Guidance on Designing Label Generation Rulesets (LGRs) Supporting Variant Labels
RFC 8228

Internet Engineering Task Force (IETF)                        A. Freytag
Request for Comments: 8228                                   August 2017
Category: Informational
ISSN: 2070-1721

   Guidance on Designing Label Generation Rulesets (LGRs) Supporting
                             Variant Labels

Abstract

   Rules for validating identifier labels and alternate representations
   of those labels (variants) are known as Label Generation Rulesets
   (LGRs); they are used for the implementation of identifier systems
   such as Internationalized Domain Names (IDNs).  This document
   describes ways to design LGRs to support variant labels.  In
   designing LGRs, it is important to ensure that the label generation
   rules are consistent and well behaved in the presence of variants.
   The design decisions can then be expressed using the XML
   representation of LGRs that is defined in RFC 7940.

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It has been approved for publication by the Internet
   Engineering Steering Group (IESG).  Not all documents approved by the
   IESG are a candidate for any level of Internet Standard; see
   Section 2 of RFC 7841.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc8228.

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Copyright Notice

   Copyright (c) 2017 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   3
   2.  Variant Relations . . . . . . . . . . . . . . . . . . . . . .   4
   3.  Symmetry and Transitivity . . . . . . . . . . . . . . . . . .   5
   4.  A Word on Notation  . . . . . . . . . . . . . . . . . . . . .   5
   5.  Variant Mappings  . . . . . . . . . . . . . . . . . . . . . .   6
   6.  Variant Labels  . . . . . . . . . . . . . . . . . . . . . . .   7
   7.  Variant Types and Label Dispositions  . . . . . . . . . . . .   7
   8.  Allocatable Variants  . . . . . . . . . . . . . . . . . . . .   8
   9.  Blocked Variants  . . . . . . . . . . . . . . . . . . . . . .   9
   10. Pure Variant Labels . . . . . . . . . . . . . . . . . . . . .  10
   11. Reflexive Variants  . . . . . . . . . . . . . . . . . . . . .  11
   12. Limiting Allocatable Variants by Subtyping  . . . . . . . . .  12
   13. Allowing Mixed Originals  . . . . . . . . . . . . . . . . . .  14
   14. Handling Out-of-Repertoire Variants . . . . . . . . . . . . .  15
   15. Conditional Variants  . . . . . . . . . . . . . . . . . . . .  16
   16. Making Conditional Variants Well Behaved  . . . . . . . . . .  18
   17. Variants for Sequences  . . . . . . . . . . . . . . . . . . .  19
   18. Corresponding XML Notation  . . . . . . . . . . . . . . . . .  21
   19. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  22
   20. Security Considerations . . . . . . . . . . . . . . . . . . .  23
   21. References  . . . . . . . . . . . . . . . . . . . . . . . . .  23
     21.1.  Normative References . . . . . . . . . . . . . . . . . .  23
     21.2.  Informative References . . . . . . . . . . . . . . . . .  23
   Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . .  24
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  24

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1.  Introduction

   Label Generation Rulesets (LGRs) that define the set of permissible
   labels may be applied to identifier systems that rely on labels, such
   as the Domain Name System (DNS) [RFC1034] [RFC1035].  To date, LGRs
   have mostly been used to define policies for implementing
   Internationalized Domain Names (IDNs) using IDNA2008 [RFC5890]
   [RFC5891] [RFC5892] [RFC5893] [RFC5894] in the DNS.  This document
   aims to discuss the generation of LGRs for such circumstances, but
   the techniques and considerations here are almost certainly
   applicable to a wider range of internationalized identifiers.

   In addition to determining whether a given label is eligible, LGRs
   may also define the condition under which alternate representations
   of these labels, so-called "variant labels", may exist and their
   status (disposition).  In the most general sense, variant labels are
   typically labels that are either visually or semantically
   indistinguishable from another label in the context of the writing
   system or script supported by the LGR.  Unlike merely similar labels,
   where there may be a measurable degree of similarity, variant labels
   considered here represent a form of equivalence in meaning or
   appearance.  What constitutes an appropriate variant in any writing
   system or given context, particularly in the DNS, is assumed to have
   been determined ahead of time and therefore is not a subject of this
   document.

   Once identified, variant labels are typically delegated to some
   entity together with the applied-for label, or permanently reserved,
   based on the disposition derived from the LGR.  Correctly defined,
   variant labels can improve the security of an LGR, yet successfully
   defining variant rules for an LGR so that the result is well behaved
   is not always trivial.  This document describes the basic
   considerations and constraints that must be taken into account and
   gives examples of what might be use cases for different types of
   variant specifications in an LGR.

   This document does not address whether variants are an appropriate
   means to solve any given issue or the basis on which they should be
   defined.  It is intended to explain in more detail the effects of
   various declarations and the trade-offs in making design choices.  It
   implicitly assumes that any LGR will be expressed using the XML
   representation defined in [RFC7940] and therefore conforms to any
   requirements stated therein.  Purely for clarity of exposition,
   examples in this document use a more compact notation than the XML
   syntax defined in [RFC7940].  However, the reader is expected to have
   some familiarity with the concepts described in that RFC (see
   Section 4).

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   The user of any identifier system, such as the DNS, interacts with it
   in the context of labels; variants are experienced as variant labels,
   i.e., two (or more) labels that are functionally "same as" under the
   conventions of the writing system used, even though their code point
   sequences are different.  An LGR specification, on the other hand,
   defines variant mappings between code points and, only in a secondary
   step, derives the variant labels from these mappings.  For a
   discussion of this process, see [RFC7940].

   The designer of an LGR can control whether some or all of the variant
   labels created from an original label should be allocatable, i.e.,
   available for allocation (to the original applicant), or whether some
   or all of these labels should be blocked instead, i.e., remain not
   allocatable (to anyone).  This document describes how this choice of
   label disposition is accomplished (see Section 7).

   The choice of desired label disposition would be based on the
   expectations of the users of the particular zone; it is not the
   subject of this document.  Likewise, this document does not address
   the possibility of an LGR defining custom label dispositions.
   Instead, this document suggests ways of designing an LGR to achieve
   the selected design choice for handling variants in the context of
   the two standard label dispositions: "allocatable" and "blocked".

   The information in this document is based on operational experience
   gained in developing LGRs for a wide number of languages and scripts
   using RFC 7940.  This information is provided here as a benefit to
   the wider community.  It does not alter or change the specification
   found in RFC 7940 in any way.

2.  Variant Relations

   A variant relation is fundamentally a "same as" relation; in other
   words, it is an equivalence relation.  Now, the strictest sense of
   "same as" would be equality, and for any equality, we have both
   symmetry

     A = B => B = A

   and transitivity

     A = B and B = C => A = C

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   The variant relation with its functional sense of "same as" must
   really satisfy the same constraint.  Once we say A is the "same as"
   B, we also assert that B is the "same as" A.  In this document, the
   symbol "~" means "has a variant relation with".  Thus, we get

     A ~ B => B ~ A

   Likewise, if we make the same claim for B and C (B ~ C), then we get
   A ~ C, because if B is the "same as" both A and C, then A must be the
   "same as" C:

     A ~ B and B ~ C => A ~ C

3.  Symmetry and Transitivity

   Not all potential relations between labels constitute equivalence,
   and those that do not are not transitive and may not be symmetric.
   For example, the degree to which labels are confusable is not
   transitive: two labels can be confusingly similar to a third without
   necessarily being confusable with each other, such as when the third
   one has a shape that is "in between" the other two.  In contrast, a
   relation based on identical or effectively identical appearance would
   meet the criterion of transitivity, and we would consider it a
   variant relation.  Examples of variant relations include other forms
   of equivalence, such as semantic equivalence.

   Using [RFC7940], a set of mappings could be defined that is neither
   symmetric nor transitive; such a specification would be formally
   valid.  However, a symmetric and transitive set of mappings is
   strongly preferred as a basis for an LGR, not least because of the
   benefits from an implementation point of view; for example, if all
   mappings are symmetric and transitive, it greatly simplifies the
   check for collisions between labels with variants.  For this reason,
   we will limit the discussion in this document to those relations that
   are symmetric and transitive.  Incidentally, it is often
   straightforward to verify mechanically whether an LGR is symmetric
   and/or transitive and to compute any mappings required to make it so
   (but see Section 15).

4.  A Word on Notation

   [RFC7940] defines an XML schema for Label Generation Rulesets in
   general and variant code points and sequences in particular (see
   Section 18).  That notation is rather verbose and can easily obscure
   salient features to anyone not trained to read XML.  For this reason,
   this document uses a symbolic shorthand notation in presenting the
   examples for discussion.  This shorthand is merely a didactic tool

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   for presentation and is not intended as an alternative to or
   replacement for the XML syntax that is used in formally specifying an
   LGR under [RFC7940].

   When it comes time to capture the LGR in a formal definition, the
   notation used for any of the examples in this document can be
   converted to the XML format as described in Section 18.

5.  Variant Mappings

   So far, we have treated variant relations as simple "same as"
   relations, ignoring that each relation representing equivalence would
   consist of a symmetric pair of reciprocal mappings.  In this
   document, the symbol "-->" means "maps to".

   A ~ B => A --> B, B --> A

   In an LGR, these mappings are not defined directly between labels but
   between code points (or code point sequences; see Section 17).  In
   the transitive case, given

   A ~ B => A --> B, B --> A

   A ~ C => A --> C, C --> A

   we also get

   B ~ C => B --> C, C --> B

   for a total of six possible mappings.  Conventionally, these are
   listed in tables in order of the source code point, like so:

     A --> B
     A --> C
     B --> A
     B --> C
     C --> A
     C --> B

   As we can see, A, B, and C can each be mapped two ways.

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6.  Variant Labels

   To create a variant label, each code point in the original label is
   successively replaced by all variant code points defined by a mapping
   from the original code point.  For a label AAA (the letter "A" three
   times), the variant labels (given the mappings from the transitive
   example above) would be

     AAB
     ABA
     ABB
     BAA
     BAB
     BBA
     BBB
     AAC
     ...
     CCC

   So far, we have merely defined what the variant labels are, but we
   have not considered their possible dispositions.  In the next
   section, we discuss how to set up the variant mappings so that some
   variant labels are mutually exclusive (blocked), but some may be
   allocated to the same applicant as the original label (allocatable).

7.  Variant Types and Label Dispositions

   Assume we wanted to allow a variant relation between code points O
   and A, and perhaps between O and B or O and C as well.  Assuming
   transitivity, this would give us:

     O ~ A ~ B ~ C

   Now, further assume that we would like to distinguish the case where
   someone applies for OOO from the case where someone applies for the
   label ABC.  In this case, we would like to allocate only the applied-
   for label OOO, but in the latter case, we would like to also allow
   the allocation of either the label OOO or the variant label ABC, or
   both, but not of any of the other possible variant labels, like OAO,
   BCO, or the like.  (A real-world example might be the case where O
   represents an unaccented letter, while A, B, and C might represent
   various accented forms of the same letter.  Because unaccented
   letters are a common fallback, there might be a desire to allocate an
   unaccented label as a variant, but not the other way around.)

   How would we specify such a distinction?

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   The answer lies in labeling the mappings A --> O, B --> O, and C -->
   O with the type "allocatable" and the mappings O --> A, O --> B, and
   O --> C with the type "blocked".  In this document, the symbol "x-->"
   means "maps with type blocked", and the symbol "a-->" means "maps
   with type allocatable".  Thus:

     O  x--> A
     O  x--> B
     O  x--> C
     A  a--> O
     B  a--> O
     C  a--> O

   When we generate all permutations of labels, we use mappings with
   different types depending on which code points we start from.  The
   set of all permuted variant labels would be the same, but the
   disposition of the variant label depends on which label we start from
   (we call that label the "original" or "applied-for" label).

   In creating an LGR with variants, all variant mappings should always
   be labeled with a type ([RFC7940] does not formally require a type,
   but any well-behaved LGR would be fully typed).  By default, these
   types correspond directly to the dispositions for variant labels,
   with the most restrictive type determining the disposition of the
   variant label.  However, as we shall see later, it is sometimes
   useful to assign types from a wider array of values than the final
   dispositions for the labels and then define explicitly how to derive
   label dispositions from them.

8.  Allocatable Variants

   If we start with AAA and use the mappings from Section 7, the
   permutation OOO will be the result of applying the mapping A a--> O
   at each code point.  That is, only mappings with type "a"
   (allocatable) were used.  To know whether we can allocate both the
   label OOO and the original label AAA, we track the types of the
   mappings used in generating the label.

   We record the variant types for each of the variant mappings used in
   creating the permutation in an ordered list.  Such an ordered list of
   variant types is called a "variant type list".  In running text, we
   often show it enclosed in square brackets.  For example, [a x -]
   means the variant label was derived from a variant mapping with the
   "a" variant type in the first code point position, "x" in the second
   code point position, and the original code point in the third
   position ("-" means "no variant mapping").

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   For our example permutation, we get the following variant type list
   (brackets dropped):

     AAA --> OOO : a a a

   From the variant type list, we derive a "variant type set", denoted
   by curly braces, that contains an unordered set of unique variant
   types in the variant type list.  For the variant type list for the
   given permutation, [a a a], the variant type set is { a }, which has
   a single element "a".

   Deciding whether to allow the allocation of a variant label then
   amounts to deriving a disposition for the variant label from the
   variant type set created from the variant mappings that were used to
   create the label.  For example, the derivation

     if "all variants" = "a" => set label disposition to "allocatable"

   would allow OOO to be allocated, because the types of all variant
   mappings used to create that variant label from AAA are "a".

   The "all-variants" condition is tolerant of an extra "-" in the
   variant set (unlike the "only-variants" condition described in
   Section 10).  So, had we started with AOA, OAA, or AAO, the variant
   set for the permuted variant OOO would have been { a - } because in
   each case one of the code points remains the same code point as the
   original.  The "-" means that because of the absence of a mapping O
   --> O, there is no variant type for the O in each of these labels.

   The "all-variants" = "a" condition ignores the "-", so using the
   derivation from above, we find that OOO is an allocatable variant for
   each of the labels AOA, OAA, or AAO.

   Allocatable variant labels, especially large numbers of allocatable
   variants per label, incur a certain cost to users of the LGR.  A
   well-behaved LGR will minimize the number of allocatable variants.

9.  Blocked Variants

   Blocked variants are not available to another registrant.  They
   therefore protect the applicant of the original label from someone
   else registering a label that is the "same as" under some user-
   perceived metric.  Blocked variants can be a useful tool even for
   scripts for which no allocatable labels are ever defined.

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   If we start with OOO and use the mappings from Section 7, the
   permutation AAA will have been the result of applying only mappings
   with type "blocked", and we cannot allocate the label AAA, only the
   original label OOO.  This corresponds to the following derivation:

     if "any variants" = "x" => set label disposition to "blocked"

   Additionally, to prevent allocating ABO as a variant label for AAA,
   we need to make sure that the mapping A --> B has been defined with
   type "blocked", as in

     A  x--> B

   so that

     AAA --> ABO: - x a.

   Thus, the set {x a} contains at least one "x" and satisfies the
   derivation of a blocked disposition for ABO when AAA is applied for.

   If an LGR results in a symmetric and transitive set of variant
   labels, then the task of determining whether a label or its variants
   collide with another label or its variants can be implemented very
   efficiently.  Symmetry and transitivity imply that sets of labels
   that are mutual variants of each other are disjoint from all other
   such sets.  Only labels within the same set can be variants of each
   other.  Identifying the variant set can be an O(1) operation, and
   enumerating all variants is not necessary.

10.  Pure Variant Labels

   Now, if we wanted to prevent allocation of AOA when we start from
   AAA, we would need a rule disallowing a mix of original code points
   and variant code points; this is easily accomplished by use of the
   "only-variants" qualifier, which requires that the label consist
   entirely of variants and that all the variants are from the same set
   of types.

     if "only-variants" = "a" => set label disposition to "allocatable"

   The two code points A in AOA are not arrived at by variant mappings,
   because the code points are unchanged and no variant mappings are
   defined for A --> A.  So, in our example, the set of variant mapping
   types is

     AAA --> AOA:  - a -

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   but unlike the "all-variants" condition, "only-variants" requires a
   variant type set { a } corresponding to a variant type list [a a a]
   (no - allowed).  By adding a final derivation

     else if "any-variants" = "a" => set label disposition to "blocked"

   and executing that derivation only on any remaining labels, we
   disallow AOA when starting from AAA but still allow OOO.

   Derivation conditions are always applied in order, with later
   derivations only applying to labels that did not match any earlier
   conditions, as indicated by the use of "else" in the last example.
   In other words, they form a cascade.

11.  Reflexive Variants

   But what if we started from AOA?  We would expect the original label
   OOO to be allocatable, but, using the mappings from Section 7, the
   variant type set would be

     AOA --> OOO:  a - a

   because the middle O is unchanged from the original code point.  Here
   is where we use a reflexive mapping.  Realizing that O is the "same
   as" O, we can map it to itself.  This is normally redundant, but
   adding an explicit reflexive mapping allows us to specify a
   disposition on that mapping:

     O  a--> O

   With that, the variant type list for AOA --> OOO becomes:

     AOA --> OOO: a a a

   and the label OOO again passes the derivation condition

     if "only-variants" = "a" => set label disposition to "allocatable"

   as desired.  This use of reflexive variants is typical whenever
   derivations with the "only-variants" qualifier are used.  If any code
   point uses a reflexive variant, a well-behaved LGR would specify an
   appropriate reflexive variant for all code points.

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12.  Limiting Allocatable Variants by Subtyping

   As we have seen, the number of variant labels can potentially be
   large, due to combinatorics.  Sometimes it is possible to divide
   variants into categories and to stipulate that only variant labels
   with variants from the same category should be allocatable.  For some
   LGRs, this constraint can be implemented by a rule that disallows
   code points from different categories to occur in the same
   allocatable label.  For other LGRs, the appropriate mechanism may be
   dividing the allocatable variants into subtypes.

   To recap, in the standard case, a code point C can have (up to) two
   types of variant mappings

     C  x--> X
     C  a--> A

   where a--> means a variant mapping with type "allocatable" and x-->
   means "blocked".  For the purpose of the following discussion, we
   name the target code point with the corresponding uppercase letter.

   Subtyping allows us to distinguish among different types of
   allocatable variants.  For example, we can define three new types:
   "s", "t", and "b".  Of these, "s" and "t" are mutually incompatible,
   but "b" is compatible with either "s" or "t" (in this case, "b"
   stands for "both").  A real-world example for this might be variant
   mappings appropriate for "simplified" or "traditional" Chinese
   variants, or appropriate for both.

   With subtypes defined as above, a code point C might have (up to)
   four types of variant mappings

     C  x--> X
     C  s--> S
     C  t--> T
     C  b--> B

   and explicit reflexive mappings of one of these types

     C  s--> C
     C  t--> C
     C  b--> C

   As before, all mappings must have one and only one type, but each
   code point may map to any number of other code points.

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   We define the compatibility of "b" with "t" or "s" by our choice of
   derivation conditions as follows

     if "any-variants" = "x" =>  blocked
     else if "only-variants" = "s" or "b" =>  allocatable
     else if "only-variants" = "t" or "b" =>  allocatable
     else if "any-variants" = "s" or "t" or "b" =>  blocked

   An original label of four code points

     CCCC

   may have many variant labels, such as this example listed with its
   corresponding variant type list:

     CCCC --> XSTB : x s t b

   This variant label is blocked because to get from C to B required
   x-->.  (Because variant mappings are defined for specific source code
   points, we need to show the starting label for each of these
   examples, not merely the code points in the variant label.)  The
   variant label

     CCCC --> SSBB : s s b b

   is allocatable, because the variant type list contains only
   allocatable mappings of subtype "s" or "b", which we have defined as
   being compatible by our choice of derivations.  The actual set of
   variant types {s, b} has only two members, but the examples are
   easier to follow if we list each type.  The label

     CCCC --> TTBB : t t b b

   is again allocatable, because the variant type set {t, b} contains
   only allocatable mappings of the mutually compatible allocatable
   subtypes "t" or "b".  In contrast,

     CCCC --> SSTT : s s t t

   is not allocatable, because the type set contains incompatible
   subtypes "t" and "s" and thus would be blocked by the final
   derivation.

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   The variant labels

     CCCC --> CSBB : c s b b
     CCCC --> CTBB : c t b b

   are only allocatable based on the subtype for the C --> C mapping,
   which is denoted here by "c" and (depending on what was chosen for
   the type of the reflexive mapping) could correspond to "s", "t", or
   "b".

   If the subtype is "s", the first of these two labels is allocatable;
   if it is "t", the second of these two labels is allocatable; if it is
   "b", both labels are allocatable.

   So far, the scheme does not seem to have brought any huge reduction
   in allocatable variant labels, but that is because we tacitly assumed
   that C could have all three types of allocatable variants "s", "t",
   and "b" at the same time.

   In a real-world example, the types "s", "t", and "b" are assigned so
   that each code point C normally has, at most, one non-reflexive
   variant mapping labeled with one of these subtypes, and all other
   mappings would be assigned type "x" (blocked).  This holds true for
   most code points in existing tables (such as those used in current
   IDN Top-Level Domains (TLDs)), although certain code points have
   exceptionally complex variant relations and may have an extra
   mapping.

13.  Allowing Mixed Originals

   If the desire is to allow original labels (but not variant labels)
   that are s/t mixed, then the scheme needs to be slightly refined to
   distinguish between reflexive and non-reflexive variants.  In this
   document, the symbol "r-n" means "a reflexive (identity) mapping of
   type 'n'".  The reflexive mappings of the preceding section thus
   become:

   C  r-s--> C
   C  r-t--> C
   C  r-b--> C

   With this convention, and redefining the derivations

   if "any-variants" = "x" =>  blocked
   else if "only-variants" = "s" or "r-s" or "b" or "r-b" => allocatable
   else if "only-variants" = "t" or "r-t" or "b" or "r-b" => allocatable
   else if "any-variants" = "s" or "t" or "b"  => blocked
   else => allocatable

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   any labels that contain only reflexive mappings of otherwise mixed
   type (in other words, any mixed original label) now fall through, and
   their disposition is set to "allocatable" in the final derivation.

   In a well-behaved LGR, it is preferable to explicitly define the
   derivation for allocatable labels instead of using a fall through.
   In the derivation above, code points without any variant mappings
   fall through and become allocatable by default if they are part of an
   original label.  Especially in a large repertoire, it can be
   difficult to identify which code points are affected.  Instead, it is
   preferable to mark them with their own reflexive mapping type
   "neither" or "r-n".

     C  r-n--> C

   With that, we can change

     else =>  allocatable

   to

     else if "only-variants" = "r-s" or "r-t" or "r-b" or "r-n"
          =>  allocatable
     else => invalid

   This makes the intent more explicit, and by ensuring that all code
   points in the LGR have a reflexive mapping of some kind, it is easier
   to verify the correct assignment of their types.

14.  Handling Out-of-Repertoire Variants

   At first, it may seem counterintuitive to define variants that map to
   code points that are not part of the repertoire.  However, for zones
   for which multiple LGRs are defined, there may be situations where
   labels valid under one LGR should be blocked if a label under another
   LGR is already delegated.  This situation can arise whether or not
   the repertoires of the affected LGRs overlap and, where repertoires
   overlap, whether or not the labels are both restricted to the common
   subset.

   In order to handle this exclusion relation through definition of
   variants, it is necessary to be able to specify variant mappings to
   some code point X that is outside an LGR's repertoire, R:

     C  x--> X : where C = elementOf(R) and X != elementOf(R)

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   Because of symmetry, it is necessary to also specify the inverse
   mapping in the LGR:

     X  x--> C : where X != elementOf(R) and C = elementOf(R)

   This makes X a source of variant mappings, and it becomes necessary
   to identify X as being outside the repertoire, so that any attempt to
   apply for a label containing X will lead to a disposition of
   "invalid", just as if X had never been listed in the LGR.  The
   mechanism to do this uses reflexive variants but with a new type of
   reflexive mapping of "out-of-repertoire-var", shown as "r-o-->":

     X  r-o--> X

   This indicates X != elementOf(R), as long as the LGR is provided with
   a suitable derivation, so that any label containing "r-o-->" is
   assigned a disposition of "invalid", just as if X was any other code
   point not part of the repertoire.  The derivation used is:

     if "any-variant" = "out-of-repertoire-var" => invalid

   It is inserted ahead of any other derivation of the "any-variant"
   kind in the chain of derivations.  As a result, instead of the
   minimum two symmetric variants, for any out-of-repertoire variants,
   there are a minimum of three variant mappings defined:

     C  x--> X
     X  x--> C
     X  r-o--> X

   where C = elementOf(R) and X != elementOf(R).

   Because no variant label with any code point outside the repertoire
   could ever be allocated, the only logical choice for the non-
   reflexive mappings to out-of-repertoire code points is "blocked".

15.  Conditional Variants

   Variant mappings are based on whether code points are "same as" to
   the user.  In some writing systems, code points change shape based on
   where they occur in the word (positional forms).  Some code points
   have matching shapes in some positions but not in others.  In such
   cases, the variant mapping exists only for some possible positions
   or, more generally, only for some contexts.  For other contexts, the
   variant mapping does not exist.

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   For example, take two code points that have the same shape at the end
   of a label (or in final position) but not in any other position.  In
   that case, they are variants only when they occur in the final
   position, something we indicate like this:

     final: C --> D

   In cursively connected scripts, like Arabic, a code point may take
   its final form when next to any following code point that interrupts
   the cursive connection, not just at the end of a label.  (We ignore
   the isolated form to keep the discussion simple; if included, "final"
   might be "final-or-isolate", for example).

   From symmetry, we expect that the mapping D --> C should also exist
   only when the code point D is in final position.  (Similar
   considerations apply to transitivity.)

   Sometimes a code point has a final form that is practically the same
   as that of some other code point while sharing initial and medial
   forms with another.

     final: C --> D
     !final: C --> E

   Here, the case where the condition is the opposite of final is shown
   as "!final".

   Because shapes differ by position, when a context is applied to a
   variant mapping, it is treated independently from the same mapping in
   other contexts.  This extends to the assignment of types.  For
   example, the mapping C --> F may be "allocatable" in final position
   but "blocked" in any other context:

     final:  C  a--> F
     !final: C  x--> F

   Now, the type assigned to the forward mapping is independent of the
   reverse symmetric mapping or any transitive mappings.  Imagine a
   situation where the symmetric mapping is defined as F a--> C, that
   is, all mappings from F to C are "allocatable":

     final: F  a--> C
     !final: F  a-->C

   Why not simply write F a--> C?  Because the forward mapping is
   divided by context.  Adding a context makes the two forward variant
   mappings distinct, and that needs to be accounted for explicitly in
   the reverse mappings so that human and machine readers can easily

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   verify symmetry and transitivity of the variant mappings in the LGR.
   (This is true even though the two opposite contexts of "final" and
   "!final" should together cover all possible cases.)

16.  Making Conditional Variants Well Behaved

   To ensure that LGR with contextual variants is well behaved, it is
   best to always use "fully qualified" variant mappings that always
   agree in the names of the context rules for forward and reverse
   mappings.  It is also necessary to ensure that no label can match
   more than one context for the same mapping.  Using mutually exclusive
   contexts, such as "final" and "!final", is an easy way to ensure
   that.

   However, it is not always necessary to define dual or multiple
   contexts that together cover all possible cases.  For example, here
   are two contexts that do not cover all possible positional contexts:

     final: C --> D
     initial: C --> D.

   A well-behaved LGR using these two contexts would define all
   symmetric and transitive mappings involving C, D, and their variants
   consistently in terms of the two conditions "final" and "initial" and
   ensure that both cannot be satisfied at the same time by some label.

   In addition to never defining the same mapping with two contexts that
   may be satisfied by the same label, a well-behaved LGR never combines
   a variant mapping with a context with the same variant mapping
   without a context:

     context: C --> D
     C --> D

   Inadvertent mixing of conditional and unconditional variants can be
   detected and flagged by a parser, but verifying that two formally
   distinct contexts are never satisfied by the same label would depend
   on the interaction between labels and context rules, which means that
   it will be up to the LGR designer to ensure that the LGR is well
   behaved.

   A well-behaved LGR never assigns conditions on a reflexive variant,
   as that is effectively no different from having a context on the code
   point itself; the latter is preferred.

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   Finally, for symmetry to work as expected, the context must be
   defined such that it is satisfied for both the original code point in
   the context of the original label and for the variant code point in
   the variant label.  In other words, the context should be "stable
   under variant substitution" anywhere in the label.

   Positional contexts usually satisfy this last condition; for example,
   a code point that interrupts a cursive connection would likely share
   this property with any of its variants.  However, as it is possible
   in principle to define other kinds of contexts, it is necessary to
   make sure that the LGR is well behaved in this aspect at the time the
   LGR is designed.

   Due to the difficulty in verifying these constraints mechanically, it
   is essential that an LGR designer document the reasons why the LGR
   can be expected to meet them and the details of the techniques used
   to ensure that outcome.  This information should be found in the
   description element of the LGR.

   In summary, conditional contexts can be useful for some cases, but
   additional care must be taken to ensure that an LGR containing
   conditional contexts is well behaved.  LGR designers would be well
   advised to avoid using conditional contexts and to prefer
   unconditional rules whenever practical, even though it will
   doubtlessly reduce the number of labels practically available.

17.  Variants for Sequences

   Variant mappings can be defined between sequences or between a code
   point and a sequence.  For example, one might define a "blocked"
   variant between the sequence "rn" and the code point "m" because they
   are practically indistinguishable in common UI fonts.

   Such variants are no different from variants defined between single
   code points, except if a sequence is defined such that there is a
   code point or shorter sequence that is a prefix (initial subsequence)
   and both it and the remainder are also part of the repertoire.  In
   that case, it is possible to create duplicate variants with
   conflicting dispositions.

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   The following shows such an example resulting in conflicting
   reflexive variants:

     A  a--> C
     AB  x--> CD

   where AB is a sequence with an initial subsequence of A.  For
   example, B might be a combining code point used in sequence AB.  If B
   only occurs in the sequence, there is no issue, but if B also occurs
   by itself, for example:

     B  a--> D

   then a label "AB" might correspond to either {A}{B}, that is, the two
   code points, or {AB}, the sequence, where the curly braces show the
   sequence boundaries as they would be applied during label validation
   and variant mapping.

   A label AB would then generate the "allocatable" variant label {C}{D}
   and the "blocked" variant label {CD}, thus creating two variant
   labels with conflicting dispositions.

   For the example of a blocked variant between "m" and "rn" (and vice
   versa), there is no issue as long as "r" and "n" do not have variant
   mappings of their own, so that there cannot be multiple variant
   labels for the same input.  However, it is preferable to avoid
   ambiguities altogether where possible.

   The easiest way to avoid an ambiguous segmentation into sequences is
   by never allowing both a sequence and all of its constituent parts
   simultaneously as independent parts of the repertoire, for example,
   by not defining B by itself as a member of the repertoire.

   Sequences are often used for combining sequences that consist of a
   base character B followed by one or more combining marks C.  By
   enumerating all sequences in which a certain combining mark is
   expected and by not listing the combining mark by itself in the LGR,
   the mark cannot occur outside of these specifically enumerated
   contexts.  In cases where enumeration is not possible or practicable,
   other techniques can be used to prevent ambiguous segmentation, for
   example, a context rule on code points that disallows B preceding C
   in any label except as part of a predefined sequence or class of
   sequences.  The details of such techniques are outside the scope of
   this document (see [RFC7940] for information on context rules for
   code points).

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18.  Corresponding XML Notation

   The XML format defined in [RFC7940] corresponds fairly directly to
   the notation used for variant mappings in this document.  (There is
   no notation in the RFC for variant type sets).  In an LGR document, a
   simple member of a repertoire that does not have any variants is
   listed as:

   <char cp="nnnn" />

   where nnnn is the [UNICODE] code point value in the standard
   uppercase hexadecimal notation padded to at least 4 digits and
   without leading "U+".  For a code point sequence of length 2, the XML
   notation becomes:

   <char cp="uuuu vvvvv" />

   Variant mappings are defined by nesting <var> elements inside the
   <char> element.  For example, a variant relation of type "blocked"

     C  x--> X

   is expressed as

     <char cp="nnnn">
       <var cp="mmmm" type="blocked" />
     </char>

   where "x-->" identifies a "blocked" type.  (Other types include
   "a-->" for "allocatable", for example.  Here, nnnn and mmmm are the
   [UNICODE] code point values for C and X, respectively.  Either C or X
   could be a code point sequence or a single code point.

   A reflexive mapping is specified the same way, except that it always
   uses the same code point value for both the <char> and <var> element,
   for example:

     X  r-o--> X

   would correspond to

   <char cp="nnnn"><var cp="nnnn" type="out-of-repertoire-var" /></char>

   Multiple <var> elements may be nested inside a single <char> element,
   but their "cp" values must be distinct (unless attributes for context
   rules are present and the combination of "cp" value and context
   attributes are distinct).

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     <char cp="nnnn">
       <var cp="kkkk" type="allocatable" />
       <var cp="mmmm" type="blocked" />
     </char>

   A set of conditional variants like

     final: C  a--> K
     !final: C  x--> K

   would correspond to

     <var cp="kkkk" when="final" type="allocatable" />
     <var cp="kkkk" not-when="final" type="blocked" />

   where the string "final" references a name of a context rule.
   Context rules are defined in [RFC7940]; they conceptually correspond
   to regular expressions.  The details of how to create and define
   these rules are outside the scope of this document.  If the label
   matches the context defined in the rule, the variant mapping is valid
   and takes part in further processing.  Otherwise, it is invalid and
   ignored.  Using the "not-when" attribute inverts the sense of the
   match.  The two attributes are mutually exclusive.

   A derivation of a variant label disposition

     if "only-variants" = "s" or "b" => allocatable

   is expressed as

     <action disp="allocatable" only-variants= "s b" />

   Instead of using "if" and "else if", the <action> elements implicitly
   form a cascade, where the first action triggered defines the
   disposition of the label.  The order of action elements is thus
   significant.

   For the full specification of the XML format, see [RFC7940].

19.  IANA Considerations

   This document does not require any IANA actions.

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20.  Security Considerations

   As described in [RFC7940], variants may be used as a tool to reduce
   certain avenues of attack in security-relevant identifiers by
   allowing certain labels to be "mutually exclusive or registered only
   to the same user".  However, if indiscriminately designed, variants
   may themselves contribute to risks to the security or usability of
   the identifiers, whether resulting from an ambiguous definition or
   from allowing too many allocatable variants per label.

   The information in this document is intended to allow the reader to
   design a specification of an LGR that is "well behaved" with respect
   to variants; as used here, this term refers to an LGR that is
   predictable in its effects to the LGR author (and reviewer) and more
   reliable in its implementation.

   A well-behaved LGR is not merely one that can be expressed in
   [RFC7940], but, in addition, it actively avoids certain edge cases
   not prevented by the schema, such as those that would result in
   ambiguities in the specification of the intended disposition for some
   variant labels.  By applying the additional considerations introduced
   in this document, including adding certain declarations that are
   optional under the schema and may not alter the results of processing
   a label, such an LGR becomes easier to review and its implementations
   easier to verify.

   It should be noted that variants are an important part, but only a
   part, of an LGR design.  There are many other features of an LGR that
   this document does not touch upon.  Also, the question of whether to
   define variants at all, or what labels are to be considered variants
   of each other, is not addressed here.

21.  References

21.1.  Normative References

   [RFC7940]  Davies, K. and A. Freytag, "Representing Label Generation
              Rulesets Using XML", RFC 7940, DOI 10.17487/RFC7940,
              August 2016, <https://www.rfc-editor.org/info/rfc7940>.

21.2.  Informative References

   [RFC1034]  Mockapetris, P., "Domain names - concepts and facilities",
              STD 13, RFC 1034, DOI 10.17487/RFC1034, November 1987,
              <https://www.rfc-editor.org/info/rfc1034>.

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   [RFC1035]  Mockapetris, P., "Domain names - implementation and
              specification", STD 13, RFC 1035, DOI 10.17487/RFC1035,
              November 1987, <https://www.rfc-editor.org/info/rfc1035>.

   [RFC5890]  Klensin, J., "Internationalized Domain Names for
              Applications (IDNA): Definitions and Document Framework",
              RFC 5890, DOI 10.17487/RFC5890, August 2010,
              <https://www.rfc-editor.org/info/rfc5890>.

   [RFC5891]  Klensin, J., "Internationalized Domain Names in
              Applications (IDNA): Protocol", RFC 5891,
              DOI 10.17487/RFC5891, August 2010,
              <https://www.rfc-editor.org/info/rfc5891>.

   [RFC5892]  Faltstrom, P., Ed., "The Unicode Code Points and
              Internationalized Domain Names for Applications (IDNA)",
              RFC 5892, DOI 10.17487/RFC5892, August 2010,
              <https://www.rfc-editor.org/info/rfc5892>.

   [RFC5893]  Alvestrand, H., Ed. and C. Karp, "Right-to-Left Scripts
              for Internationalized Domain Names for Applications
              (IDNA)", RFC 5893, DOI 10.17487/RFC5893, August 2010,
              <https://www.rfc-editor.org/info/rfc5893>.

   [RFC5894]  Klensin, J., "Internationalized Domain Names for
              Applications (IDNA): Background, Explanation, and
              Rationale", RFC 5894, DOI 10.17487/RFC5894, August 2010,
              <https://www.rfc-editor.org/info/rfc5894>.

   [UNICODE]  The Unicode Consortium, "The Unicode Standard",
              <http://www.unicode.org/versions/latest/>.

Acknowledgments

   Contributions that have shaped this document have been provided by
   Marc Blanchet, Ben Campbell, Patrik Faltstrom, Scott Hollenbeck,
   Mirja Kuehlewind, Sarmad Hussain, John Klensin, Alexey Melnikov,
   Nicholas Ostler, Michel Suignard, Andrew Sullivan, Wil Tan, and
   Suzanne Woolf.

Author's Address

   Asmus Freytag

   Email: asmus@unicode.org

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