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+# Definitions related to run-time type checking.  Used in particular
+# to type-check NixOS configurations.
+{ lib }:
+
+let
+  inherit (lib)
+    elem
+    flip
+    functionArgs
+    isAttrs
+    isBool
+    isDerivation
+    isFloat
+    isFunction
+    isInt
+    isList
+    isString
+    isStorePath
+    setFunctionArgs
+    toDerivation
+    toList
+    ;
+  inherit (lib.lists)
+    all
+    concatLists
+    count
+    elemAt
+    filter
+    foldl'
+    head
+    imap1
+    last
+    length
+    tail
+    ;
+  inherit (lib.attrsets)
+    attrNames
+    filterAttrs
+    hasAttr
+    mapAttrs
+    optionalAttrs
+    zipAttrsWith
+    ;
+  inherit (lib.options)
+    getFiles
+    getValues
+    mergeDefaultOption
+    mergeEqualOption
+    mergeOneOption
+    mergeUniqueOption
+    showFiles
+    showOption
+    ;
+  inherit (lib.strings)
+    concatMapStringsSep
+    concatStringsSep
+    escapeNixString
+    isCoercibleToString
+    ;
+  inherit (lib.trivial)
+    boolToString
+    ;
+
+  inherit (lib.modules)
+    mergeDefinitions
+    fixupOptionType
+    mergeOptionDecls
+    ;
+  outer_types =
+rec {
+  isType = type: x: (x._type or "") == type;
+
+  setType = typeName: value: value // {
+    _type = typeName;
+  };
+
+
+  # Default type merging function
+  # takes two type functors and return the merged type
+  defaultTypeMerge = f: f':
+    let wrapped = f.wrapped.typeMerge f'.wrapped.functor;
+        payload = f.binOp f.payload f'.payload;
+    in
+    # cannot merge different types
+    if f.name != f'.name
+       then null
+    # simple types
+    else if    (f.wrapped == null && f'.wrapped == null)
+            && (f.payload == null && f'.payload == null)
+       then f.type
+    # composed types
+    else if (f.wrapped != null && f'.wrapped != null) && (wrapped != null)
+       then f.type wrapped
+    # value types
+    else if (f.payload != null && f'.payload != null) && (payload != null)
+       then f.type payload
+    else null;
+
+  # Default type functor
+  defaultFunctor = name: {
+    inherit name;
+    type    = types.${name} or null;
+    wrapped = null;
+    payload = null;
+    binOp   = a: b: null;
+  };
+
+  isOptionType = isType "option-type";
+  mkOptionType =
+    { # Human-readable representation of the type, should be equivalent to
+      # the type function name.
+      name
+    , # Description of the type, defined recursively by embedding the wrapped type if any.
+      description ? null
+    , # Function applied to each definition that should return true if
+      # its type-correct, false otherwise.
+      check ? (x: true)
+    , # Merge a list of definitions together into a single value.
+      # This function is called with two arguments: the location of
+      # the option in the configuration as a list of strings
+      # (e.g. ["boot" "loader "grub" "enable"]), and a list of
+      # definition values and locations (e.g. [ { file = "/foo.nix";
+      # value = 1; } { file = "/bar.nix"; value = 2 } ]).
+      merge ? mergeDefaultOption
+    , # Whether this type has a value representing nothingness. If it does,
+      # this should be a value of the form { value = <the nothing value>; }
+      # If it doesn't, this should be {}
+      # This may be used when a value is required for `mkIf false`. This allows the extra laziness in e.g. `lazyAttrsOf`.
+      emptyValue ? {}
+    , # Return a flat list of sub-options.  Used to generate
+      # documentation.
+      getSubOptions ? prefix: {}
+    , # List of modules if any, or null if none.
+      getSubModules ? null
+    , # Function for building the same option type with a different list of
+      # modules.
+      substSubModules ? m: null
+    , # Function that merge type declarations.
+      # internal, takes a functor as argument and returns the merged type.
+      # returning null means the type is not mergeable
+      typeMerge ? defaultTypeMerge functor
+    , # The type functor.
+      # internal, representation of the type as an attribute set.
+      #   name: name of the type
+      #   type: type function.
+      #   wrapped: the type wrapped in case of compound types.
+      #   payload: values of the type, two payloads of the same type must be
+      #            combinable with the binOp binary operation.
+      #   binOp: binary operation that merge two payloads of the same type.
+      functor ? defaultFunctor name
+    , # The deprecation message to display when this type is used by an option
+      # If null, the type isn't deprecated
+      deprecationMessage ? null
+    , # The types that occur in the definition of this type. This is used to
+      # issue deprecation warnings recursively. Can also be used to reuse
+      # nested types
+      nestedTypes ? {}
+    }:
+    { _type = "option-type";
+      inherit name check merge emptyValue getSubOptions getSubModules substSubModules typeMerge functor deprecationMessage nestedTypes;
+      description = if description == null then name else description;
+    };
+
+
+  # When adding new types don't forget to document them in
+  # nixos/doc/manual/development/option-types.xml!
+  types = rec {
+
+    raw = mkOptionType rec {
+      name = "raw";
+      description = "raw value";
+      check = value: true;
+      merge = mergeOneOption;
+    };
+
+    anything = mkOptionType {
+      name = "anything";
+      description = "anything";
+      check = value: true;
+      merge = loc: defs:
+        let
+          getType = value:
+            if isAttrs value && isCoercibleToString value
+            then "stringCoercibleSet"
+            else builtins.typeOf value;
+
+          # Returns the common type of all definitions, throws an error if they
+          # don't have the same type
+          commonType = foldl' (type: def:
+            if getType def.value == type
+            then type
+            else throw "The option `${showOption loc}' has conflicting option types in ${showFiles (getFiles defs)}"
+          ) (getType (head defs).value) defs;
+
+          mergeFunction = {
+            # Recursively merge attribute sets
+            set = (attrsOf anything).merge;
+            # Safe and deterministic behavior for lists is to only accept one definition
+            # listOf only used to apply mkIf and co.
+            list =
+              if length defs > 1
+              then throw "The option `${showOption loc}' has conflicting definitions, in ${showFiles (getFiles defs)}."
+              else (listOf anything).merge;
+            # This is the type of packages, only accept a single definition
+            stringCoercibleSet = mergeOneOption;
+            lambda = loc: defs: arg: anything.merge
+              (loc ++ [ "<function body>" ])
+              (map (def: {
+                file = def.file;
+                value = def.value arg;
+              }) defs);
+            # Otherwise fall back to only allowing all equal definitions
+          }.${commonType} or mergeEqualOption;
+        in mergeFunction loc defs;
+    };
+
+    unspecified = mkOptionType {
+      name = "unspecified";
+    };
+
+    bool = mkOptionType {
+      name = "bool";
+      description = "boolean";
+      check = isBool;
+      merge = mergeEqualOption;
+    };
+
+    int = mkOptionType {
+        name = "int";
+        description = "signed integer";
+        check = isInt;
+        merge = mergeEqualOption;
+      };
+
+    # Specialized subdomains of int
+    ints =
+      let
+        betweenDesc = lowest: highest:
+          "${toString lowest} and ${toString highest} (both inclusive)";
+        between = lowest: highest:
+          assert lib.assertMsg (lowest <= highest)
+            "ints.between: lowest must be smaller than highest";
+          addCheck int (x: x >= lowest && x <= highest) // {
+            name = "intBetween";
+            description = "integer between ${betweenDesc lowest highest}";
+          };
+        ign = lowest: highest: name: docStart:
+          between lowest highest // {
+            inherit name;
+            description = docStart + "; between ${betweenDesc lowest highest}";
+          };
+        unsign = bit: range: ign 0 (range - 1)
+          "unsignedInt${toString bit}" "${toString bit} bit unsigned integer";
+        sign = bit: range: ign (0 - (range / 2)) (range / 2 - 1)
+          "signedInt${toString bit}" "${toString bit} bit signed integer";
+
+      in {
+        /* An int with a fixed range.
+        *
+        * Example:
+        *   (ints.between 0 100).check (-1)
+        *   => false
+        *   (ints.between 0 100).check (101)
+        *   => false
+        *   (ints.between 0 0).check 0
+        *   => true
+        */
+        inherit between;
+
+        unsigned = addCheck types.int (x: x >= 0) // {
+          name = "unsignedInt";
+          description = "unsigned integer, meaning >=0";
+        };
+        positive = addCheck types.int (x: x > 0) // {
+          name = "positiveInt";
+          description = "positive integer, meaning >0";
+        };
+        u8 = unsign 8 256;
+        u16 = unsign 16 65536;
+        # the biggest int Nix accepts is 2^63 - 1 (9223372036854775808)
+        # the smallest int Nix accepts is -2^63 (-9223372036854775807)
+        u32 = unsign 32 4294967296;
+        # u64 = unsign 64 18446744073709551616;
+
+        s8 = sign 8 256;
+        s16 = sign 16 65536;
+        s32 = sign 32 4294967296;
+      };
+
+    # Alias of u16 for a port number
+    port = ints.u16;
+
+    float = mkOptionType {
+        name = "float";
+        description = "floating point number";
+        check = isFloat;
+        merge = mergeEqualOption;
+    };
+
+    str = mkOptionType {
+      name = "str";
+      description = "string";
+      check = isString;
+      merge = mergeEqualOption;
+    };
+
+    nonEmptyStr = mkOptionType {
+      name = "nonEmptyStr";
+      description = "non-empty string";
+      check = x: str.check x && builtins.match "[ \t\n]*" x == null;
+      inherit (str) merge;
+    };
+
+    # Allow a newline character at the end and trim it in the merge function.
+    singleLineStr =
+      let
+        inherit (strMatching "[^\n\r]*\n?") check merge;
+      in
+      mkOptionType {
+        name = "singleLineStr";
+        description = "(optionally newline-terminated) single-line string";
+        inherit check;
+        merge = loc: defs:
+          lib.removeSuffix "\n" (merge loc defs);
+      };
+
+    strMatching = pattern: mkOptionType {
+      name = "strMatching ${escapeNixString pattern}";
+      description = "string matching the pattern ${pattern}";
+      check = x: str.check x && builtins.match pattern x != null;
+      inherit (str) merge;
+    };
+
+    # Merge multiple definitions by concatenating them (with the given
+    # separator between the values).
+    separatedString = sep: mkOptionType rec {
+      name = "separatedString";
+      description = if sep == ""
+        then "Concatenated string" # for types.string.
+        else "strings concatenated with ${builtins.toJSON sep}"
+      ;
+      check = isString;
+      merge = loc: defs: concatStringsSep sep (getValues defs);
+      functor = (defaultFunctor name) // {
+        payload = sep;
+        binOp = sepLhs: sepRhs:
+          if sepLhs == sepRhs then sepLhs
+          else null;
+      };
+    };
+
+    lines = separatedString "\n";
+    commas = separatedString ",";
+    envVar = separatedString ":";
+
+    # Deprecated; should not be used because it quietly concatenates
+    # strings, which is usually not what you want.
+    string = separatedString "" // {
+      name = "string";
+      deprecationMessage = "See https://github.com/NixOS/nixpkgs/pull/66346 for better alternative types.";
+    };
+
+    attrs = mkOptionType {
+      name = "attrs";
+      description = "attribute set";
+      check = isAttrs;
+      merge = loc: foldl' (res: def: res // def.value) {};
+      emptyValue = { value = {}; };
+    };
+
+    # A package is a top-level store path (/nix/store/hash-name). This includes:
+    # - derivations
+    # - more generally, attribute sets with an `outPath` or `__toString` attribute
+    #   pointing to a store path, e.g. flake inputs
+    # - strings with context, e.g. "${pkgs.foo}" or (toString pkgs.foo)
+    # - hardcoded store path literals (/nix/store/hash-foo) or strings without context
+    #   ("/nix/store/hash-foo"). These get a context added to them using builtins.storePath.
+    package = mkOptionType {
+      name = "package";
+      check = x: isDerivation x || isStorePath x;
+      merge = loc: defs:
+        let res = mergeOneOption loc defs;
+        in if builtins.isPath res || (builtins.isString res && ! builtins.hasContext res)
+          then toDerivation res
+          else res;
+    };
+
+    shellPackage = package // {
+      check = x: isDerivation x && hasAttr "shellPath" x;
+    };
+
+    path = mkOptionType {
+      name = "path";
+      check = x: isCoercibleToString x && builtins.substring 0 1 (toString x) == "/";
+      merge = mergeEqualOption;
+    };
+
+    listOf = elemType: mkOptionType rec {
+      name = "listOf";
+      description = "list of ${elemType.description}s";
+      check = isList;
+      merge = loc: defs:
+        map (x: x.value) (filter (x: x ? value) (concatLists (imap1 (n: def:
+          imap1 (m: def':
+            (mergeDefinitions
+              (loc ++ ["[definition ${toString n}-entry ${toString m}]"])
+              elemType
+              [{ inherit (def) file; value = def'; }]
+            ).optionalValue
+          ) def.value
+        ) defs)));
+      emptyValue = { value = []; };
+      getSubOptions = prefix: elemType.getSubOptions (prefix ++ ["*"]);
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: listOf (elemType.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = elemType; };
+      nestedTypes.elemType = elemType;
+    };
+
+    nonEmptyListOf = elemType:
+      let list = addCheck (types.listOf elemType) (l: l != []);
+      in list // {
+        description = "non-empty " + list.description;
+        emptyValue = { }; # no .value attr, meaning unset
+      };
+
+    attrsOf = elemType: mkOptionType rec {
+      name = "attrsOf";
+      description = "attribute set of ${elemType.description}s";
+      check = isAttrs;
+      merge = loc: defs:
+        mapAttrs (n: v: v.value) (filterAttrs (n: v: v ? value) (zipAttrsWith (name: defs:
+            (mergeDefinitions (loc ++ [name]) elemType defs).optionalValue
+          )
+          # Push down position info.
+          (map (def: mapAttrs (n: v: { inherit (def) file; value = v; }) def.value) defs)));
+      emptyValue = { value = {}; };
+      getSubOptions = prefix: elemType.getSubOptions (prefix ++ ["<name>"]);
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: attrsOf (elemType.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = elemType; };
+      nestedTypes.elemType = elemType;
+    };
+
+    # A version of attrsOf that's lazy in its values at the expense of
+    # conditional definitions not working properly. E.g. defining a value with
+    # `foo.attr = mkIf false 10`, then `foo ? attr == true`, whereas with
+    # attrsOf it would correctly be `false`. Accessing `foo.attr` would throw an
+    # error that it's not defined. Use only if conditional definitions don't make sense.
+    lazyAttrsOf = elemType: mkOptionType rec {
+      name = "lazyAttrsOf";
+      description = "lazy attribute set of ${elemType.description}s";
+      check = isAttrs;
+      merge = loc: defs:
+        zipAttrsWith (name: defs:
+          let merged = mergeDefinitions (loc ++ [name]) elemType defs;
+          # mergedValue will trigger an appropriate error when accessed
+          in merged.optionalValue.value or elemType.emptyValue.value or merged.mergedValue
+        )
+        # Push down position info.
+        (map (def: mapAttrs (n: v: { inherit (def) file; value = v; }) def.value) defs);
+      emptyValue = { value = {}; };
+      getSubOptions = prefix: elemType.getSubOptions (prefix ++ ["<name>"]);
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: lazyAttrsOf (elemType.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = elemType; };
+      nestedTypes.elemType = elemType;
+    };
+
+    # TODO: drop this in the future:
+    loaOf = elemType: types.attrsOf elemType // {
+      name = "loaOf";
+      deprecationMessage = "Mixing lists with attribute values is no longer"
+        + " possible; please use `types.attrsOf` instead. See"
+        + " https://github.com/NixOS/nixpkgs/issues/1800 for the motivation.";
+      nestedTypes.elemType = elemType;
+    };
+
+    # Value of given type but with no merging (i.e. `uniq list`s are not concatenated).
+    uniq = elemType: mkOptionType rec {
+      name = "uniq";
+      inherit (elemType) description check;
+      merge = mergeOneOption;
+      emptyValue = elemType.emptyValue;
+      getSubOptions = elemType.getSubOptions;
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: uniq (elemType.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = elemType; };
+      nestedTypes.elemType = elemType;
+    };
+
+    unique = { message }: type: mkOptionType rec {
+      name = "unique";
+      inherit (type) description check;
+      merge = mergeUniqueOption { inherit message; };
+      emptyValue = type.emptyValue;
+      getSubOptions = type.getSubOptions;
+      getSubModules = type.getSubModules;
+      substSubModules = m: uniq (type.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = type; };
+      nestedTypes.elemType = type;
+    };
+
+    # Null or value of ...
+    nullOr = elemType: mkOptionType rec {
+      name = "nullOr";
+      description = "null or ${elemType.description}";
+      check = x: x == null || elemType.check x;
+      merge = loc: defs:
+        let nrNulls = count (def: def.value == null) defs; in
+        if nrNulls == length defs then null
+        else if nrNulls != 0 then
+          throw "The option `${showOption loc}` is defined both null and not null, in ${showFiles (getFiles defs)}."
+        else elemType.merge loc defs;
+      emptyValue = { value = null; };
+      getSubOptions = elemType.getSubOptions;
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: nullOr (elemType.substSubModules m);
+      functor = (defaultFunctor name) // { wrapped = elemType; };
+      nestedTypes.elemType = elemType;
+    };
+
+    functionTo = elemType: mkOptionType {
+      name = "functionTo";
+      description = "function that evaluates to a(n) ${elemType.description}";
+      check = isFunction;
+      merge = loc: defs:
+        fnArgs: (mergeDefinitions (loc ++ [ "[function body]" ]) elemType (map (fn: { inherit (fn) file; value = fn.value fnArgs; }) defs)).mergedValue;
+      getSubOptions = elemType.getSubOptions;
+      getSubModules = elemType.getSubModules;
+      substSubModules = m: functionTo (elemType.substSubModules m);
+    };
+
+    # A submodule (like typed attribute set). See NixOS manual.
+    submodule = modules: submoduleWith {
+      shorthandOnlyDefinesConfig = true;
+      modules = toList modules;
+    };
+
+    # The type of a type!
+    optionType = mkOptionType {
+      name = "optionType";
+      description = "optionType";
+      check = value: value._type or null == "option-type";
+      merge = loc: defs:
+        if length defs == 1
+        then (head defs).value
+        else let
+          # Prepares the type definitions for mergeOptionDecls, which
+          # annotates submodules types with file locations
+          optionModules = map ({ value, file }:
+            {
+              _file = file;
+              # There's no way to merge types directly from the module system,
+              # but we can cheat a bit by just declaring an option with the type
+              options = lib.mkOption {
+                type = value;
+              };
+            }
+          ) defs;
+          # Merges all the types into a single one, including submodule merging.
+          # This also propagates file information to all submodules
+          mergedOption = fixupOptionType loc (mergeOptionDecls loc optionModules);
+        in mergedOption.type;
+    };
+
+    submoduleWith =
+      { modules
+      , specialArgs ? {}
+      , shorthandOnlyDefinesConfig ? false
+      }@attrs:
+      let
+        inherit (lib.modules) evalModules;
+
+        shorthandToModule = if shorthandOnlyDefinesConfig == false
+          then value: value
+          else value: { config = value; };
+
+        allModules = defs: imap1 (n: { value, file }:
+          if isFunction value
+          then setFunctionArgs
+                (args: lib.modules.unifyModuleSyntax file "${toString file}-${toString n}" (value args))
+                (functionArgs value)
+          else if isAttrs value
+          then
+            lib.modules.unifyModuleSyntax file "${toString file}-${toString n}" (shorthandToModule value)
+          else value
+        ) defs;
+
+        base = evalModules {
+          inherit specialArgs;
+          modules = [{
+            # This is a work-around for the fact that some sub-modules,
+            # such as the one included in an attribute set, expects an "args"
+            # attribute to be given to the sub-module. As the option
+            # evaluation does not have any specific attribute name yet, we
+            # provide a default for the documentation and the freeform type.
+            #
+            # This is necessary as some option declaration might use the
+            # "name" attribute given as argument of the submodule and use it
+            # as the default of option declarations.
+            #
+            # We use lookalike unicode single angle quotation marks because
+            # of the docbook transformation the options receive. In all uses
+            # &gt; and &lt; wouldn't be encoded correctly so the encoded values
+            # would be used, and use of `<` and `>` would break the XML document.
+            # It shouldn't cause an issue since this is cosmetic for the manual.
+            _module.args.name = lib.mkOptionDefault "‹name›";
+          }] ++ modules;
+        };
+
+        freeformType = base._module.freeformType;
+
+      in
+      mkOptionType rec {
+        name = "submodule";
+        description = freeformType.description or name;
+        check = x: isAttrs x || isFunction x || path.check x;
+        merge = loc: defs:
+          (base.extendModules {
+            modules = [ { _module.args.name = last loc; } ] ++ allModules defs;
+            prefix = loc;
+          }).config;
+        emptyValue = { value = {}; };
+        getSubOptions = prefix: (base.extendModules
+          { inherit prefix; }).options // optionalAttrs (freeformType != null) {
+            # Expose the sub options of the freeform type. Note that the option
+            # discovery doesn't care about the attribute name used here, so this
+            # is just to avoid conflicts with potential options from the submodule
+            _freeformOptions = freeformType.getSubOptions prefix;
+          };
+        getSubModules = modules;
+        substSubModules = m: submoduleWith (attrs // {
+          modules = m;
+        });
+        nestedTypes = lib.optionalAttrs (freeformType != null) {
+          freeformType = freeformType;
+        };
+        functor = defaultFunctor name // {
+          type = types.submoduleWith;
+          payload = {
+            modules = modules;
+            specialArgs = specialArgs;
+            shorthandOnlyDefinesConfig = shorthandOnlyDefinesConfig;
+          };
+          binOp = lhs: rhs: {
+            modules = lhs.modules ++ rhs.modules;
+            specialArgs =
+              let intersecting = builtins.intersectAttrs lhs.specialArgs rhs.specialArgs;
+              in if intersecting == {}
+              then lhs.specialArgs // rhs.specialArgs
+              else throw "A submoduleWith option is declared multiple times with the same specialArgs \"${toString (attrNames intersecting)}\"";
+            shorthandOnlyDefinesConfig =
+              if lhs.shorthandOnlyDefinesConfig == null
+              then rhs.shorthandOnlyDefinesConfig
+              else if rhs.shorthandOnlyDefinesConfig == null
+              then lhs.shorthandOnlyDefinesConfig
+              else if lhs.shorthandOnlyDefinesConfig == rhs.shorthandOnlyDefinesConfig
+              then lhs.shorthandOnlyDefinesConfig
+              else throw "A submoduleWith option is declared multiple times with conflicting shorthandOnlyDefinesConfig values";
+          };
+        };
+      };
+
+    # A value from a set of allowed ones.
+    enum = values:
+      let
+        inherit (lib.lists) unique;
+        show = v:
+               if builtins.isString v then ''"${v}"''
+          else if builtins.isInt v then builtins.toString v
+          else if builtins.isBool v then boolToString v
+          else ''<${builtins.typeOf v}>'';
+      in
+      mkOptionType rec {
+        name = "enum";
+        description =
+          # Length 0 or 1 enums may occur in a design pattern with type merging
+          # where an "interface" module declares an empty enum and other modules
+          # provide implementations, each extending the enum with their own
+          # identifier.
+          if values == [] then
+            "impossible (empty enum)"
+          else if builtins.length values == 1 then
+            "value ${show (builtins.head values)} (singular enum)"
+          else
+            "one of ${concatMapStringsSep ", " show values}";
+        check = flip elem values;
+        merge = mergeEqualOption;
+        functor = (defaultFunctor name) // { payload = values; binOp = a: b: unique (a ++ b); };
+      };
+
+    # Either value of type `t1` or `t2`.
+    either = t1: t2: mkOptionType rec {
+      name = "either";
+      description = "${t1.description} or ${t2.description}";
+      check = x: t1.check x || t2.check x;
+      merge = loc: defs:
+        let
+          defList = map (d: d.value) defs;
+        in
+          if   all (x: t1.check x) defList
+               then t1.merge loc defs
+          else if all (x: t2.check x) defList
+               then t2.merge loc defs
+          else mergeOneOption loc defs;
+      typeMerge = f':
+        let mt1 = t1.typeMerge (elemAt f'.wrapped 0).functor;
+            mt2 = t2.typeMerge (elemAt f'.wrapped 1).functor;
+        in
+           if (name == f'.name) && (mt1 != null) && (mt2 != null)
+           then functor.type mt1 mt2
+           else null;
+      functor = (defaultFunctor name) // { wrapped = [ t1 t2 ]; };
+      nestedTypes.left = t1;
+      nestedTypes.right = t2;
+    };
+
+    # Any of the types in the given list
+    oneOf = ts:
+      let
+        head' = if ts == [] then throw "types.oneOf needs to get at least one type in its argument" else head ts;
+        tail' = tail ts;
+      in foldl' either head' tail';
+
+    # Either value of type `coercedType` or `finalType`, the former is
+    # converted to `finalType` using `coerceFunc`.
+    coercedTo = coercedType: coerceFunc: finalType:
+      assert lib.assertMsg (coercedType.getSubModules == null)
+        "coercedTo: coercedType must not have submodules (it’s a ${
+          coercedType.description})";
+      mkOptionType rec {
+        name = "coercedTo";
+        description = "${finalType.description} or ${coercedType.description} convertible to it";
+        check = x: (coercedType.check x && finalType.check (coerceFunc x)) || finalType.check x;
+        merge = loc: defs:
+          let
+            coerceVal = val:
+              if coercedType.check val then coerceFunc val
+              else val;
+          in finalType.merge loc (map (def: def // { value = coerceVal def.value; }) defs);
+        emptyValue = finalType.emptyValue;
+        getSubOptions = finalType.getSubOptions;
+        getSubModules = finalType.getSubModules;
+        substSubModules = m: coercedTo coercedType coerceFunc (finalType.substSubModules m);
+        typeMerge = t1: t2: null;
+        functor = (defaultFunctor name) // { wrapped = finalType; };
+        nestedTypes.coercedType = coercedType;
+        nestedTypes.finalType = finalType;
+      };
+
+    # Obsolete alternative to configOf.  It takes its option
+    # declarations from the ‘options’ attribute of containing option
+    # declaration.
+    optionSet = mkOptionType {
+      name = "optionSet";
+      description = "option set";
+      deprecationMessage = "Use `types.submodule' instead";
+    };
+    # Augment the given type with an additional type check function.
+    addCheck = elemType: check: elemType // { check = x: elemType.check x && check x; };
+
+  };
+};
+
+in outer_types // outer_types.types