Editor: Steven Pemberton, CWI, Amsterdam
Version: 2022-06-20 (edited in-place on 2022-09-29 to add a link to the errata page)
Please consult the errata page for additional changes to the specification after publication.
This document describes the final version of ixml version 1.0.
Data is an abstraction: there is no essential difference between the JSON
{"temperature": {"scale": "C", "value": 21}}
and an equivalent XML
<temperature scale="C" value="21"/>
or
<temperature> <scale>C</scale> <value>21</value> </temperature>
since the underlying abstractions being represented are the same.
We choose which representations of our data to use, CSV, JSON, XML, or whatever, depending on habit, convenience, and the context in which it occurs. On the other hand, having an interoperable generic toolchain such as that provided by XML to process data is of immense value. How do we resolve the conflicting requirements of convenience, habit, and context, and still enable a generic toolchain?
Invisible XML (ixml) is a method for treating non-XML documents as if they were XML, enabling authors to write documents and data in a format they prefer while providing XML for processes that are more effective with XML content. For example, it can turn CSS code like
body {color: blue; font-weight: bold}
into XML like
<css>
<rule>
<selector>body</selector>
<block>
<property>
<name>color</name>
<value>blue</value>
</property>
<property>
<name>font-weight</name>
<value>bold</value>
</property>
</block>
</rule>
</css>
or, if preferred, as:
<css>
<rule>
<simple-selector name="body"/>
<property name="color" value="blue"/>
<property name="font-weight" value="bold"/>
</rule>
</css>
As another example, the expression
pi×(10+b)
can result in the XML
<prod>
<id>pi</id>
<sum>
<number>10</number>
<id>b</id>
</sum>
</prod>
or
<prod>
<id name='pi'/>
<sum>
<number value='10'/>
<id name='b'/>
</sum>
</prod>
and the URL
http://www.w3.org/TR/1999/xhtml.html
can give
<url>
<scheme name='http'/>
<authority>
<host>
<sub name='www'/>
<sub name='w3'/>
<sub name='org'/>
</host>
</authority>
<path>
<seg sname='TR'/>
<seg sname='1999'/>
<seg sname='xhtml.html'/>
</path>
</url>
or
<url scheme='http'> <host>www.w3.org</host> <path>/TR/1999/xhtml.html</path> </url>
The JSON value:
{"name": "pi", "value": 3.145926}
can give
<json>
<object>
<pair string='name'>
<string>pi</string>
</pair>
<pair string='value'>
<number>3.145926</number>
</pair>
</object>
</json>
A grammar is used to describe the input format. An input is parsed using this grammar, and the resulting parse tree is serialized as XML. Special marks in the grammar affect details of this serialization, for example excluding parts of the tree, or serializing parts as attributes instead of elements.
As an example, consider this simplified grammar for URLs:
url: scheme, ":", authority, path.
scheme: letter+.
authority: "//", host.
host: sub++".".
sub: letter+.
path: ("/", seg)+.
seg: fletter*.
-letter: ["a"-"z"]; ["A"-"Z"]; ["0"-"9"].
-fletter: letter; ".".
This means that a URL consists of a scheme (whatever that is), followed by a colon, followed by an authority, and then a path. A scheme, is one or more letters (whatever a letter is). An authority starts with two slashes, followed by a host. A host is one or more subs, separated by points. A sub is one or more letters. A path is a slash followed by a seg, repeated one or more times. A seg is zero or more fletters. A letter is a lowercase letter, an uppercase letter, or a digit. A fletter is a letter or a point.
So, given the input string
http://www.w3.org/TR/1999/xhtml.html, this would produce the
serialization
<url>
<scheme>http</scheme>:
<authority>//
<host>
<sub>www</sub>.
<sub>w3</sub>.
<sub>org</sub>
</host>
</authority>
<path>
/<seg>TR</seg>
/<seg>1999</seg>
/<seg>xhtml.html</seg>
</path>
</url>
(Here and in other examples, whitespace has been added to the XML for legibility.)
If the rule for letter had not had a "-" before it, the
serialization for scheme, for instance, would have been:
<scheme><letter>h</letter><letter>t</letter><letter>t</letter><letter>p</letter></scheme>
Changing the rule for scheme to
scheme: name. @name: letter+.
would change the serialization for scheme to:
<scheme name="http"/>:
Changing the rule for scheme instead to:
@scheme: letter+.
would change the serialization for url to:
<url scheme="http">
Changing the definitions of sub and seg from
sub: letter+. seg: fletter*.
to
-sub: letter+. -seg: fletter*.
would prevent the sub and seg elements appearing
in the serialized result, giving:
<url scheme='http'>:// <host>www.w3.org</host> <path>/TR/1999/xhtml.html</path> </url>
Changing the rule
url: scheme, ":", authority, path.
to
url: scheme, -":", authority, path.
and
authority: "//", host.
to
authority: -"//", host.
would remove the spurious characters from the serialization:
<url scheme='http'> <host>www.w3.org</host> <path>/TR/1999/xhtml.html</path> </url>
Here we describe the format of the grammar used to describe documents. Note that it is in its own format, and therefore describes itself.
A grammar is an optional prolog, followed by a sequence of one or more rules, surrounded and separated by spacing and comments. Spacing and comments are entirely optional, except that rules must be separated by at least one of either (error S01).
ixml: s, prolog?, rule++RS, s.
An s stands for an optional sequence of spacing and comments;
RS for at least one space or comment. A comment is enclosed in
braces, and can included nested comments, to enable commenting out parts of a
grammar:
-s: (whitespace; comment)*. {Optional spacing}
-RS: (whitespace; comment)+. {Required spacing}
-whitespace: -[Zs]; tab; lf; cr.
-tab: -#9.
-lf: -#a.
-cr: -#d.
comment: -"{", (cchar; comment)*, -"}".
-cchar: ~["{}"].
The optional prolog declares the version of ixml being used. If absent, version 1.0 is assumed. A grammar must conform to the syntax and semantics of the version declared or assumed (error S12).
prolog: version, s.
version: -"ixml", RS, -"version", RS, string, s, -'.' .
If an implementation recognizes the version string, it must process the grammar using the syntax and semantics of that version.
If it does not recognize the version string, it must nevertheless attempt to process the grammar. If it
finds a syntactically valid interpretation of the grammar, it must proceed using the semantics of the version under
which it found a valid interpretation, otherwise it must reject the grammar. In either case, the document
element of the serialization must include an
attribute named ixml:state, with the word
'version-mismatch' in its value. The ixml namespace URI is
"http://invisiblexml.org/NS".
A rule consists of an optional mark, a name, and one or more alternatives. The grammar here uses colons to define rules; an equals sign is also allowed.
rule: (mark, s)?, name, s, -["=:"], s, -alts, -".".
A mark is one of ^, @ or -, and
indicates whether the item so marked will be serialized as an element with its
children (^) which is the default, as an attribute
(@), or deleted, so that only its children are serialized
(-).
@mark: ["@^-"].
A name starts with a letter or underscore, and continues with a letter, digit, underscore, a small number of punctuation characters, and the Unicode combiner characters; Unicode classes are used to define the sets of characters used, for instance, for letters and digits. This is close to, but not identical with the XML definition of a name; it is the grammar author's responsibility to ensure that all serialized names match the requirements for an XML name [XML].
@name: namestart, namefollower*. -namestart: ["_"; L]. -namefollower: namestart; ["-.·‿⁀"; Nd; Mn].
Alternatives are separated by a semicolon or a vertical bar. The grammar here uses semicolons.
alts: alt++(-[";|"], s).
An alternative is zero or more terms, separated by commas:
alt: term**(-",", s).
A term is a singleton factor, an optional factor, or a repeated factor, repeated zero or more times, or one or more times.
-term: factor;
option;
repeat0;
repeat1.
A factor is a terminal, a nonterminal, an insertion, or a bracketed series of alternatives:
-factor: terminal;
nonterminal;
insertion;
-"(", s, alts, -")", s.
A factor repeated zero or more times is followed by an asterisk, or followed
by a double asterisk and a separator, e.g. abc* and
abc**",". For instance "a"**"#" would match the empty
string, a, a#a, a#a#a etc.
repeat0: factor, (-"*", s; -"**", s, sep).
Similarly, a factor repeated one or more times is followed by a plus, or a
double plus and a separator, e.g. abc+ and abc++",".
For instance "a"++"#" would match a,
a#a, a#a#a etc., but not the empty string.
repeat1: factor, (-"+", s; -"++", s, sep).
An optional factor is followed by a question mark, e.g. abc?.
For instance "a"? would match a or the empty
string.
option: factor, -"?", s.
A separator can be any factor, for example abc**def or
abc**(","; "."). For instance "a"++("#"; "!") would
match a#a, a!a, a#a!a,
a!a#a, a#a#a etc.
sep: factor.
A nonterminal is an optionally marked name:
nonterminal: (mark, s)?, name, s.
This name refers to the rule that defines this name, which must exist (error S02), and there must only be one such rule (error S03).
A terminal is a literal or a set of characters. It matches characters in the input. A terminal marked as deleted (-) serializes to the empty string.
-terminal: literal;
charset.
A literal is either a quoted string, or a hexadecimally encoded character:
literal: quoted;
encoded.
A quoted string is an optionally marked string of one or more characters,
enclosed with single or double quotes. A string matches only the exact same
string in the input. Examples: "yes" 'yes'.
A string cannot extend over a line-break (error S11). The enclosing quote is represented in a string
by doubling it; these two strings are identical: 'Isn''t it?' and
"Isn't it?", as are these: "He said ""Don't!""" and
'He said "Don''t!"'.
-quoted: (tmark, s)?, string, s.
@tmark: ["^-"].
@string: -'"', dchar+, -'"';
-"'", schar+, -"'".
dchar: ~['"'; #a; #d];
'"', -'"'. {all characters except line breaks; quotes must be doubled}
schar: ~["'"; #a; #d];
"'", -"'". {all characters except line breaks; quotes must be doubled}
An encoded character is an optionally marked hexadecimal
number. It starts with a hash symbol, followed by any number of hexadecimal
digits, for example #a0. The digits are interpreted as a number in
hexadecimal (error S06) , and the
character at that Unicode code-point is used [Unicode].
The number must be within the Unicode
code-point range (error S07), and must not denote a Noncharacter or Surrogate
code point (error S08).
An encoded character matches that one character in the input.
-encoded: (tmark, s)?, -"#", hex, s.
@hex: ["0"-"9"; "a"-"f"; "A"-"F"]+.
A character set is an inclusion or an exclusion: an inclusion matches one character in the input that is in the set, an exclusion matches one character not in the set.
An inclusion is enclosed in square brackets, and represents the set of
characters defined by any combination of literal characters, a range of
characters, hex encoded characters, or Unicode classes. Examples
["a"-"z"], ["xyz"], [Lc], and
["0"-"9"; "!@#"; Lc]. Note that ["abc"], ["a";
"b"; "c"], ["a"-"c"], and [#61-#63] all
represent the same set of characters.
An exclusion is an inclusion preceded by a tilde ~. For
example, ~["{}"] matches any character that is not an opening or
closing brace.
Note that the empty inclusion [] will fail to match any
character in the input; on the other hand ~[] will match any one
character, whatever it is.
-charset: inclusion;
exclusion.
inclusion: (tmark, s)?, set.
exclusion: (tmark, s)?, -"~", s, set.
-set: -"[", s, (member, s)**(-[";|"], s), -"]", s.
member: string;
-"#", hex;
range;
class.
A range represents all characters in the range from the from
character to the to character, inclusive, using the Unicode
ordering. The from character must not be later in the ordering than the
to character (error S09).
-range: from, s, -"-", s, to. @from: character. @to: character.
A character is a string of length one, or a hex encoded character:
-character: -'"', dchar, -'"';
-"'", schar, -"'";
"#", hex.
A class is one or two letters, representing any character from the Unicode
character category [Categories] of that name, which
must exist (error S10). E.g. [Ll] matches any lower-case
letter, [Ll; Lu] matches any upper- or lower-case character.
-class: code.
@code: capital, letter?.
-capital: ["A"-"Z"].
-letter: ["a"-"z"].
An insertion is a string or hex proceeded by a plus +. An
insertion matches zero characters in the input, and only appears in the
serialization.
insertion: -"+", s, (string; -"#", hex), s.
The root symbol of the grammar is the name of the first rule in the grammar.
Processors must accept and parse any conforming
grammar, and produce at least one parse of supplied input that matches the
grammar starting at the root symbol. If more than one parse results, one is
chosen; it is not defined how this choice is made, but the resulting
serialization should include the attribute
ixml:state on the document element with a value that includes the
word ambiguous. Different processors may vary in whether input is detected as ambiguous or
not. Known algorithms that accept and parse any context-free grammar include
[Earley], [Unger], [CYK], [GLR], and [GLL];
see also [Grune].
If the parse fails, some XML document must be
produced with ixml:state on the document element with a value that
includes the word failed. The document should provide helpful information about where and why
it failed; it may be a partial parse tree that
includes parts of the parse that succeeded.
If the parse succeeds, the resulting parse-tree is serialized as XML by serializing the root node of the parse tree.
A parse node is a nonterminal, which has a name and children, a terminal, which has a string, or an insertion, which has a string.
A nonterminal can be unmarked, or marked as included (^), as an attribute (@), or as deleted (-). The mark comes from the use of the nonterminal in a rule if present, otherwise, from the definition of the rule for that nonterminal.
A terminal can be unmarked, or marked as included (^), or as deleted (-).
An insertion is serialized as its string.
Grammars must be written so that any serialization of a parse tree produced from the grammar is well-formed XML (error D01).
Note: This requirement means for instance that names of serialized elements and attributes must match the XML requirements (error D03); an element must not contain more than one attribute of a given name (error D02); an element must not contain an attribute named “xmlns” (error D07); the names of all elements and attributes must conform to the requirements for XML names; non-XML characters must not be serialized (error D04); a nonterminal being serialized as root element must not be marked as an attribute (error D05); in order to match the XML requirement of a single-rooted document, if the root rule is marked as hidden, all of its productions must produce exactly one non-hidden non-attribute nonterminal and no non-hidden terminals before or after that nonterminal (error D06).
A (necessarily contrived) example grammar that illustrates serialization rules is:
expr: open, -arith, @close, -";".
@open: "(".
close: ")".
arith: left, op, ^right.
left: operand.
-right: operand.
-operand: name; -number.
@name: ["a"-"z"].
@number: ["0"-"9"].
-op: sign.
@sign: "+"; "-".
Applied to the string (a+1); it yields the serialization
<expr open='(' sign='+' close=')'>
<left name='a'/>
<right>1</right>
</expr>
Points to note: how the semicolon is suppressed from the serialization; the
two ways open and close have been defined as
attributes; similarly the two ways left and right
have been defined as elements; how number appears as content and
not as an attribute; and how sign being an exposed attribute
appears on its nearest non-hidden ancestor. Also of note is how the content of
some attributes can appear earlier in the serialization than in the input.
Insertions allow characters to be inserted into the serialization that were not present in the input. For instance, the grammar
data: value++-",", @source.
source: +"ixml".
value: pos; neg.
-pos: +"+", digit+.
-neg: +"-", -"(", digit+, -")".
-digit: ["0"-"9"].
With input:
100,200,(300),400
would produce
<data source="ixml"> <value>+100</value> <value>+200</value> <value>-300</value> <value>+400</value> </data>
In this specification, the verb "must" expresses unconditional requirements for conformance to the specification; the verb "should" expresses requirements that are encouraged but which are not conditions of conformance; the verb "may" expresses optional features which are neither required nor prohibited.
Conformance to this specification can meaningfully be claimed for grammars and for processors; it cannot be claimed for input streams or input + grammar pairs.
An ixml grammar in ixml form conforms to this specification if it is described by the grammar given in this specification, and it satisfies all the other requirements specified for ixml grammars.
An ixml grammar in XML form conforms to this specification if, after removal of namespace qualified elements and attributes, it can be derived from an ixml grammar in ixml form by parsing as described in this specification, and it satisfies all the other requirements specified for ixml grammars.
Note: The normative formulations of conformance requirements are those given elsewhere in this specification. For convenience the requirements that go beyond what is expressed in the grammar itself can be summarized as follows. (Reasonable effort has been used to make this list complete, but omission of any conformance requirement from this list does not affect its status as a conformance requirement.)
from character of a range must
not be later in the Unicode ordering than the to
character.A conforming processor must accept grammars in ixml form, and should accept grammars in XML form; it must not accept non-conforming grammars. Both grammars and input must be accepted in UTF-8 encoding, and may be accepted in other encodings.
For any conforming grammar and any input, under normal operation:
ixml:state on the document element with a value that includes
the word ambiguous. Processors may provide a user option to suppress that
attribute; they may also provide a user option
to produce more than one parse tree.ixml:state on the document element with a value that includes
the word failed, with helpful information about where and why
it failed; it may be a partial parse tree that
includes parts of the parse that succeeded.ixml:state containing the word prefix,
or if the parse is ambiguous, the words ambiguous prefix.ixml:state attribute must include
the word version-mismatch. Many parsing algorithms only mention terminals and nonterminals, and don't
explain how to deal with the repetition constructs used in ixml. However, these
can be handled simply by converting them to equivalent simple constructs. In
the examples below, f and sep are
factors from the grammar above. The other nonterminals are
generated nonterminals.
Optional factor:
f? ⇒ f-option -f-option: f; ().
Zero or more repetitions:
f* ⇒ f-star -f-star: (f, f-star)?.
One or more repetitions:
f+ ⇒ f-plus -f-plus: f, f*.
One or more repetitions with separator:
f++sep ⇒ f-plus-sep -f-plus-sep: f, (sep, f)*.
Zero or more repetitions with separator:
f**sep ⇒ f-star-sep -f-star-sep: (f++sep)?.
ixml: s, prolog?, rule++RS, s.
-s: (whitespace; comment)*. {Optional spacing}
-RS: (whitespace; comment)+. {Required spacing}
-whitespace: -[Zs]; tab; lf; cr.
-tab: -#9.
-lf: -#a.
-cr: -#d.
comment: -"{", (cchar; comment)*, -"}".
-cchar: ~["{}"].
prolog: version, s.
version: -"ixml", RS, -"version", RS, string, s, -'.' .
rule: (mark, s)?, name, s, -["=:"], s, -alts, -".".
@mark: ["@^-"].
alts: alt++(-[";|"], s).
alt: term**(-",", s).
-term: factor;
option;
repeat0;
repeat1.
-factor: terminal;
nonterminal;
insertion;
-"(", s, alts, -")", s.
repeat0: factor, (-"*", s; -"**", s, sep).
repeat1: factor, (-"+", s; -"++", s, sep).
option: factor, -"?", s.
sep: factor.
nonterminal: (mark, s)?, name, s.
@name: namestart, namefollower*.
-namestart: ["_"; L].
-namefollower: namestart; ["-.·‿⁀"; Nd; Mn].
-terminal: literal;
charset.
literal: quoted;
encoded.
-quoted: (tmark, s)?, string, s.
@tmark: ["^-"].
@string: -'"', dchar+, -'"';
-"'", schar+, -"'".
dchar: ~['"'; #a; #d];
'"', -'"'. {all characters except line breaks; quotes must be doubled}
schar: ~["'"; #a; #d];
"'", -"'". {all characters except line breaks; quotes must be doubled}
-encoded: (tmark, s)?, -"#", hex, s.
@hex: ["0"-"9"; "a"-"f"; "A"-"F"]+.
-charset: inclusion;
exclusion.
inclusion: (tmark, s)?, set.
exclusion: (tmark, s)?, -"~", s, set.
-set: -"[", s, (member, s)**(-[";|"], s), -"]", s.
member: string;
-"#", hex;
range;
class.
-range: from, s, -"-", s, to.
@from: character.
@to: character.
-character: -'"', dchar, -'"';
-"'", schar, -"'";
"#", hex.
-class: code.
@code: capital, letter?.
-capital: ["A"-"Z"].
-letter: ["a"-"z"].
insertion: -"+", s, (string; -"#", hex), s.
Since the ixml grammar is expressed in its own notation, the above grammar can be processed into an XML document by parsing it using itself, and then serializing. Note that all semantically significant terminals are recorded in attributes, and non-significant characters are not serialized. The serialization begins as below, but the entire serialization is available:
<ixml>
<rule name='ixml'>
<alt>
<nonterminal name='s'/>
<option>
<nonterminal name='prolog'/>
</option>
<repeat1>
<nonterminal name='rule'/>
<sep>
<nonterminal name='RS'/>
</sep>
</repeat1>
<nonterminal name='s'/>
</alt>
</rule>
<rule mark='-' name='s'>
<alt>
<repeat0>
<alts>
<alt>
<nonterminal name='whitespace'/>
</alt>
<alt>
<nonterminal name='comment'/>
</alt>
</alts>
</repeat0>
</alt>
</rule>
<comment>Optional spacing</comment>
<rule mark='-' name='RS'>
<alt>
<repeat1>
<alts>
<alt>
<nonterminal name='whitespace'/>
</alt>
<alt>
<nonterminal name='comment'/>
</alt>
</alts>
</repeat1>
</alt>
</rule>
<comment>Required spacing</comment>
<rule mark='-' name='whitespace'>
<alt>
<inclusion tmark='-'>
<member code='Zs'/>
</inclusion>
</alt>
<alt>
<nonterminal name='tab'/>
</alt>
<alt>
<nonterminal name='lf'/>
</alt>
<alt>
<nonterminal name='cr'/>
</alt>
</rule>
<rule mark='-' name='tab'>
<alt>
<literal tmark='-' hex='9'/>
</alt>
</rule>
<rule mark='-' name='lf'>
<alt>
<literal tmark='-' hex='a'/>
</alt>
</rule>
<rule mark='-' name='cr'>
<alt>
<literal tmark='-' hex='d'/>
</alt>
</rule>
<rule name='comment'>
<alt>
<literal tmark='-' string='{'/>
<repeat0>
<alts>
<alt>
<nonterminal name='cchar'/>
</alt>
<alt>
<nonterminal name='comment'/>
</alt>
</alts>
</repeat0>
<literal tmark='-' string='}'/>
</alt>
</rule>
<rule mark='-' name='cchar'>
<alt>
<exclusion>
<member string='{}'/>
</exclusion>
</alt>
</rule>
<rule name='prolog'>
<alt>
<nonterminal name='version'/>
<nonterminal name='s'/>
</alt>
</rule>
<rule name='version'>
<alt>
<literal tmark='-' string='ixml'/>
<nonterminal name='RS'/>
<literal tmark='-' string='version'/>
<nonterminal name='RS'/>
<nonterminal name='string'/>
<nonterminal name='s'/>
<literal tmark='-' string='.'/>
</alt>
</rule>
<rule name='rule'>
<alt>
<option>
<alts>
<alt>
<nonterminal name='mark'/>
<nonterminal name='s'/>
</alt>
</alts>
</option>
<nonterminal name='name'/>
<nonterminal name='s'/>
<inclusion tmark='-'>
<member string='=:'/>
</inclusion>
<nonterminal name='s'/>
<nonterminal mark='-' name='alts'/>
<literal tmark='-' string='.'/>
</alt>
</rule>
This section summarizes errors identified in this specification. Static errors are errors that can be identified by inspecting the grammar.
Dynamic errors arise when a particular input is processed with a grammar.
Note: if error codes are reported in a context where it makes sense for them to appear in a namespace, they should be in the Invisible XML namespace.
[Unicode] The Unicode Consortium (ed.), The Unicode Standard — Version 13.0. Unicode Consortium, 2020, ISBN 978-1-936213-26-9, http://www.unicode.org/versions/Unicode13.0.0/
[Categories] The Unicode Consortium (ed.), Unicode Standard Annex #44: Unicode Character Database -- General Category Values https://unicode.org/reports/tr44/#General_Category_Values (See also http://www.fileformat.info/info/unicode/category/index.htm)
[XML] Tim Bray et al. (eds.), Extensible Markup Language (XML) 1.0 (Fifth Edition), W3C, 2008, https://www.w3.org/TR/xml/
[CYK] Sakai, Itiroo. Syntax in universal translation. In 1961 International Conference on Machine Translation of Languages and Applied Language Analysis, pages 593–608. https://aclanthology.org/www.mt-archive.info/50/NPL-1961-Sakai.pdf
[Earley] Earley, J. An efficient context-free parsing algorithm. Communications of the ACM, 13(2):94–102, February 1970, doi:10.1145/362007.362035
[GLL] Elizabeth Scott and Adrian Johnstone, GLL Parsing. Electronic Notes in Theoretical Computer Science, Volume 253, Issue 7, 17 September 2010, pages 177-189. doi:10.1016/j.entcs.2010.08.041
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This specification was produced by members of the W3C ixml community group: Tomos Hillman, John Lumley, Steven Pemberton, C. M. Sperberg-McQueen, Bethan Tovey-Walsh, Norman Tovey-Walsh. Other current and former members of the group have also contributed.
Thanks are due to Hans-Dieter Hiep for an early close reading of the specification, and consequent many helpful comments.