit.left 32 result.c) result.d
+      else
+        {
+          ipv6 = result;
+        };
+
+    # left :: integer -> (ip | mac | integer) -> (ip | mac | integer)
+    left = i: right (-i);
+
+    # right :: integer -> (ip | mac | integer) -> (ip | mac | integer)
+    right =
+      let
+        step = i: x: {
+          _1 = bit.mask 32 (bit.right (i + 96) x);
+          _2 = bit.mask 32 (bit.right (i + 64) x);
+          _3 = bit.mask 32 (bit.right (i + 32) x);
+          _4 = bit.mask 32 (bit.right i x);
+          _5 = bit.mask 32 (bit.right (i - 32) x);
+          _6 = bit.mask 32 (bit.right (i - 64) x);
+          _7 = bit.mask 32 (bit.right (i - 96) x);
+        };
+        ors = builtins.foldl' bit.or 0;
+      in
+      i: x:
+      if x ? ipv6 then
+        let
+          a' = step i x.ipv6.a;
+          b' = step i x.ipv6.b;
+          c' = step i x.ipv6.c;
+          d' = step i x.ipv6.d;
+        in
+        {
+          ipv6 = {
+            a = ors [
+              a'._4
+              b'._3
+              c'._2
+              d'._1
+            ];
+            b = ors [
+              a'._5
+              b'._4
+              c'._3
+              d'._2
+            ];
+            c = ors [
+              a'._6
+              b'._5
+              c'._4
+              d'._3
+            ];
+            d = ors [
+              a'._7
+              b'._6
+              c'._5
+              d'._4
+            ];
+          };
+        }
+      else if x ? ipv4 then
+        {
+          ipv4 = bit.mask 32 (bit.right i x.ipv4);
+        }
+      else if x ? mac then
+        {
+          mac = bit.mask 48 (bit.right i x.mac);
+        }
+      else
+        bit.right i x;
+
+    # shadow :: integer -> (ip | mac | integer) -> (ip | mac | integer)
+    shadow = n: a: and (right n (left n (coerce a (-1)))) a;
+
+    # coshadow :: integer -> (ip | mac | integer) -> (ip | mac | integer)
+    coshadow = n: a: and (not (right n (left n (coerce a (-1))))) a;
+
+    # coerce :: (ip | mac | integer) -> (ip | mac | integer) -> (ip | mac | integer)
+    coerce =
+      target: value:
+      if target ? ipv6 then
+        if value ? ipv6 then
+          value
+        else if value ? ipv4 then
+          {
+            ipv6 = {
+              a = 0;
+              b = 0;
+              c = 0;
+              d = value.ipv4;
+            };
+          }
+        else if value ? mac then
+          {
+            ipv6 = {
+              a = 0;
+              b = 0;
+              c = bit.right 32 value.mac;
+              d = bit.mask 32 value.mac;
+            };
+          }
+        else
+          {
+            ipv6 = {
+              a = bit.mask 32 (bit.right 96 value);
+              b = bit.mask 32 (bit.right 64 value);
+              c = bit.mask 32 (bit.right 32 value);
+              d = bit.mask 32 value;
+            };
+          }
+      else if target ? ipv4 then
+        if value ? ipv6 then
+          {
+            ipv4 = value.ipv6.d;
+          }
+        else if value ? ipv4 then
+          value
+        else if value ? mac then
+          {
+            ipv4 = bit.mask 32 value.mac;
+          }
+        else
+          {
+            ipv4 = bit.mask 32 value;
+          }
+      else if target ? mac then
+        if value ? ipv6 then
+          {
+            mac = bit.or (bit.left 32 (bit.mask 16 value.ipv6.c)) value.ipv6.d;
+          }
+        else if value ? ipv4 then
+          {
+            mac = value.ipv4;
+          }
+        else if value ? mac then
+          value
+        else
+          {
+            mac = bit.mask 48 value;
+          }
+      else if value ? ipv6 then
+        builtins.foldl' bit.or 0 [
+          (bit.left 96 value.ipv6.a)
+          (bit.left 64 value.ipv6.b)
+          (bit.left 32 value.ipv6.c)
+          value.ipv6.d
+        ]
+      else if value ? ipv4 then
+        value.ipv4
+      else if value ? mac then
+        value.mac
+      else
+        value;
+  };
+
+  implementations = {
+    ip = {
+      # add :: (ip | mac | integer) -> ip -> ip
+      add = arithmetic.add;
+
+      # diff :: ip -> ip -> (ipv6 | integer)
+      diff = arithmetic.diff;
+
+      # subtract :: (ip | mac | integer) -> ip -> ip
+      subtract = arithmetic.subtract;
+    };
+
+    mac = {
+      # add :: (ip | mac | integer) -> mac -> mac
+      add = arithmetic.add;
+
+      # diff :: mac -> mac -> (ipv6 | integer)
+      diff = arithmetic.diff;
+
+      # subtract :: (ip | mac | integer) -> mac -> mac
+      subtract = arithmetic.subtract;
+    };
+
+    cidr = rec {
+      # add :: (ip | mac | integer) -> cidr -> cidr
+      add =
+        delta: cidr:
+        let
+          size' = size cidr;
+        in
+        {
+          base = arithmetic.left size' (arithmetic.add delta (arithmetic.right size' cidr.base));
+          inherit (cidr) length;
+        };
+
+      # capacity :: cidr -> integer
+      capacity =
+        cidr:
+        let
+          size' = size cidr;
+        in
+        if size' > 62 then
+          9223372036854775807 # maxBound to prevent overflow
+        else
+          bit.left size' 1;
+
+      # child :: cidr -> cidr -> bool
+      child = subcidr: cidr: length subcidr > length cidr && contains (host 0 subcidr) cidr;
+
+      # contains :: ip -> cidr -> bool
+      contains = ip: cidr: host 0 (make cidr.length ip) == host 0 cidr;
+
+      # host :: (ip | mac | integer) -> cidr -> ip
+      host =
+        index: cidr:
+        let
+          index' = arithmetic.coerce cidr.base index;
+        in
+        arithmetic.or (arithmetic.shadow cidr.length index') cidr.base;
+
+      # length :: cidr -> integer
+      length = cidr: cidr.length;
+
+      # netmask :: cidr -> ip
+      netmask = cidr: arithmetic.coshadow cidr.length (arithmetic.coerce cidr.base (-1));
+
+      # size :: cidr -> integer
+      size = cidr: (if cidr.base ? ipv6 then 128 else 32) - cidr.length;
+
+      # subnet :: integer -> (ip | mac | integer) -> cidr -> cidr
+      subnet =
+        length: index: cidr:
+        let
+          length' = cidr.length + length;
+          index' = arithmetic.coerce cidr.base index;
+          size = (if cidr.base ? ipv6 then 128 else 32) - length';
+        in
+        make length' (host (arithmetic.left size index') cidr);
+
+      # make :: integer -> ip -> cidr
+      make =
+        length: base:
+        let
+          length' = math.clamp 0 (if base ? ipv6 then 128 else 32) length;
+        in
+        {
+          base = arithmetic.coshadow length' base;
+          length = length';
+        };
+    };
+  };
+
+  typechecks =
+    let
+      fail =
+        description: function: argument:
+        builtins.throw "${function}: ${argument} parameter must be ${description}";
+
+      meta =
+        parser: description: function: argument: input:
+        let
+          error = fail description function argument;
+        in
+        if !builtins.isString input then
+          error
+        else
+          let
+            result = parser input;
+          in
+          if builtins.isNull result then error else result;
+    in
+    {
+      int =
+        function: argument: input:
+        if builtins.isInt input then input else fail "an integer" function argument;
+      ip = meta parsers.ip "an IPv4 or IPv6 address";
+      cidr = meta parsers.cidr "an IPv4 or IPv6 address range in CIDR notation";
+      mac = meta parsers.mac "a MAC address";
+      numeric =
+        function: argument: input:
+        if builtins.isInt input then
+          input
+        else
+          meta parsers.numeric "an integer or IPv4, IPv6 or MAC address" function argument input;
+    };
+in
+{
+  inherit typechecks builders implementations;
+}