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<rfc category="info" ipr="trust200902" docName="draft-freytag-lager-variant-rules-06" >
  <!-- ***** FRONT MATTER ***** -->
  <front>
    <title abbrev="Variant Rules">Guidance on Designing Label
Generation Rulesets (LGR) Supporting Variant Labels</title>
    <!-- add 'role="editor"' below for the editors if appropriate -->
    <author fullname="Asmus Freytag" initials="A." surname="Freytag">
      <organization/>
      <address>
      <email>asmus@unicode.org</email>
      </address>
    </author>
    <date />
    <!-- Meta-data Declarations
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    <!-- You can add <keyword/> elements here.  They will be incorporated into HTML output
         files in a meta tag but they have no effect on text or nroff output. -->
    <keyword>LGR</keyword> <keyword>Variant</keyword> <keyword>IDN</keyword>
    <abstract>
      <t>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 of designing Label Generation Rulesets 
      (LGRs) that 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 RFC7940.</t>
    </abstract>
  </front>
  <middle>
    <section title="Introduction" anchor="Introduction">
      <t>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, <xref target="RFC1034" /> <xref target="RFC1035" />).  To date, LGRs have mostly been used to define 
        policies for implementing Internationalized Domain Names (IDNs) using IDNA2008 <xref target="RFC5890" />
        <xref target="RFC5891" /> <xref target="RFC5892" /> <xref target="RFC5893" /> <xref target="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.</t> 
      <t>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 also define 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, particular in the DNS, is 
        assumed to have been determined ahead of time, and therefore
        is not subject of this document.</t>
      <t>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.
       </t>
      <t>This document does not address the question whether variants are an appropriate
        means to solve any given issue, nor on what basis they should be defined. It is 
        intended to explain in more detail the effects of various declarations and the 
        tradeoffs in making design choices. It implicitly assumes that any LGR will be expressed using
        the XML representation defined in <xref target="RFC7940" /> and therefore conform
        to any requirements stated therein. Purely for clarity of exposition, examples in this 
        document are using a more compact notation than the XML syntax defined in 
        <xref target="RFC7940" />. However, the reader is expected to have some familiarity 
        with the concepts described in that RFC (see <xref target="Notation" /> below).</t>
      <t>The user of any identifier system, such as the DNS, interacts with it in the 
        context of labels; variants are experienced as variant labels: two (or more) labels 
        that are functionally "the same" 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 <xref target="RFC7940" />.</t>
      <t>The designer of an LGR can control whether some or all of the variant labels created 
        from an original label should be allocatable, that is available for allocation (to the original 
        applicant) or whether some or all of these labels should be blocked instead, that 
        is, remain not allocatable (to anyone). This document describes how this choice of
        label disposition is accomplished (see <xref target="Variant_Types_and_Label_Dispositions" />).</t>
      <t>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".</t>
        <t>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.</t>
    </section>
    
    <section title="Variant Relationships" anchor="Variant_Relationships">
      <t>A variant relationship is fundamentally a &quot;same as&quot;, in other words, it 
        is an equivalence relationship. Now the strictest sense of &quot;same as&quot; would be 
        equality, and for any equality, we have both symmetry</t>
      <figure>
        <artwork>
<![CDATA[  A = B => B = A ]]>
        </artwork>
      </figure>
      <t> and transitivity</t>
      <figure>
        <artwork>
<![CDATA[  A = B and B = C => A = C ]]>
        </artwork>
      </figure>
      <t>The variant relationship with its functional sense of &quot;same as&quot; must really 
        satisfy the same constraint. Once we say A is the &quot;same as&quot; B, we also assert that 
        B is the "same as" A. In this document, the symbol "~" means "has a variant relationship 
        with". Thus, we get</t>
      <figure>
        <artwork>
<![CDATA[  A ~ B => B ~ A ]]>
        </artwork>
      </figure>
      <t>Likewise, if we make the same claim for B and C (B ~ C) then we do get 
        A ~ C, because if B is &quot;the same&quot; as both A and C then A must be &quot;the same as&quot; C:</t>
      <figure>
        <artwork>
<![CDATA[  A ~ B and B ~ C => A ~ C ]]>
        </artwork>
      </figure>
      </section>
      <section title="Symmetry and Transitivity" anchor="Symmetry_and_Transitivity" >
      <t>Not all potential relationships 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 relationship. Examples of variant relations include other forms of
        equivalence, such as semantic equivalence.</t>
        <t>Using <xref target="RFC7940" />, a set of mappings could be defined that are neither 
        symmetric nor transitive; such a specification would be formally valid. However, 
        a symmetric and transitive set of mappings are 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 <xref target="Conditional_Variants" />).</t>
    </section>
    
    <section title="A Word on Notation" anchor="Notation">
      <t><xref target="RFC7940" /> defines an XML schema for Label Generation Rulesets in general,
      and variant code points and sequences in particular,
      see <xref target="Corresponding_XML_Notation" />. 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 for presentation and not intended as alternative to or 
      replacement for the XML syntax that is used in formally specifying an LGR under <xref target="RFC7940" />.</t>
      <t> When it comes time to capture the LGR in a formal definition, the notation used for
      any of examples in this document can be converted to the XML format as described in 
      <xref target="Corresponding_XML_Notation"/>.</t>
    </section>
    
    <section title="Variant Mappings" anchor="Variant_Mappings">
      <t>So far, we have treated variant relationships as simple "same as" ignoring 
        that each relationship representing equivalence would consist of a symmetric pair 
        of reciprocal mappings. In this document, the symbol "-->" means "maps to".</t>
      <t>A ~ B =&gt; A --> B, B --> A</t>
      <t>In an LGR, these mappings are not defined directly between labels, but between code 
        points (or code point sequences, see <xref target="Variants_for_Sequences"/>). 
        In the transitive case, given</t>
      <t>A ~ B =&gt; A --> B, B --> A</t>
      <t>A ~ C =&gt; A --> C, C --> A</t>
      <t>we also get</t>
      <t>B ~ C =&gt; B --> C, C --> B</t>
      <t>for a total of six possible mappings. Conventionally, these are listed 
        in tables in order of the source code point, like so</t>
      <figure>
        <artwork>
<![CDATA[  A --> B
  A --> C
  B --> A
  B --> C
  C --> A
  C --> B ]]>
        </artwork>
      </figure>
      <t>As we can see, each of A, B and C can be mapped two ways.</t>
    </section>
    
    <section title="Variant Labels" anchor="Variant_Labels">
      <t>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 transitive example above) would be</t>
      <figure>
        <artwork>
<![CDATA[  AAB
  ABA
  ABB
  BAA
  BAB
  BBA
  BBB
  AAC
  ...    
  CCC]]>
        </artwork>
      </figure>
      <t>So far, we have mere 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).</t>
    </section>
    
    <section title="Variant Types and Label Dispositions" anchor="Variant_Types_and_Label_Dispositions">
      <t>Assume we wanted to allow a variant relation between some code points O and 
        A, and perhaps between O and B or O and C as well. By transitivity we would 
        have</t>
      <figure>
        <artwork>
<![CDATA[  O ~ A ~ B ~ C ]]>
        </artwork>
      </figure>
      <t>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 the  
        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.)</t>
      <t>How would we specify such a distinction?</t>
      <t>The answer lies in labeling the mappings A --> O, B --> O, and C --> O with the 
        type &quot;allocatable&quot; and the mappings O --> A, O --> B, and O --> C with the 
        type &quot;blocked&quot;. In this document, the symbol "x-->" 
        means "maps with type blocked" and the symbol "a-->" means "maps with type allocatable". 
        Thus:</t>
      <figure>
        <artwork>
<![CDATA[  O  x--> A
  O  x--> B
  O  x--> C  
  A  a--> O 
  B  a--> O 
  C  a--> O ]]>
        </artwork>
      </figure>
      <t>When we generate all permutations of labels, we use mappings with different 
        types depending from which code points we start. 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).</t>
      <t>In creating an LGR with variants, all variant mappings should always be labeled 
        with a type; (<xref target="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. </t>
    </section>
    
    <section title="Allocatable Variants" anchor="Allocatable_Variants">
      <t>If we start with AAA, and using the mappings from <xref target="Variant_Types_and_Label_Dispositions" />, 
        the permutation OOO will have been the result of 
        applying the mapping A a--> O at each code point. That is, only mappings with type 
        &quot;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. </t>
      <t>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 &quot;a&quot; variant type in the first code point position, &quot;x&quot; 
        in the second code point position, and that the third position is the original 
        code point ("-" means "no variant mapping"). </t>
      <t>For our example permutation we get the following variant type list (brackets 
        dropped):</t>
      <figure>
        <artwork>
<![CDATA[  AAA --> OOO : a a a ]]>
        </artwork>
      </figure>
      <t>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".</t>
      <t>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</t>
      <figure>
        <artwork>
<![CDATA[  if "all variants" = "a" => set label disposition to "allocatable" ]]>
        </artwork>
      </figure>
      <t>would allow OOO to be allocated, because the types of all variants mappings 
        used to create that variant label from AAA are "a".</t>
      <t>The "all-variants" condition is tolerant of an extra "-" in the variant 
        set (unlike the "only-variants" condition described below). 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 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.</t>
      <t>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.</t>
      <t>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 allocatable variants.</t>
    </section>
    
    <section title="Blocked Variants" anchor="Blocked_Variants">
      <t>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.</t>
      <t>If we start with OOO, and using the mappings from <xref target="Variant_Types_and_Label_Dispositions" />,
        the permutation AAA will have been the result of 
        applying only mappings with type &quot;blocked&quot; and we cannot allocate the label AAA, 
        only the original label OOO. This corresponds to the following derivation:</t>
      <figure>
        <artwork>
<![CDATA[  if "any variants" = "x" => set label disposition to "blocked" ]]>
        </artwork>
      </figure>
      <t>To additionally prevent allocating ABO as a variant label for AAA we further need to 
        make sure that the mapping A --> B has been defined with type &quot;blocked&quot; as in</t>
      <figure>
        <artwork>
<![CDATA[  A  x--> B ]]>
        </artwork>
      </figure>
      <t>so that </t>
      <figure>
        <artwork>
<![CDATA[  AAA --> ABO: - x a. ]]>
        </artwork>
      </figure>
      <t>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. </t>
      <t>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
        implies that each set of labels that are mutually variants of each other is 
        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.</t>
    </section>
    
    <section title="Pure Variant Labels" anchor="Pure_Variant_Labels">
      <t>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, which is easily accomplished by use of the &quot;only-variants&quot; qualifier, which 
        requires that the label consist entirely of variants and all the variants are from 
        the same set of types.</t>
      <figure>
        <artwork>
<![CDATA[  if "only-variants" = "a" => set label disposition to "allocatable" ]]>
        </artwork>
      </figure>
      <t>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</t>
      <figure>
        <artwork>
<![CDATA[  AAA --> AOA:  - a - ]]>
        </artwork>
      </figure>
      <t>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</t>
      <figure>
        <artwork>
<![CDATA[  else if "any-variants" = "a" => set label disposition to "blocked" ]]>
        </artwork>
      </figure>
      <t>and executing that derivation only on any remaining labels, we disallow 
        AOA when starting from AAA, but still allow OOO.</t>
      <t>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.</t>
    </section>
    
    <section title="Reflexive Variants" anchor="Reflexive_Variants">
      <t>But what if we started from AOA? We would expect the original label OOO to be allocatable, 
        but, using the mappings from <xref target="Variant_Types_and_Label_Dispositions" />, the variant type set would be</t>
      <figure>
        <artwork>
<![CDATA[  AOA --> OOO:  a - a ]]>
        </artwork>
      </figure>
      <t>because the middle O is unchanged from the original code point. Here is where we use a reflexive 
        mapping, by realizing that O is "the same as" O, which is normally redundant, but 
        allows us to specify a disposition on the mapping</t>
      <figure>
        <artwork>
<![CDATA[  O  a--> O ]]>
        </artwork>
      </figure>
      <t>with that, the variant type list for AOA --> OOO becomes:</t>
      <figure>
        <artwork>
<![CDATA[  AOA --> OOO: a a a ]]>
        </artwork>
      </figure>
      <t>and the label OOO again passes the derivation condition</t>
      <figure>
        <artwork>
<![CDATA[  if "only-variants" = "a" => set label disposition to "allocatable" ]]>
        </artwork>
      </figure>
      <t>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.</t>
    </section>
    
    <section title="Limiting Allocatable Variants by Subtyping" anchor="Limiting_Allocatable_Variants_by_Subtyping">
      <t>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.</t>
      <t>To recap, in the standard case a code point C can have (up to) two types 
        of variant mappings</t>
      <figure>
        <artwork>
<![CDATA[  C  x--> X
  C  a--> A ]]>
        </artwork>
      </figure>
      <t>where a--> means a variant mapping with type &quot;allocatable&quot;, and 
        x--> means &quot;blocked&quot;. For the purpose of the following discussion, 
        we name the target code point with the corresponding uppercase letter.</t>
      <t>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.</t>
        <t>With subtypes defined as above, a code point C might 
        have (up to) four types of variant mappings</t>
 
      <figure>
        <artwork>
<![CDATA[  C  x--> X
  C  s--> S
  C  t--> T
  C  b--> B ]]>
        </artwork>
      </figure>
      <t>and explicit reflexive mappings of one of these types</t>
      <figure>
        <artwork>
<![CDATA[  C  s--> C 
  C  t--> C  
  C  b--> C ]]>
        </artwork>
      </figure>
      <t>As before, all mappings must have one and only one type, but each code 
        point may map to any number of other code points.</t>
      <t>We define the compatibility of "b" with "t" or "s" by our choice of derivation 
        conditions as follows</t>
      <figure>
        <artwork>
<![CDATA[  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 ]]>
        </artwork>
      </figure>
      <t>An original label of four code points</t>
      <figure>
        <artwork>
<![CDATA[  CCCC ]]>
        </artwork>
      </figure>
      <t>may have many variant labels such as this example listed with its corresponding 
        variant type list:</t>
      <figure>
        <artwork>
<![CDATA[  CCCC --> XSTB : x s t b ]]>
        </artwork>
      </figure>
      <t>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</t>
      <figure>
        <artwork>
<![CDATA[  CCCC --> SSBB : s s b b ]]>
        </artwork>
      </figure>
      <t>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</t>
      <figure>
        <artwork>
<![CDATA[  CCCC --> TTBB : t t b b ]]>
        </artwork>
      </figure>
      <t>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,</t>
      <figure>
        <artwork>
<![CDATA[  CCCC --> SSTT : s s t t ]]>
        </artwork>
      </figure>
      <t>is not allocatable, because the type set contains incompatible subtypes 
        "t" and "s" and thus would be blocked by the final derivation.</t>
      <t>The variant labels</t>
      <figure>
        <artwork>
<![CDATA[  CCCC --> CSBB : c s b b
  CCCC --> CTBB : c t b b ]]>
        </artwork>
      </figure>
      <t>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".</t>
      <t>If it 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.</t>
      <t>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.</t>
      <t>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 TLDs), although certain code points have exceptionally complex variant relations 
        and may have an extra mapping.</t>
    </section>
    
    <section title="Allowing Mixed Originals" anchor="Allowing_Mixed_Originals">
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  C  r-s--> C 
  C  r-t--> C 
  C  r-b--> C ]]>
        </artwork>
      </figure>
      <t>With this convention, and redefining the derivations</t>
      <figure>
        <artwork>
<![CDATA[  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 ]]>
        </artwork>
      </figure>
      <t>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.</t>
      <t>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".</t>
      <figure>
        <artwork>
<![CDATA[  C  r-n--> C ]]>
        </artwork>
      </figure>
      <t>With that we can change</t>
      <figure>
        <artwork>
<![CDATA[  else =>  allocatable ]]>
        </artwork>
      </figure>
      <t>to</t>
<figure>
        <artwork>
<![CDATA[  else if "only-variants" = "r-s" or "r-t" or "r-b" or "r-n" 
       =>  allocatable
  else => invalid ]]>
        </artwork>
      </figure>
      <t>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.</t>
    </section>
    
    <section title="Handling Out-of-Repertoire Variants" anchor="Handling_Out_Of_Repertoire_Variants">
      <t>At first, it may seem counterintuitive to define variants that map to code 
        points 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.</t>
      <t>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: </t>
      <figure>
        <artwork>
<![CDATA[  C  x--> X : where C = elementOf(R) and X != elementOf(R) ]]>
        </artwork>
      </figure>
      <t>Because of symmetry, it is necessary to also specify the inverse mapping 
        in the LGR:</t>
      <figure>
        <artwork>
<![CDATA[  X  x--> C : where X != elementOf(R) and C = elementOf(R)]]>
        </artwork>
      </figure>
      <t>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, again uses reflexive variants, but with a new 
        type of reflexive mapping of "out-of-repertoire-var", shown as "r-o-->":</t>
      <figure>
        <artwork>
<![CDATA[  X  r-o--> X]]>
        </artwork>
      </figure>
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  if "any-variant" = "out-of-repertoire-var" => invalid ]]>
        </artwork>
      </figure>
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  C  x--> X  
  X  x--> C  
  X  r-o--> X ]]>
        </artwork>
      </figure>
      <t>where C = elementOf(R) and X != elementOf(R).</t>
      <t>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".</t>
    </section>
    <section title="Conditional Variants" anchor="Conditional_Variants">
      <t>Variant mappings are based on whether code points are "the same" 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 only exists for some possible 
        positions, or more general, only for some contexts. For other contexts, the variant 
        mapping does not exist.</t>
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  final: C --> D ]]>
        </artwork>
      </figure>
      <t>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 
      it was included, "final" might be "final-or-isolate", for example).</t>
      <t>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). </t>
      <t>Sometimes a code point has a final form that is practically the same as 
        that of some code point while sharing initial and medial forms with another.</t>
      <figure>
        <artwork>
<![CDATA[  final: C --> D
  !final: C --> E ]]>
        </artwork>
      </figure>
      <t>Here the case where the condition is the opposite of final is shown as 
        "!final".</t>
      <t>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: </t>
      <figure>
        <artwork>
<![CDATA[  final:  C  a--> F
  !final: C  x--> F ]]>
        </artwork>
      </figure>
      <t>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":</t>
      <figure>
        <artwork>
<![CDATA[  final: F  a--> C
  !final: F  a-->C ]]>
        </artwork>
      </figure>
      <t>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 verify symmetry and transitivity of the variant mappings in the 
        LGR. (This is true even though the two opposite contexts "final" and "!final" should 
        together cover all possible cases).</t>
    </section>
    
    <section title="Making Conditional Variants Well-Behaved" anchor="Making_Conditional_Variants_and_Well_Behaved">
      <t>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 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. </t>
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  final: C --> D
  initial: C --> D. ]]>
        </artwork>
      </figure>
      <t>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 both cannot be satisfied 
        at the same time by some label.</t>
      <t>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 context with the same variant mapping without a context: </t>
      <figure>
        <artwork>
<![CDATA[  context: C --> D
  C --> D ]]>
        </artwork>
      </figure>
      <t>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 the LGR is well-behaved.</t>
      <t>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.</t>
      <t>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.</t>
      <t>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 in principle possible 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.</t>
      <t>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.</t>
      <t>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
        doubtless reduce the number of labels practically available.</t>
    </section>
    
    <section title="Variants for Sequences" anchor="Variants_for_Sequences">
      <t>Variants 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.</t>
      <t>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.</t>
      <t>The following shows such an example resulting in conflicting reflexive 
        variants:</t>
      <figure>
        <artwork>
<![CDATA[  A  a--> C
  AB  x--> CD ]]>
        </artwork>
      </figure>
      <t>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:</t>
      <figure>
        <artwork>
<![CDATA[  B  a--> D ]]>
        </artwork>
      </figure>
      <t>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.</t>
      <t>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.</t>
       <t>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.</t>
      <t>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. </t>
      <t>Sequences are often used for combining sequences, which 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 <xref target="RFC7940" /> for information 
        on context rules for code points).</t>
    </section>
    <section title="Corresponding XML Notation" anchor="Corresponding_XML_Notation">
      <t>The XML format defined in <xref target="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:</t>
       <figure>
        <artwork>
<![CDATA[<char cp="nnnn" />]]>
        </artwork>
      </figure>
      <t>where nnnn is the <xref target="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 two, the XML notation becomes:</t>
      <figure> 
        <artwork>
<![CDATA[<char cp="uuuu vvvvv" />]]>
        </artwork>
      </figure>
      <t>Variant mappings are defined by nesting &lt;var&gt; elements inside the &lt;char&gt;
        element. For example, a variant relation of type "blocked" </t>
      <figure>
        <artwork>
<![CDATA[  C  x--> X ]]>
        </artwork>
      </figure>
      <t>is expressed as</t>
      <figure>
        <artwork>
<![CDATA[  <char cp="nnnn">
    <var cp="mmmm" type="blocked" />
  </char>
  ]]>
        </artwork>
      </figure>
      <t>where "x-->" identifies a "blocked" type. (Other types include "a-->" for 
        "allocatable", for example). Here, nnnn and mmmm are the <xref target="Unicode" /> code point values for 
        C and X, respectively. Either C or X could be a code point sequence or a single code point.</t>
      <t>A reflexive mapping is specified the same way, except that it always uses the same code point value 
        for both the &lt;char&gt; and &lt;var&gt; element, for example</t>
      <figure>
        <artwork>
<![CDATA[  X  r-o--> X ]]>
        </artwork>
      </figure>
      <t>would correspond to </t>
      <figure>
        <artwork>
<![CDATA[  <char cp="nnnn"><var cp="nnnn" type="out-of-repertoire-var" /></char> ]]>
        </artwork>
      </figure>
      <t>Multiple &lt;var&gt; elements may be nested inside a single &lt;char&gt; 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).</t>
      <figure>
        <artwork>
<![CDATA[  <char cp="nnnn">
    <var cp="kkkk" type="allocatable" />
    <var cp="mmmm" type="blocked" />
  </char> ]]>
        </artwork>
      </figure>
      <t>A set of conditional variants like</t>
      <figure>
        <artwork>
<![CDATA[  final: C  a--> K
  !final: C  x--> K ]]>
        </artwork>
      </figure>
      <t>would correspond to</t>
      <figure>
        <artwork>
<![CDATA[  <var cp="kkkk" when="final" type="allocatable" />
  <var cp="kkkk" not-when="final" type="blocked" /> ]]>
        </artwork>
      </figure>
      <t>where the string "final" references a name of a context rule. Context rules 
        are defined in <xref target="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.</t>
      <t>A derivation of a variant label disposition</t>
      <figure>
        <artwork>
<![CDATA[  if "only-variants" = "s" or "b" => allocatable ]]>
        </artwork>
      </figure>
      <t>is expressed as</t>
      <figure>
        <artwork>
<![CDATA[  <action disp="allocatable" only-variants= "s b" /> ]]>
        </artwork>
      </figure>
      <t>Instead of using "if" and "else if" the &lt;action&gt; elements implicitly form 
        a cascade, where the first action triggered defines the disposition of the label. 
        The order of action elements is thus significant.</t>
      <t>For the full specification of the XML format see <xref target="RFC7940" />.</t>
    </section>
    <section title="IANA Considerations">
      <t>This document does not specify any IANA actions.</t>
     </section>

     <section title="Security Considerations">
       <t>As described in <xref target="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, variants, if indiscriminately designed, 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.</t>
       <t>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.</t>
         <t>A well-behaved LGR is not merely one that can be expressed in <xref target="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.</t>
         <t>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 are all, or what
         labels are to be considered variants of each other is not addressed here.</t>
     </section>
  </middle>
  <!--  *****BACK MATTER ***** -->
  <back>
    <references title="Normative References"> &rfc7940; </references>
    <references title="Informative References">
    &rfc1034;
	&rfc1035;
	&rfc5890;
	&rfc5891;
	&rfc5892;
	&rfc5893;
	&rfc5894;
      <!--     <reference anchor="placeholder">
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           <title> Reference to be supplied &lt;&lt;???&gt;&gt; </title>
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           <date />
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      <reference anchor="Unicode"
                target="http://www.unicode.org/versions/Unicode9.0.0/">
        <front>
          <title>The Unicode Standard, Version 9.0.0</title>
          <author>
            <organization>The Unicode Consortium</organization>
            <address>
            <postal>
              <street/>
              <city>Mountain View</city>
              <region>CA</region>
              <country>USA</country>
            </postal>
            </address>
          </author>
          <date year="2016" />
        </front>
        <seriesInfo name="ISBN" value="978-1-936213-13-9"  />
        <annotation> Preferred Citation:
          The Unicode Consortium. The Unicode Standard, Version
          9.0.0, (Mountain View, CA: The Unicode Consortium, 2016.
          ISBN 978-1-936213-13-9) </annotation>
      </reference>
    </references>
    <!--   Sections below here become  Appendices.  -->
    
    <section title="Acknowledgments">
        <t>Contributions that have shaped this document have been provided by Marc Blanchet, Ben Campbell, Patrik Faltstrom, Scott Hollenbeck, Mirja Kuhlewind, Sarmad Hussain, John Klensin, Alexey Melnikov, Nicholas Ostler, Michel Suignard, Andrew Sullivan, Wil Tan and Suzanne Woolf.</t>
    </section>

    <section title="Change Log" anchor="ChangeLog">
      <t>RFC Editor: Please remove this appendix before
        publication.</t>
        <t>
      <list style="hanging" hangIndent="5">
          <t hangText="-00">Initial draft.</t>
       </list>
       <list style="hanging" hangIndent="5">
          <t hangText="-01">Minor fix to references.</t>
       </list>
       <list style="hanging" hangIndent="5">
          <t hangText="-02">Some formatting and grammar issues as well as typos fixed. 
          Added a few real-world 
          examples where required for context. Added "r-n" to description of subtyping.</t>
       </list>
      <list style="hanging" hangIndent="5">
          <t hangText="-03">Fix ID nits and other typos. Expanded security section. Minor tweaks.</t>
       </list>
      <list style="hanging" hangIndent="5">
          <t hangText="-04">Additional context. Added to introduction. Introduced sections on
          notation and symmetry and transitivity. Expanded the section on XML notation.</t>
       </list>
             <list style="hanging" hangIndent="5">
          <t hangText="-05">Additional change to introduction. </t>
       </list>
       <list style="hanging" hangIndent="5">
          <t hangText="-05">Swapped short and long title. Fixed examples in section 11. Clarified
         use of "original" and "applied-for" label. Updated opening paragraph in intro and clarified
         sections 3 and 16 to better indicate preferred options.</t>
       </list>

       </t>
    </section>
  </back>
</rfc>
