path: root/lib/types.nix

# Definitions related to run-time type checking.  Used in particular
# to type-check NixOS configurations.
{ lib }:

let
  inherit (lib)
    all
    elem
    flip
    hasContext
    functionArgs
    isAttrs
    isBool
    isDerivation
    isFloat
    isFunction
    isInt
    isList
    isPath
    isStorePath
    isString
    substring
    sort
    toDerivation
    toList
    types
    ;
  inherit (lib.lists)
    concatLists
    concatMap
    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
    showDefs
    showOption
    ;
  inherit (lib.strings)
    concatMapStringsSep
    concatStringsSep
    escapeNixString
    hasInfix
    isStringLike
    ;
  inherit (lib.trivial)
    boolToString
    ;

  inherit (lib.modules)
    mergeDefinitions
    fixupOptionType
    mergeOptionDecls
    defaultOrderPriority
    defaultOverridePriority
    mkDefinition
    mkOrder
    mkOverride
    ;
  inherit (lib.fileset)
    isFileset
    unions
    empty
    ;
  inherit (lib.path) hasStorePathPrefix;

  inAttrPosSuffix =
    v: name:
    let
      pos = builtins.unsafeGetAttrPos name v;
    in
    if pos == null then "" else " at ${pos.file}:${toString pos.line}:${toString pos.column}";

  hasColonInfix = hasInfix ":";
  hasNewlineInfix = hasInfix "\n";

  # Internal functor to help for migrating functor.wrapped to functor.payload.elemType
  # Note that individual attributes can be overridden if needed.
  elemTypeFunctor =
    name:
    { elemType, ... }@payload:
    {
      inherit name payload;
      type = types.${name};
      binOp =
        a: b:
        let
          merged = a.elemType.typeMerge b.elemType.functor;
        in
        if merged == null then null else { elemType = merged; };
    };

  checkDefsForError =
    check: loc: defs:
    if all (def: check def.value) defs then
      null
    else
      let
        invalidDefs = filter (def: !check def.value) defs;
      in
      {
        message = "Definition values: ${showDefs invalidDefs}";
      };

  # Check that a type with v2 merge has a coherent check attribute.
  # Throws an error if the type uses an ad-hoc `type // { check }` override.
  # Returns the last argument like `seq`, allowing usage: checkV2MergeCoherence loc type expr
  checkV2MergeCoherence =
    loc: type: result:
    if type.check.isV2MergeCoherent or false then
      result
    else
      throw ''
        The option `${showOption loc}' has a type `${type.description}' that uses
        an ad-hoc `type // { check = ...; }' override, which is incompatible with
        the v2 merge mechanism.

        Please use `lib.types.addCheck` instead of `type // { check }' to add
        custom validation. For example:

          lib.types.addCheck baseType (value: /* your check */)

        instead of:

          baseType // { check = value: /* your check */; }
      '';

in
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
      mergedPayload = f.binOp f.payload f'.payload;

      hasPayload =
        assert (f'.payload != null) == (f.payload != null);
        f.payload != null;
    in
    # Abort early: cannot merge different types
    if f.name != f'.name then
      null
    else

    if hasPayload then
      if mergedPayload == null then null else f.type mergedPayload
    else
      f.type;

  # Default type functor
  defaultFunctor = name: {
    inherit name;
    type = lib.types.${name} or 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,
      # A hint for whether or not this description needs parentheses. Possible values:
      #  - "noun": a noun phrase
      #    Example description: "positive integer",
      #  - "conjunction": a phrase with a potentially ambiguous "or" connective
      #    Example description: "int or string"
      #  - "composite": a phrase with an "of" connective
      #    Example description: "list of string"
      #  - "nonRestrictiveClause": a noun followed by a comma and a clause
      #    Example description: "positive integer, meaning >0"
      # See the `optionDescriptionPhrase` function.
      descriptionClass ? null,
      # DO NOT USE WITHOUT KNOWING WHAT YOU ARE DOING!
      # Function applied to each definition that must return false when a definition
      # does not match the type. It should not check more than the root of the value,
      # because checking nested values reduces laziness, leading to unnecessary
      # infinite recursions in the module system.
      # Further checks of nested values should be performed by throwing in
      # the merge function.
      # Strict and deep type checking can be performed by calling lib.deepSeq on
      # the merged value.
      #
      # See https://github.com/NixOS/nixpkgs/pull/6794 that introduced this change,
      # https://github.com/NixOS/nixpkgs/pull/173568 and
      # https://github.com/NixOS/nixpkgs/pull/168295 that attempted to revert this,
      # https://github.com/NixOS/nixpkgs/issues/191124 and
      # https://github.com/NixOS/nixos-search/issues/391 for what happens if you ignore
      # this disclaimer.
      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 attrset 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
        deprecationMessage
        nestedTypes
        descriptionClass
        functor
        ;
      description = if description == null then name else description;
    };

  # optionDescriptionPhrase :: (str -> bool) -> optionType -> str
  #
  # Helper function for producing unambiguous but readable natural language
  # descriptions of types.
  #
  # Parameters
  #
  #     optionDescriptionPhase unparenthesize optionType
  #
  # `unparenthesize`: A function from descriptionClass string to boolean.
  #   It must return true when the class of phrase will fit unambiguously into
  #   the description of the caller.
  #
  # `optionType`: The option type to parenthesize or not.
  #   The option whose description we're returning.
  #
  # Returns value
  #
  # The description of the `optionType`, with parentheses if there may be an
  # ambiguity.
  optionDescriptionPhrase =
    unparenthesize: t:
    if unparenthesize (t.descriptionClass or null) then t.description else "(${t.description})";

  noCheckForDocsModule = {
    # When generating documentation, our goal isn't to check anything.
    # Quite the opposite in fact. Generating docs is somewhat of a
    # challenge, evaluating modules in a *lacking* context. Anything
    # that makes the docs avoid an error is a win.
    config._module.check = lib.mkForce false;
    _file = "<built-in module that disables checks for the purpose of documentation generation>";
  };

  # When adding new types don't forget to document them in
  # nixos/doc/manual/development/option-types.section.md!

  raw = mkOptionType {
    name = "raw";
    description = "raw value";
    descriptionClass = "noun";
    check = value: true;
    merge = mergeOneOption;
  };

  anything = mkOptionType {
    name = "anything";
    description = "anything";
    descriptionClass = "noun";
    check = value: true;
    merge =
      loc: defs:
      let
        getType =
          value: if isAttrs value && isStringLike 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;
            # 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";
    description = "unspecified value";
    descriptionClass = "noun";
  };

  bool = mkOptionType {
    name = "bool";
    description = "boolean";
    descriptionClass = "noun";
    check = isBool;
    merge = mergeEqualOption;
  };

  boolByOr = mkOptionType {
    name = "boolByOr";
    description = "boolean (merged using or)";
    descriptionClass = "noun";
    check = isBool;
    merge =
      loc: defs:
      foldl' (
        result: def:
        # Under the assumption that .check always runs before merge, we can assume that all defs.*.value
        # have been forced, and therefore we assume we don't introduce order-dependent strictness here
        result || def.value
      ) false defs;
  };

  int = mkOptionType {
    name = "int";
    description = "signed integer";
    descriptionClass = "noun";
    check = isInt;
    merge = mergeEqualOption;
  };

  # Specialized subdomains of int
  ints =
    let
      betweenDesc = lowest: highest: "${toString lowest} and ${toString highest} (both inclusive)";
      between =
        lowest: highest:
        assert lowest <= highest || throw "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
    {
      # TODO: Deduplicate with docs in nixos/doc/manual/development/option-types.section.md
      /**
        An int with a fixed range.

        # Example
        :::{.example}
        ## `lib.types.ints.between` usage example

        ```nix
        (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 lib.types.int (x: x >= 0) // {
        name = "unsignedInt";
        description = "unsigned integer, meaning >=0";
        descriptionClass = "nonRestrictiveClause";
      };
      positive = addCheck lib.types.int (x: x > 0) // {
        name = "positiveInt";
        description = "positive integer, meaning >0";
        descriptionClass = "nonRestrictiveClause";
      };
      u8 = unsign 8 256;
      u16 = unsign 16 65536;
      # the biggest int Nix accepts is 2^63 - 1 (9223372036854775807)
      # the smallest int Nix accepts is -2^63 (-9223372036854775808)
      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";
    descriptionClass = "noun";
    check = isFloat;
    merge = mergeEqualOption;
  };

  number = either int float;

  numbers =
    let
      betweenDesc =
        lowest: highest: "${builtins.toJSON lowest} and ${builtins.toJSON highest} (both inclusive)";
    in
    {
      between =
        lowest: highest:
        assert lowest <= highest || throw "numbers.between: lowest must be smaller than highest";
        addCheck number (x: x >= lowest && x <= highest)
        // {
          name = "numberBetween";
          description = "integer or floating point number between ${betweenDesc lowest highest}";
        };

      nonnegative = addCheck number (x: x >= 0) // {
        name = "numberNonnegative";
        description = "nonnegative integer or floating point number, meaning >=0";
        descriptionClass = "nonRestrictiveClause";
      };
      positive = addCheck number (x: x > 0) // {
        name = "numberPositive";
        description = "positive integer or floating point number, meaning >0";
        descriptionClass = "nonRestrictiveClause";
      };
    };

  str = mkOptionType {
    name = "str";
    description = "string";
    descriptionClass = "noun";
    check = isString;
    merge = mergeEqualOption;
  };

  nonEmptyStr = mkOptionType {
    name = "nonEmptyStr";
    description = "non-empty string";
    descriptionClass = "noun";
    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;
      removeNewlineSuffix = lib.removeSuffix "\n";
    in
    mkOptionType {
      name = "singleLineStr";
      description = "(optionally newline-terminated) single-line string";
      descriptionClass = "noun";
      inherit check;
      merge = loc: defs: removeNewlineSuffix (merge loc defs);
    };

  strMatching =
    pattern:
    mkOptionType {
      name = "strMatching ${escapeNixString pattern}";
      description = "string matching the pattern ${pattern}";
      descriptionClass = "noun";
      check = x: str.check x && builtins.match pattern x != null;
      inherit (str) merge;
      functor = defaultFunctor "strMatching" // {
        type = payload: strMatching payload.pattern;
        payload = { inherit pattern; };
        binOp = lhs: rhs: if lhs == rhs then lhs else null;
      };
    };

  # Merge multiple definitions by concatenating them (with the given
  # separator between the values).
  separatedString =
    sep:
    mkOptionType rec {
      name = "separatedString";
      description = "strings concatenated with ${builtins.toJSON sep}";
      descriptionClass = "noun";
      check = isString;
      merge = loc: defs: concatStringsSep sep (getValues defs);
      functor = (defaultFunctor name) // {
        payload = { inherit sep; };
        type = payload: lib.types.separatedString payload.sep;
        binOp = lhs: rhs: if lhs.sep == rhs.sep then { inherit (lhs) sep; } else null;
      };
    };

  lines = separatedString "\n";
  commas = separatedString ",";
  envVar = separatedString ":";

  passwdEntry =
    entryType:
    addCheck entryType (str: !(hasColonInfix str || hasNewlineInfix str))
    // {
      name = "passwdEntry ${entryType.name}";
      description = "${
        optionDescriptionPhrase (class: class == "noun") entryType
      }, not containing newlines or colons";
      descriptionClass = "nonRestrictiveClause";
    };

  attrs = mkOptionType {
    name = "attrs";
    description = "attribute set";
    check = isAttrs;
    merge = loc: foldl' (res: def: res // def.value) { };
    emptyValue = {
      value = { };
    };
  };

  fileset = mkOptionType {
    name = "fileset";
    description = "fileset";
    descriptionClass = "noun";
    check = isFileset;
    merge = loc: defs: unions (getValues defs);
    emptyValue.value = empty;
  };

  # 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.
  # If you don't need a *top-level* store path, consider using pathInStore instead.
  package = mkOptionType {
    name = "package";
    descriptionClass = "noun";
    check = x: isDerivation x || isStorePath x;
    merge =
      loc: defs:
      let
        res = mergeOneOption loc defs;
      in
      if isPath res || (isString res && !hasContext res) then toDerivation res else res;
  };

  shellPackage = package // {
    check = x: isDerivation x && hasAttr "shellPath" x;
  };

  pkgs = addCheck (
    unique { message = "A Nixpkgs pkgs set can not be merged with another pkgs set."; } attrs
    // {
      name = "pkgs";
      descriptionClass = "noun";
      description = "Nixpkgs package set";
    }
  ) (x: (x._type or null) == "pkgs");

  path = pathWith {
    absolute = true;
  };

  pathInStore = pathWith {
    inStore = true;
  };

  externalPath = pathWith {
    absolute = true;
    inStore = false;
  };

  pathWith =
    {
      inStore ? null,
      absolute ? null,
    }:
    if inStore != null && absolute != null && inStore && !absolute then
      throw "In pathWith, inStore means the path must be absolute"
    else
      mkOptionType {
        name = "path";
        description = (
          (if absolute == null then "" else (if absolute then "absolute " else "relative "))
          + "path"
          + (
            if inStore == null then "" else (if inStore then " in the Nix store" else " not in the Nix store")
          )
        );
        descriptionClass = "noun";

        merge = mergeEqualOption;
        functor = defaultFunctor "path" // {
          type = pathWith;
          payload = { inherit inStore absolute; };
          binOp = lhs: rhs: if lhs == rhs then lhs else null;
        };

        check =
          x:
          let
            isInStore = hasStorePathPrefix (
              if isPath x then
                x
              # Discarding string context is necessary to convert the value to
              # a path and safe as the result is never used in any derivation.
              else
                /. + builtins.unsafeDiscardStringContext x
            );
            isAbsolute = x.type or null == "derivation" || substring 0 1 (toString x) == "/";
            isExpectedType = (
              if inStore == null || inStore then isStringLike x else isString x # Do not allow a true path, which could be copied to the store later on.
            );
          in
          isExpectedType
          && (inStore == null || inStore == isInStore)
          && (absolute == null || absolute == isAbsolute);
      };

  listOf =
    elemType:
    mkOptionType rec {
      name = "listOf";
      description = "list of ${
        optionDescriptionPhrase (class: class == "noun" || class == "composite") elemType
      }";
      descriptionClass = "composite";
      check = {
        __functor = _self: isList;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }:
          let
            evals = filter (x: x.optionalValue ? value) (
              concatLists (
                imap1 (
                  n: def:
                  imap1 (
                    m: def':
                    (mergeDefinitions (loc ++ [ "[definition ${toString n}-entry ${toString m}]" ]) elemType [
                      {
                        inherit (def) file;
                        value = def';
                      }
                    ])
                  ) def.value
                ) defs
              )
            );
          in
          {
            headError = checkDefsForError check loc defs;
            value = map (x: x.optionalValue.value or x.mergedValue) evals;
            valueMeta.list = map (v: v.checkedAndMerged.valueMeta) evals;
          };
      };
      emptyValue = {
        value = [ ];
      };
      getSubOptions = prefix: elemType.getSubOptions (prefix ++ [ "*" ]);
      getSubModules = elemType.getSubModules;
      substSubModules = m: listOf (elemType.substSubModules m);
      functor = (elemTypeFunctor name { inherit elemType; }) // {
        type = payload: lib.types.listOf payload.elemType;
      };
      nestedTypes.elemType = elemType;
    };

  nonEmptyListOf =
    elemType:
    let
      list = addCheck (lib.types.listOf elemType) (l: l != [ ]);
    in
    list
    // {
      description = "non-empty ${optionDescriptionPhrase (class: class == "noun") list}";
      emptyValue = { }; # no .value attr, meaning unset
      substSubModules = m: nonEmptyListOf (elemType.substSubModules m);
    };

  attrListOf = elemType: attrListWith { inherit elemType; };

  attrListWith =
    {
      elemType,
      asAttrs ? false,
      mergeAttrValues ? _name: values: values,
    }:
    mkOptionType rec {
      name = "attrListOf";
      description = "attribute list of ${
        optionDescriptionPhrase (class: class == "noun" || class == "composite") elemType
      }";
      descriptionClass = "composite";
      check = {
        __functor = _self: x: isList x || isAttrs x;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }:
          let
            # Peel order and override properties from a value in any nesting order.
            # Returns { value, prio, overridePrio }.
            # mkOrder is stripped (we consume it for sorting).
            # mkOverride is preserved in value (mergeDefinitions strips it).
            peelProperties =
              value:
              let
                type = value._type or null;
              in
              if type == "order" then
                let
                  inner = peelProperties value.content;
                in
                {
                  inherit (inner) value overridePrio;
                  prio = value.priority;
                }
              else if type == "override" then
                let
                  inner = peelProperties value.content;
                in
                {
                  inherit (inner) prio;
                  overridePrio = value.priority;
                  # Re-wrap mkOverride around the inner value (with mkOrder stripped)
                  value = mkOverride value.priority inner.value;
                }
              else
                {
                  inherit value;
                  prio = defaultOrderPriority;
                  overridePrio = defaultOverridePriority;
                };

            # Extract { file, key, value, prio, overridePrio } from a single-key attrset,
            # optionally wrapped in mkOrder at the element level (list format).
            extractItem =
              file: raw:
              let
                hasOrder = isType "order" raw;
                item = if hasOrder then raw.content else raw;
                key = head (attrNames item);
                peeled = peelProperties item.${key};
              in
              if isAttrs item && length (attrNames item) == 1 then
                peeled
                // {
                  inherit file key;
                  prio = if hasOrder then raw.priority else peeled.prio;
                }
              else
                throw "A definition for option `${showOption loc}' is not of type `${description}'. ${
                  if !isAttrs item then
                    "Each list element must be an attribute set, but got ${builtins.typeOf item}"
                  else
                    "Each list element must be a single-key attribute set, but got ${toString (length (attrNames item))} keys"
                }.${
                  showDefs [
                    {
                      inherit file;
                      value = raw;
                    }
                  ]
                }";

            # Convert a definition to a flat list of { file, key, value, prio, overridePrio }
            defToItems =
              def:
              if isList def.value then
                map (extractItem def.file) def.value
              else
                # isAttrs: properties are on the values directly
                map (
                  key:
                  peelProperties def.value.${key}
                  // {
                    inherit (def) file;
                    inherit key;
                  }
                ) (attrNames def.value);

            allItems = concatMap defToItems defs;

            # Per key, find the highest override priority (lowest number)
            winningOverridePrio = foldl' (
              acc: item:
              let
                prev = acc.${item.key} or defaultOverridePriority;
              in
              if item.overridePrio < prev then
                acc // { ${item.key} = item.overridePrio; }
              else
                # minimize `//` operations
                acc
            ) { } allItems;

            # Keep only items at the winning override priority for their key
            items = sort (a: b: a.prio < b.prio) (
              filter (
                item: item.overridePrio == winningOverridePrio.${item.key} or defaultOverridePriority
              ) allItems
            );

            evals = filter (e: e.eval.optionalValue ? value) (
              map (item: {
                inherit (item) key file prio;
                eval = mergeDefinitions (loc ++ [ item.key ]) elemType [
                  {
                    inherit (item) file value;
                  }
                ];
              }) items
            );

            attrListValue = map (e: { ${e.key} = e.eval.optionalValue.value or e.eval.mergedValue; }) evals;
          in
          {
            headError = checkDefsForError check loc defs;
            value = if asAttrs then zipAttrsWith mergeAttrValues attrListValue else attrListValue;
            valueMeta.attrList = map (e: e.eval.checkedAndMerged.valueMeta) evals;
            /**
              The ordered list representation, especially useful when asAttrs is set.
            */
            valueMeta.attrListValue = attrListValue;
            valueMeta.definitions = map (
              e:
              mkDefinition {
                inherit (e) file;
                value = mkOrder e.prio { ${e.key} = e.eval.optionalValue.value or e.eval.mergedValue; };
              }
            ) evals;
          };
      };
      emptyValue = {
        value = if asAttrs then { } else [ ];
      };
      getSubOptions = prefix: elemType.getSubOptions (prefix ++ [ "*" ]);
      getSubModules = elemType.getSubModules;
      substSubModules =
        m:
        attrListWith {
          inherit asAttrs mergeAttrValues;
          elemType = elemType.substSubModules m;
        };
      typeMerge = t: null; # Disable type merging
      nestedTypes.elemType = elemType;
    };

  attrsOf = elemType: attrsWith { inherit 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:
    attrsWith {
      inherit elemType;
      lazy = true;
    };

  # base type for lazyAttrsOf and attrsOf
  attrsWith =
    let
      # Push down position info.
      pushPositions = map (
        def:
        mapAttrs (n: v: {
          inherit (def) file;
          value = v;
        }) def.value
      );
      binOp =
        lhs: rhs:
        let
          elemType = lhs.elemType.typeMerge rhs.elemType.functor;
          lazy = if lhs.lazy == rhs.lazy then lhs.lazy else null;
          placeholder =
            if lhs.placeholder == rhs.placeholder then
              lhs.placeholder
            else if lhs.placeholder == "name" then
              rhs.placeholder
            else if rhs.placeholder == "name" then
              lhs.placeholder
            else
              null;
        in
        if elemType == null || lazy == null || placeholder == null then
          null
        else
          {
            inherit elemType lazy placeholder;
          };
    in
    {
      elemType,
      lazy ? false,
      placeholder ? "name",
    }:
    mkOptionType rec {
      name = if lazy then "lazyAttrsOf" else "attrsOf";
      description =
        (if lazy then "lazy attribute set" else "attribute set")
        + " of ${optionDescriptionPhrase (class: class == "noun" || class == "composite") elemType}";
      descriptionClass = "composite";
      check = {
        __functor = _self: isAttrs;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }:
          let
            evals =
              if lazy then
                zipAttrsWith (name: defs: mergeDefinitions (loc ++ [ name ]) elemType defs) (pushPositions defs)
              else
                # Filtering makes the merge function more strict
                # Meaning it is less lazy
                filterAttrs (n: v: v.optionalValue ? value) (
                  zipAttrsWith (name: defs: mergeDefinitions (loc ++ [ name ]) elemType defs) (pushPositions defs)
                );
          in
          {
            headError = checkDefsForError check loc defs;
            value = mapAttrs (
              n: v:
              if lazy then
                v.optionalValue.value or elemType.emptyValue.value or v.mergedValue
              else
                v.optionalValue.value
            ) evals;
            valueMeta.attrs = mapAttrs (n: v: v.checkedAndMerged.valueMeta) evals;
          };
      };

      emptyValue = {
        value = { };
      };
      getSubOptions = prefix: elemType.getSubOptions (prefix ++ [ "<${placeholder}>" ]);
      getSubModules = elemType.getSubModules;
      substSubModules =
        m:
        attrsWith {
          elemType = elemType.substSubModules m;
          inherit lazy placeholder;
        };
      functor =
        (elemTypeFunctor "attrsWith" {
          inherit elemType lazy placeholder;
        })
        // {
          # Custom type merging required because of the "placeholder" attribute
          inherit binOp;
        };
      nestedTypes.elemType = elemType;
    };

  # TODO: deprecate this in the future:
  loaOf =
    elemType:
    lib.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;
    };

  attrTag =
    tags:
    let
      tags_ = tags;
    in
    let
      tags = mapAttrs (
        n: opt:
        builtins.addErrorContext
          "while checking that attrTag tag ${lib.strings.escapeNixIdentifier n} is an option with a type${inAttrPosSuffix tags_ n}"
          (
            if opt._type or null != "option" then
              throw "In attrTag, each tag value must be an option, but tag ${lib.strings.escapeNixIdentifier n} ${
                if opt ? _type then
                  if opt._type == "option-type" then
                    "was a bare type, not wrapped in mkOption."
                  else
                    "was of type ${lib.strings.escapeNixString opt._type}."
                else
                  "was not."
              }"
            else
              opt
              // {
                declarations =
                  opt.declarations or (
                    let
                      pos = builtins.unsafeGetAttrPos n tags_;
                    in
                    if pos == null then [ ] else [ pos.file ]
                  );
                declarationPositions =
                  opt.declarationPositions or (
                    let
                      pos = builtins.unsafeGetAttrPos n tags_;
                    in
                    if pos == null then [ ] else [ pos ]
                  );
              }
          )
      ) tags_;
      choicesStr = concatMapStringsSep ", " lib.strings.escapeNixIdentifier (attrNames tags);
    in
    mkOptionType {
      name = "attrTag";
      description = "attribute-tagged union with choices: ${choicesStr}";
      descriptionClass = "noun";
      getSubOptions =
        prefix: mapAttrs (tagName: tagOption: tagOption // { loc = prefix ++ [ tagName ]; }) tags;
      check = v: isAttrs v && length (attrNames v) == 1 && tags ? ${head (attrNames v)};
      merge =
        loc: defs:
        let
          choice = head (attrNames (head defs).value);
          checkedValueDefs = map (
            def:
            assert (length (attrNames def.value)) == 1;
            if (head (attrNames def.value)) != choice then
              throw "The option `${showOption loc}` is defined both as `${choice}` and `${head (attrNames def.value)}`, in ${showFiles (getFiles defs)}."
            else
              {
                inherit (def) file;
                value = def.value.${choice};
              }
          ) defs;
        in
        if tags ? ${choice} then
          {
            ${choice} = (lib.modules.evalOptionValue (loc ++ [ choice ]) tags.${choice} checkedValueDefs).value;
          }
        else
          throw "The option `${showOption loc}` is defined as ${lib.strings.escapeNixIdentifier choice}, but ${lib.strings.escapeNixIdentifier choice} is not among the valid choices (${choicesStr}). Value ${choice} was defined in ${showFiles (getFiles defs)}.";
      nestedTypes = tags;
      getSubModules =
        let
          tagsWithSubModules = filterAttrs (_: mods: mods != null) (
            mapAttrs (_: opt: opt.type.getSubModules) tags
          );
        in
        if tagsWithSubModules == { } then null else [ tagsWithSubModules ];
      substSubModules =
        allWrappedModules:
        let
          tagsWithNewTypes = zipAttrsWith (tag: tags.${tag}.type.substSubModules) (
            concatMap (
              { _file, imports }: map (mapAttrs (_: imports: { inherit _file imports; })) imports
            ) allWrappedModules
          );
        in
        attrTag (
          mapAttrs (
            tag: opt: opt // (optionalAttrs (tagsWithNewTypes ? ${tag}) { type = tagsWithNewTypes.${tag}; })
          ) tags
        );
      functor = defaultFunctor "attrTag" // {
        type = { tags, ... }: lib.types.attrTag tags;
        payload = { inherit tags; };
        binOp =
          let
            # Add metadata in the format that submodules work with
            wrapOptionDecl = option: {
              options = option;
              _file = "<attrTag {...}>";
              pos = null;
            };
          in
          a: b: {
            tags =
              a.tags
              // b.tags
              // mapAttrs (
                tagName: bOpt:
                lib.mergeOptionDecls
                  # FIXME: loc is not accurate; should include prefix
                  #        Fortunately, it's only used for error messages, where a "relative" location is kinda ok.
                  #        It is also returned though, but use of the attribute seems rare?
                  [ tagName ]
                  [
                    (wrapOptionDecl a.tags.${tagName})
                    (wrapOptionDecl bOpt)
                  ]
                // {
                  # mergeOptionDecls is not idempotent in these attrs:
                  declarations = a.tags.${tagName}.declarations ++ bOpt.declarations;
                  declarationPositions = a.tags.${tagName}.declarationPositions ++ bOpt.declarationPositions;
                }
              ) (builtins.intersectAttrs a.tags b.tags);
          };
      };
    };

  # A value produced by `lib.mkLuaInline`
  luaInline = mkOptionType {
    name = "luaInline";
    description = "inline lua";
    descriptionClass = "noun";
    check = x: x._type or null == "lua-inline";
    merge = mergeEqualOption;
  };

  uniq = unique { message = ""; };

  unique =
    { message }:
    type:
    mkOptionType rec {
      name = "unique";
      inherit (type) description descriptionClass check;
      merge = mergeUniqueOption {
        inherit message;
        inherit (type) merge;
      };
      emptyValue = type.emptyValue;
      getSubOptions = type.getSubOptions;
      getSubModules = type.getSubModules;
      substSubModules = m: uniq (type.substSubModules m);
      functor = elemTypeFunctor name { elemType = type; } // {
        type = payload: lib.types.unique { inherit message; } payload.elemType;
      };
      nestedTypes.elemType = type;
    };

  # Null or value of ...
  nullOr =
    elemType:
    mkOptionType rec {
      name = "nullOr";
      description = "null or ${
        optionDescriptionPhrase (class: class == "noun" || class == "conjunction") elemType
      }";
      descriptionClass = "conjunction";
      check = {
        __functor = _self: x: x == null || elemType.check x;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          let
            inherit (self.v2 { inherit loc defs; }) headError value;
          in
          if headError.causedByMixedNulls or false then throw headError.message else value;
        v2 =
          { loc, defs }:
          if all (def: def.value != null) defs then
            # There are no null values
            if elemType.merge ? v2 then
              checkV2MergeCoherence loc elemType (elemType.merge.v2 { inherit loc defs; })
            else
              {
                value = elemType.merge loc defs;
                headError = checkDefsForError elemType.check loc defs;
                valueMeta = { };
              }
          else
            # There are some null values
            {
              headError =
                if length defs == 1 || all (def: def.value == null) defs then
                  null
                else
                  {
                    message = "The option `${showOption loc}` is defined both null and not null, in ${showFiles (getFiles defs)}.";
                    causedByMixedNulls = true;
                  };
              value = null;
              valueMeta = { };
            };
      };
      emptyValue = {
        value = null;
      };
      getSubOptions = elemType.getSubOptions;
      getSubModules = elemType.getSubModules;
      substSubModules = m: nullOr (elemType.substSubModules m);
      functor = (elemTypeFunctor name { inherit elemType; }) // {
        type = payload: lib.types.nullOr payload.elemType;
      };
      nestedTypes.elemType = elemType;
    };

  functionTo =
    elemType:
    mkOptionType {
      name = "functionTo";
      description = "function that evaluates to a(n) ${
        optionDescriptionPhrase (class: class == "noun" || class == "composite") elemType
      }";
      descriptionClass = "composite";
      check = isFunction;
      merge = loc: defs: {
        # An argument attribute has a default when it has a default in all definitions
        __functionArgs = zipAttrsWith (_: all (x: x)) (map (fn: functionArgs fn.value) defs);
        __functor =
          _: callerArgs:
          (mergeDefinitions (loc ++ [ "<function body>" ]) elemType (
            map (fn: {
              inherit (fn) file;
              value = fn.value callerArgs;
            }) defs
          )).mergedValue;
      };
      getSubOptions = prefix: elemType.getSubOptions (prefix ++ [ "<function body>" ]);
      getSubModules = elemType.getSubModules;
      substSubModules = m: functionTo (elemType.substSubModules m);
      functor = (elemTypeFunctor "functionTo" { inherit elemType; }) // {
        type = payload: lib.types.functionTo payload.elemType;
      };
      nestedTypes.elemType = elemType;
    };

  # A submodule (like typed attribute set). See NixOS manual.
  submodule =
    modules:
    submoduleWith {
      shorthandOnlyDefinesConfig = true;
      modules = toList modules;
    };

  # A module to be imported in some other part of the configuration.
  deferredModule = deferredModuleWith { };

  # A module to be imported in some other part of the configuration.
  # `staticModules`' options will be added to the documentation, unlike
  # options declared via `config`.
  deferredModuleWith =
    attrs@{
      staticModules ? [ ],
    }:
    mkOptionType {
      name = "deferredModule";
      description = "module";
      descriptionClass = "noun";
      check = x: isAttrs x || isFunction x || path.check x;
      merge = loc: defs: {
        imports =
          staticModules
          ++ map (
            def: lib.setDefaultModuleLocation "${def.file}, via option ${showOption loc}" def.value
          ) defs;
      };
      inherit (submoduleWith { modules = staticModules; })
        getSubOptions
        getSubModules
        ;
      substSubModules =
        m:
        deferredModuleWith (
          attrs
          // {
            staticModules = m;
          }
        );
      functor = defaultFunctor "deferredModuleWith" // {
        type = lib.types.deferredModuleWith;
        payload = {
          inherit staticModules;
        };
        binOp = lhs: rhs: {
          staticModules = lhs.staticModules ++ rhs.staticModules;
        };
      };
    };

  optionDeclaration = mkOptionType {
    name = "optionDeclaration";
    description = "option declaration";
    descriptionClass = "noun";
    check = opt: isType "option" opt && !(opt ? value);
  };

  # The type of a type!
  optionType = mkOptionType {
    name = "optionType";
    description = "optionType";
    descriptionClass = "noun";
    check = isType "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,
      description ? null,
      class ? null,
    }@attrs:
    let
      inherit (lib.modules) evalModules;

      allModules =
        defs:
        map (
          { value, file }:
          if isAttrs value && shorthandOnlyDefinesConfig then
            {
              _file = file;
              config = value;
            }
          else
            {
              _file = file;
              imports = [ value ];
            }
        ) defs;

      base = evalModules {
        inherit class 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;

      name = "submodule";

      check = {
        __functor = _self: x: isAttrs x || isFunction x || path.check x;
        isV2MergeCoherent = true;
      };
    in
    mkOptionType {
      inherit name;
      description =
        if description != null then
          description
        else
          let
            docsEval = base.extendModules { modules = [ noCheckForDocsModule ]; };
          in
          if docsEval._module.freeformType ? description then
            "open ${name} of ${
              optionDescriptionPhrase (
                class: class == "noun" || class == "composite"
              ) docsEval._module.freeformType
            }"
          else
            name;
      inherit check;
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }:
          let
            configuration = base.extendModules {
              modules = [ { _module.args.name = last loc; } ] ++ allModules defs;
              prefix = loc;
            };
          in
          {
            headError = checkDefsForError check loc defs;
            value = configuration.config;
            valueMeta = { inherit configuration; };
          };
      };
      emptyValue = {
        value = base.config;
      };
      getSubOptions =
        prefix:
        let
          docsEval = (
            base.extendModules {
              inherit prefix;
              modules = [ noCheckForDocsModule ];
            }
          );
          # Intentionally shadow the freeformType from the possibly *checked*
          # configuration. See `noCheckForDocsModule` comment.
          inherit (docsEval._module) freeformType;
        in
        docsEval.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 = lib.types.submoduleWith;
        payload = {
          inherit
            modules
            class
            specialArgs
            shorthandOnlyDefinesConfig
            description
            ;
        };
        binOp = lhs: rhs: {
          class =
            # `or null` was added for backwards compatibility only. `class` is
            # always set in the current version of the module system.
            if lhs.class or null == null then
              rhs.class or null
            else if rhs.class or null == null then
              lhs.class or null
            else if lhs.class or null == rhs.class then
              lhs.class or null
            else
              throw "A submoduleWith option is declared multiple times with conflicting class values \"${toString lhs.class}\" and \"${toString rhs.class}\".";
          modules = lhs.modules ++ rhs.modules;
          specialArgs =
            let
              intersecting = builtins.intersectAttrs lhs.specialArgs rhs.specialArgs;
            in
            if intersecting == { } then
              lhs.specialArgs // rhs.specialArgs
            else
              throw "A submoduleWith option is declared multiple times with the same specialArgs \"${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";
          description =
            if lhs.description == null then
              rhs.description
            else if rhs.description == null then
              lhs.description
            else if lhs.description == rhs.description then
              lhs.description
            else
              throw "A submoduleWith option is declared multiple times with conflicting descriptions";
        };
      };
    };

  # A value from a set of allowed ones.
  enum =
    values:
    let
      inherit (lib.lists) unique;
      show =
        v:
        if builtins.isString v then
          ''"${v}"''
        else if builtins.isInt v then
          toString v
        else if builtins.isBool v then
          boolToString v
        else
          "<${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}";
      descriptionClass = if builtins.length values < 2 then "noun" else "conjunction";
      check = flip elem values;
      merge = mergeEqualOption;
      functor = (defaultFunctor name) // {
        payload = { inherit values; };
        type = payload: lib.types.enum payload.values;
        binOp = a: b: { values = unique (a.values ++ b.values); };
      };
    };

  /**
    Creates a value type suitable for serialization formats.

    Parameters:
    - typeName: String describing the format (e.g. "JSON", "YAML", "XML")
    - nullable: Whether the structured value type allows `null` values.

    Returns a type suitable for structured data formats that supports:
    - Basic types: boolean, integer, float, string, path
    - Complex types: attribute sets and lists
  */
  serializableValueWith =
    {
      typeName,
      nullable ? true,
    }:
    let
      baseType = oneOf [
        bool
        int
        float
        str
        path
        (attrsOf valueType)
        (listOf valueType)
      ];
      valueType = (if nullable then nullOr baseType else baseType) // {
        description = "${typeName} value";
      };
    in
    valueType;

  json = serializableValueWith { typeName = "JSON"; };

  toml = serializableValueWith {
    typeName = "TOML";
    nullable = false;
  };

  # Either value of type `t1` or `t2`.
  either =
    t1: t2:
    mkOptionType rec {
      name = "either";
      description =
        if t1.descriptionClass or null == "nonRestrictiveClause" then
          # Plain, but add comma
          "${t1.description}, or ${
            optionDescriptionPhrase (class: class == "noun" || class == "conjunction") t2
          }"
        else
          "${optionDescriptionPhrase (class: class == "noun" || class == "conjunction") t1} or ${
            optionDescriptionPhrase (
              class: class == "noun" || class == "conjunction" || class == "composite"
            ) t2
          }";
      descriptionClass = "conjunction";
      check = {
        __functor = _self: x: t1.check x || t2.check x;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }@args:
          let
            t1CheckedAndMerged =
              if t1.merge ? v2 then
                checkV2MergeCoherence loc t1 (t1.merge.v2 args)
              else
                {
                  value = t1.merge loc defs;
                  headError = checkDefsForError t1.check loc defs;
                  valueMeta = { };
                };
            t2CheckedAndMerged =
              if t2.merge ? v2 then
                checkV2MergeCoherence loc t2 (t2.merge.v2 args)
              else
                {
                  value = t2.merge loc defs;
                  headError = checkDefsForError t2.check loc defs;
                  valueMeta = { };
                };

            checkedAndMerged =
              if t1CheckedAndMerged.headError == null then
                t1CheckedAndMerged
              else if t2CheckedAndMerged.headError == null then
                t2CheckedAndMerged
              else
                rec {
                  valueMeta = {
                    inherit headError;
                  };
                  headError = {
                    message = "The option `${showOption loc}` is neither a value of type `${t1.description}` nor `${t2.description}`, Definition values: ${showDefs defs}";
                  };
                  value = lib.warn ''
                    One or more definitions did not pass the type-check of the 'either' type.
                    ${headError.message}
                    If `either`, `oneOf` or similar is used in freeformType, ensure that it is preceded by an 'attrsOf' such as: `freeformType = types.attrsOf (types.either t1 t2)`.
                    Otherwise consider using the correct type for the option `${showOption loc}`.  This will be an error in Nixpkgs 26.05.
                  '' (mergeOneOption loc defs);
                };
          in
          checkedAndMerged;
      };
      typeMerge =
        f':
        let
          mt1 = t1.typeMerge (head f'.payload.elemType).functor;
          mt2 = t2.typeMerge (elemAt f'.payload.elemType 1).functor;
        in
        if (name == f'.name) && (mt1 != null) && (mt2 != null) then functor.type mt1 mt2 else null;
      functor = elemTypeFunctor name {
        elemType = [
          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;
    in
    foldl' either head' (tail ts);

  # Either value of type `coercedType` or `finalType`, the former is
  # converted to `finalType` using `coerceFunc`.
  coercedTo =
    coercedType: coerceFunc: finalType:
    assert
      coercedType.getSubModules == null
      || throw "coercedTo: coercedType must not have submodules (it’s a ${coercedType.description})";
    mkOptionType rec {
      name = "coercedTo";
      description = "${optionDescriptionPhrase (class: class == "noun") finalType} or ${
        optionDescriptionPhrase (class: class == "noun") coercedType
      } convertible to it";
      check = {
        __functor = _self: x: (coercedType.check x && finalType.check (coerceFunc x)) || finalType.check x;
        isV2MergeCoherent = true;
      };
      merge = {
        __functor =
          self: loc: defs:
          (self.v2 { inherit loc defs; }).value;
        v2 =
          { loc, defs }:
          let
            finalDefs = (
              map (
                def:
                def
                // {
                  value =
                    if coercedType.merge ? v2 then
                      let
                        merged = checkV2MergeCoherence loc coercedType (
                          coercedType.merge.v2 {
                            inherit loc;
                            defs = [ def ];
                          }
                        );
                      in
                      if merged.headError == null then coerceFunc def.value else def.value
                    else if coercedType.check def.value then
                      coerceFunc def.value
                    else
                      def.value;
                }
              ) defs
            );
          in
          if finalType.merge ? v2 then
            checkV2MergeCoherence loc finalType (
              finalType.merge.v2 {
                inherit loc;
                defs = finalDefs;
              }
            )
          else
            {
              value = finalType.merge loc finalDefs;
              valueMeta = { };
              headError = checkDefsForError check loc defs;
            };
      };
      emptyValue = finalType.emptyValue;
      getSubOptions = finalType.getSubOptions;
      getSubModules = finalType.getSubModules;
      substSubModules = m: coercedTo coercedType coerceFunc (finalType.substSubModules m);
      typeMerge = t: null;
      functor = defaultFunctor name;
      nestedTypes.coercedType = coercedType;
      nestedTypes.finalType = finalType;
    };

  /**
    Augment the given type with an additional type check function.

    :::{.warning}
    This function has some broken behavior see: [#396021](https://github.com/NixOS/nixpkgs/issues/396021)
    Fixing is not trivial, we appreciate any help!
    :::
  */
  addCheck =
    elemType: check:
    if elemType.merge ? v2 then
      elemType
      // {
        check = {
          __functor = _self: x: elemType.check x && check x;
          isV2MergeCoherent = true;
        };
        merge = {
          __functor =
            self: loc: defs:
            (self.v2 { inherit loc defs; }).value;
          v2 =
            { loc, defs }@args:
            let
              orig = checkV2MergeCoherence loc elemType (elemType.merge.v2 args);
              headError' = if orig.headError != null then orig.headError else checkDefsForError check loc defs;
            in
            orig
            // {
              headError = headError';
            };
        };
      }
    else
      elemType
      // {
        check = x: elemType.check x && check x;
      };

  /**
    Merges two option types together.

    :::{.note}
    Uses the type merge function of the first type, to merge it with the second type.

    Usually types can only be merged if they are of the same type
    :::

    # Inputs

    : `a` (option type): The first option type.
    : `b` (option type): The second option type.

    # Returns

    - The merged option type.
    - `{ _type = "merge-error"; error = "Cannot merge types"; }` if the types can't be merged.

    # Examples
    :::{.example}
    ## `lib.types.mergeTypes` usage example
    ```nix
    let
      enumAB = lib.types.enum ["A" "B"];
      enumXY = lib.types.enum ["X" "Y"];
      # This operation could be notated as: [ A ] | [ B ] -> [ A B ]
      merged = lib.types.mergeTypes enumAB enumXY; # -> enum [ "A" "B" "X" "Y" ]
    in
      assert merged.check "A"; # true
      assert merged.check "B"; # true
      assert merged.check "X"; # true
      assert merged.check "Y"; # true
      merged.check "C" # false
    ```
    :::
  */
  mergeTypes =
    a: b:
    assert isOptionType a && isOptionType b;
    let
      merged = a.typeMerge b.functor;
    in
    if merged == null then setType "merge-error" { error = "Cannot merge types"; } else merged;

  # TODO: Migrate usage of lib.types.types in nixpkgs
  # Then add a deprecation warning
  types = lib.types;
}