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<b>Common Lisp the Language, 2nd Edition</b>
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<H2><A NAME=SECTION002612000000000000000>22.1.2. Parsing of Numbers and Symbols</A></H2>
<P>
<A NAME=PARSETOKENSSECTION>When</A>
an extended token is read, it is interpreted as a number or symbol.
In general, the token is interpreted as a number if it satisfies
the syntax for numbers specified in table <A HREF="node189.html#NUMBERSYNTAXTABLE">22-2</A>;
this is discussed in more detail below.
<P>
The characters of the extended token may serve various syntactic
functions as shown
in table <A HREF="node189.html#StandardReadtableAttributesTable">22-3</A>, but it must be
remembered that any character included in a token under the control
of an escape character is treated as <i>alphabetic</i> rather than
according to the attributes shown in the table.
One consequence of this rule is that a whitespace, macro, or escape
character will always be treated as alphabetic within an extended token
because such a character cannot be included in an extended
token except under the control of an escape character.
<P>
To allow for extensions to the syntax of numbers, a
syntax for <i>potential numbers</i> is defined in Common Lisp that is
more general than the actual syntax for numbers.
Any token that is not a potential number and does not consist
entirely of dots will always be taken to be a symbol,
now and in the future; programs may rely on this fact.
Any token that is a potential number but does not fit the
actual number syntax defined below is a <i>reserved token</i> and
has an implementation-dependent interpretation;
an implementation may signal an error, quietly treat the token
as a symbol, or take some other action. Programmers should avoid
the use of such reserved tokens. (A symbol whose name looks like a reserved
token can always be written using one or more escape characters.)
<P>
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
Just as <i>bignum</i> is the standard term used by Lisp implementors for
very large integers, and <i>flonum</i> (rhymes with ``low hum'') refers
to a floating-point number, the term <i>potnum</i> has been used widely
as an abbreviation for ``potential number.'' ``Potnum'' rhymes with ``hot rum.''
<br><img align=bottom alt="change_end" src="gif/change_end.gif">
<A NAME=NUMBERSYNTAXTABLE>&#160;</A>
<pre>
----------------------------------------------------------------
Table 22-2: Actual Syntax of Numbers
<i>number</i> ::= <i>integer</i> | <i>ratio</i> | <i>floating-point-number</i>
<i>integer</i> ::= [<i>sign</i>] {<i>digit</i>}+ [<i>decimal-point</i>]
<i>ratio</i> ::= [<i>sign</i>] {<i>digit</i>}+ / {<i>digit</i>}+
<i>floating-point-number</i> ::= [<i>sign</i>] {<i>digit</i>}* <i>decimal-point</i> {<i>digit</i>}+ [<i>exponent</i>]
| [<i>sign</i>] {<i>digit</i>}+ [<i>decimal-point</i> {<i>digit</i>}*] <i>exponent</i>
<i>sign</i> ::= + | -
<i>decimal-point</i> ::= .
<i>digit</i> ::= 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
<i>exponent</i> ::= <i>exponent-marker</i> [<i>sign</i>] {<i>digit</i>}+
<i>exponent-marker</i> ::= e | s | f | d | l | E | S | F | D | L
----------------------------------------------------------------
</pre>
<P>
<A NAME=StandardReadtableAttributesTable>&#160;</A>
<pre>
----------------------------------------------------------------
Table 22-3: Standard Constituent Character Attributes
! <i>alphabetic</i> &lt;page&gt; <i>illegal</i> &lt;backspace&gt; <i>illegal</i>
" <i>alphabetic</i> * &lt;return&gt; <i>illegal</i> * &lt;tab&gt; <i>illegal</i> *
# <i>alphabetic</i> * &lt;space&gt; <i>illegal</i> * &lt;newline&gt; <i>illegal</i> *
$ <i>alphabetic</i> &lt;rubout&gt; <i>illegal</i> &lt;linefeed&gt; <i>illegal</i> *
% <i>alphabetic</i> . <i>alphabetic</i>, <i>dot</i>, <i>decimal point</i>
& <i>alphabetic</i> + <i>alphabetic</i>, <i>plus sign</i>
' <i>alphabetic</i> * - <i>alphabetic</i>, <i>minus sign</i>
( <i>alphabetic</i> * * <i>alphabetic</i>
) <i>alphabetic</i> * / <i>alphabetic</i>, <i>ratio marker</i>
, <i>alphabetic</i> * @ <i>alphabetic</i>
0 <i>alphadigit</i> A, a <i>alphadigit</i>
1 <i>alphadigit</i> B, b <i>alphadigit</i>
2 <i>alphadigit</i> C, c <i>alphadigit</i>
3 <i>alphadigit</i> D, d <i>alphadigit</i>, <i>double-float exponent marker</i>
4 <i>alphadigit</i> E, e <i>alphadigit</i>, <i>float exponent marker</i>
5 <i>alphadigit</i> F, f <i>alphadigit</i>, <i>single-float exponent marker</i>
6 <i>alphadigit</i> G, g <i>alphadigit</i>
7 <i>alphadigit</i> H, h <i>alphadigit</i>
8 <i>alphadigit</i> I, i <i>alphadigit</i>
9 <i>alphadigit</i> J, j <i>alphadigit</i>
: <i>package marker</i> K, k <i>alphadigit</i>
; <i>alphabetic</i> * L, l <i>alphadigit</i>, <i>long-float exponent marker</i>
< <i>alphabetic</i> M, m <i>alphadigit</i>
= <i>alphabetic</i> N, n <i>alphadigit</i>
> <i>alphabetic</i> O, o <i>alphadigit</i>
? <i>alphabetic</i> P, p <i>alphadigit</i>
[ <i>alphabetic</i> Q, q <i>alphadigit</i>
\ <i>alphabetic</i> * R, r <i>alphadigit</i>
] <i>alphabetic</i> S, s <i>alphadigit</i>, <i>short-float exponent marker</i>
^ <i>alphabetic</i> T, t <i>alphadigit</i>
_ <i>alphabetic</i> U, u <i>alphadigit</i>
` <i>alphabetic</i> * V, v <i>alphadigit</i>
{ <i>alphabetic</i> W, w <i>alphadigit</i>
| <i>alphabetic</i> * X, x <i>alphadigit</i>
} <i>alphabetic</i> Y, y <i>alphadigit</i>
~ <i>alphabetic</i> Z, z <i>alphadigit</i>
----------------------------------------------------------------
</pre>
<P>
A token is a potential number if it satisfies the following
requirements:
<UL><LI>
It consists entirely of digits, signs (<tt>+</tt> or <tt>-</tt>),
ratio markers (<tt>/</tt>), decimal points (<tt>.</tt>), extension characters
(<tt>^</tt> or <tt>_</tt>), and number markers. (A number marker is
a letter. Whether a letter may be treated as a number marker depends
on context, but no letter that is adjacent to another letter may ever be
treated as a number marker. Floating-point exponent markers are instances
of number markers.)
<P>
<LI>
It contains at least one digit. (Letters may be considered to be
digits, depending on the value of <tt>*read-base*</tt>, but only
in tokens containing no decimal points.)
<P>
<LI>
It begins with a digit, sign, decimal point, or extension character.
<P>
<LI>
It does not end with a sign.
</UL>
As examples, the following tokens are potential numbers,
but they are <i>not</i> actually numbers as defined below, and so are
reserved tokens. (They do indicate some interesting possibilities
for future extensions.)
<pre>
1b5000 777777q 1.7J -3/4+6.7J 12/25/83
27^19 3^4/5 6//7 3.1.2.6 ^-43^
3.141_592_653_589_793_238_4 -3.7+2.6i-6.17j+19.6k
</pre>
The following tokens are <i>not</i> potential numbers but are always
treated as symbols:
<P><pre>
/ /5 + 1+ 1-
foo+ ab.cd _ ^ ^/-
</pre><P>
The following tokens are potential numbers if the value of
<tt>*read-base*</tt> is <tt>16</tt> (an abnormal situation), but they are
always treated as symbols if the value of <tt>*read-base*</tt>
is <tt>10</tt> (the usual value):
<P><pre>
bad-face 25-dec-83 a/b fad_cafe f^
</pre><P>
It is possible for there to be an ambiguity as to whether
a letter should be treated as a digit or as a number marker.
In such a case, the letter is always treated as a digit
rather than as a number marker.
<P>
Note that the printed representation for a potential
number may not contain any escape characters.
An escape character robs the following character of all syntactic
qualities, forcing it to be strictly alphabetic and therefore unsuitable
for use in a potential number. For example,
all of the following representations are interpreted as symbols, not numbers:
<pre>
\256 25\64 1.0\E6 |100| 3\.14159 |3/4| 3\/4 5||
</pre>
In each case, removing the escape character(s) would allow the token
to be treated as a number.
<P>
If a potential number can in fact
be interpreted as a number according to the BNF
syntax in table <A HREF="node189.html#NUMBERSYNTAXTABLE">22-2</A>, then a number object of the
appropriate type is constructed and returned. It should be noted that in
a given implementation it may be that not all tokens conforming to the
actual syntax for numbers can actually be converted into number objects.
For example, specifying too large or too small an exponent for a floating-point
number may make the number impossible to represent in the implementation.
Similarly, a ratio with denominator zero (such as <tt>-35/000</tt>)
cannot be represented in <i>any</i> implementation.
In any such circumstance where
a token with the syntax of a number cannot be converted to an internal
number object, an error is signaled. (On the other hand, an error
must not be signaled for specifying too many significant digits
for a floating-point number; an appropriately truncated or rounded
value should be produced.)
<P>
There is an omission in the syntax of numbers
as described in table <A HREF="node189.html#NUMBERSYNTAXTABLE">22-2</A>,
in that the syntax does not account for the possible
use of letters as digits.
The radix used for reading integers and ratios is normally decimal.
However, this radix is actually determined by the value of
the variable <tt>*read-base*</tt>, whose initial value is <tt>10</tt>.
<tt>*read-base*</tt> may take on any integral value between <tt>2</tt> and <tt>36</tt>;
let this value be <i>n</i>. Then a token <i>x</i> is interpreted as
an integer or ratio in base <i>n</i> if it could be properly
so interpreted in the syntax <tt>#<i>n</i>R<i>x</i></tt>
(see section <A HREF="node191.html#SHARPSIGNMACROCHARACTERSECTION">22.1.4</A>).
So, for example, if the value of <tt>*read-base*</tt> is <tt>16</tt>,
then the printed representation
<P><pre>
(a small face in a bad place)
</pre><P>
would be interpreted as if the following representation had
been read with <tt>*read-base*</tt> set to <tt>10</tt>:
<P><pre>
(10 small 64206 in 10 2989 place)
</pre><P>
because four of the seven tokens in the list can be interpreted
as hexadecimal numbers. This facility is intended to be used
in reading files of data that for some reason contain numbers
not in decimal radix; it may also be used for reading programs
written in Lisp dialects (such as MacLisp) whose default number radix is not
decimal. Non-decimal constants in Common Lisp programs
or portable Common Lisp data files should be written using
<tt>#O</tt>, <tt>#X</tt>, <tt>#B</tt>, or <tt>#<i>n</i>R</tt> syntax.
<P>
When <tt>*read-base*</tt> has a value greater than <tt>10</tt>, an ambiguity
is introduced into the actual syntax for numbers because a letter can serve
as either a digit or an exponent marker; a simple example is <tt>1E0</tt>
when the value of <tt>*read-base*</tt> is <tt>16</tt>. The ambiguity is resolved
in accordance with the general principle that interpretation
as a digit is preferred to interpretation as a number marker.
The consequence in this case is that
if a token can be interpreted as either an integer or a floating-point
number, then it is taken to be an integer.
<P>
If a token consists solely of dots (with no escape characters), then an
error is signaled, except in one circumstance: if the token is a single
dot and occurs in a situation appropriate to ``dotted list'' syntax,
then it is accepted as a part of such syntax. Signaling an error
catches not only misplaced dots in dotted list syntax but also
lists that were truncated by <tt>*print-length*</tt> cutoff,
because such lists end with a three-dot sequence (<tt>...</tt>).
Examples:
<P><pre>
(a . b) ;A dotted pair of <tt>a</tt> and <tt>b</tt>
(a.b) ;A list of one element, the symbol named <tt>a.b</tt>
(a. b) ;A list of two elements <tt>a.</tt> and <tt>b</tt>
(a .b) ;A list of two elements <tt>a</tt> and <tt>.b</tt>
(a . b) ;A list of three elements <tt>a</tt>, <tt>.</tt>, and <tt>b</tt>
(a |.| b) ;A list of three elements <tt>a</tt>, <tt>.</tt>, and <tt>b</tt>
(a ... b) ;A list of three elements <tt>a</tt>, <tt>...</tt>, and <tt>b</tt>
(a |...| b) ;A list of three elements <tt>a</tt>, <tt>...</tt>, and <tt>b</tt>
(a b . c) ;A dotted list of <tt>a</tt> and <tt>b</tt> with <tt>c</tt> at the end
.iot ;The symbol whose name is <tt>.iot</tt>
(. b) ;Illegal; an error is signaled
(a .) ;Illegal; an error is signaled
(a .. b) ;Illegal; an error is signaled
(a . . b) ;Illegal; an error is signaled
(a b c ...) ;Illegal; an error is signaled
</pre><P>
<P>
In all other cases, the token is construed to be the name of a symbol.
If there are any package markers
(colons) in the token, they divide the token into pieces used to
control the lookup and creation of the symbol.
<P>
<img align=bottom alt="old_change_begin" src="gif/old_change_begin.gif"><br>
If there is a single package marker, and it occurs at the beginning of the
token, then the token is interpreted as a keyword, that is, a symbol in the
<tt>keyword</tt> package. The part of the token after the package marker must
not have the syntax of a number.
<P>
If there is a single package marker not at the beginning or end of the
token, then it divides the token into two parts. The first part
specifies a package; the second part is the name of an external symbol
available in that package. Neither of the two parts may have the syntax
of a number.
<P>
If there are two adjacent package markers not at the beginning or end of the
token, then they divide the token into two parts. The first part
specifies a package; the second part is the name of a symbol within
that package (possibly an internal symbol).
Neither of the two parts may have the syntax of a number.
<br><img align=bottom alt="old_change_end" src="gif/old_change_end.gif">
<P>
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
X3J13 voted in March 1988
(COLON-NUMBER) <A NAME=20763>&#160;</A>
to clarify that, in the situations described in the
preceding three paragraphs, the restriction on the syntax of the parts should
be strengthened: none of the parts may have the syntax of even
a <i>potential</i> number. Tokens such as <tt>:3600</tt>, <tt>:1/2</tt>,
and <tt>editor:3.14159</tt> were already ruled out; this clarification further
declares that such tokens as <tt>:2^ 3</tt>, <tt>compiler:1.7J</tt>,
and <tt>Christmas:12/25/83</tt> are also in error and therefore should not be used
in portable programs. Implementations may differ in their treatment of
such package-marked potential numbers.
<br><img align=bottom alt="change_end" src="gif/change_end.gif">
<P>
If a symbol token contains no package markers, then the entire token
is the name of the symbol. The symbol is looked up in
the default package, which is the value
of the variable <tt>*package*</tt>.
<P>
All other patterns of package markers,
including the cases where there are more than two
package markers or where a package marker appears at the end of the token,
at present do not mean anything in Common Lisp (see chapter <A HREF="node111.html#XPACK">11</A>).
It is therefore currently an error to use such patterns in a Common Lisp program.
The valid patterns for tokens may be summarized as follows:
<PRE>
<i>nnnnn</i> a number
<i>xxxxx</i> a symbol in the current package
<tt>:<i>xxxxx</i></tt> a symbol in the keyword package
<tt><i>ppppp</i>:<i>xxxxx</i></tt> an external symbol in the <i>ppppp</i> package
<tt><i>ppppp</i>::<i>xxxxx</i></tt> a (possibly internal) symbol in the <i>ppppp</i> package
</PRE>
where <i>nnnnn</i> has the syntax of a number, and <i>xxxxx</i> and <i>ppppp</i> do
not have the syntax of a number.
<P>
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
In accordance with the X3J13 decision noted above
(COLON-NUMBER) <A NAME=20789>&#160;</A> , <i>xxxxx</i> and <i>ppppp</i> may not have the syntax of even
a potential number.
<br><img align=bottom alt="change_end" src="gif/change_end.gif">
<P>
<BR><b>[Variable]</b><BR>
<tt>*read-base*</tt><P>The value of <tt>*read-base*</tt> controls the interpretation of tokens
by <tt>read</tt> as being integers or ratios. Its value is the radix
in which integers and ratios are to be read; the value may be any integer
from <tt>2</tt> to <tt>36</tt> (inclusive) and is normally <tt>10</tt> (decimal radix).
Its value affects only the reading of integers and ratios.
In particular, floating-point numbers are always read in decimal radix.
The value of <tt>*read-base*</tt> does not affect the radix for rational numbers
whose radix is explicitly indicated by
<tt>#O</tt>, <tt>#X</tt>, <tt>#B</tt>, or <tt>#<i>n</i>R</tt> syntax
or by a trailing decimal point.
<P>
Care should be taken when setting <tt>*read-base*</tt> to a value larger
than <tt>10</tt>, because tokens that would normally be interpreted as
symbols may be interpreted as numbers instead. For example,
with <tt>*read-base*</tt> set to <tt>16</tt> (hexadecimal radix), variables
with names such as <tt>a</tt>, <tt>b</tt>, <tt>f</tt>, <tt>bad</tt>, and <tt>face</tt>
will be treated by the reader as numbers (with decimal values
10, 11, 15, 2989, and 64206, respectively). The ability to alter
the input radix is provided in Common Lisp primarily for the purpose of
reading data files in special formats, rather than for the purpose of altering
the default radix in which to read programs. The user is strongly
encouraged to use <tt>#O</tt>, <tt>#X</tt>, <tt>#B</tt>, or <tt>#<i>n</i>R</tt> syntax when
notating non-decimal constants in programs.
<P>
<hr>
<b>Compatibility note:</b> This variable corresponds to the variable
called <tt>ibase</tt> in MacLisp and to the function called <tt>radix</tt>
in Interlisp.
<hr>
<P>
<BR><b>[Variable]</b><BR>
<tt>*read-suppress*</tt><P>When the value of <tt>*read-suppress*</tt> is <tt>nil</tt>, the Lisp reader
operates normally. When it is not <tt>nil</tt>, then most of the interesting
operations of the reader are suppressed; input characters are parsed,
but much of what is read is not interpreted.
<P>
The primary purpose of <tt>*read-suppress*</tt> is to support the operation of
the read-time conditional constructs <tt>#+</tt> and <tt>#-</tt>
(see section <A HREF="node191.html#SHARPSIGNMACROCHARACTERSECTION">22.1.4</A>). It is important for these
constructs to be able to skip over the printed representation of a Lisp
expression despite the possibility that the syntax of the skipped
expression may not be entirely legal for the current implementation; this
is because a primary application of <tt>#+</tt> and <tt>#-</tt> is to allow the
same program to be shared among several Lisp implementations despite
small incompatibilities of syntax.
<P>
A non-<tt>nil</tt> value of <tt>*read-suppress*</tt> has the following specific
effects on the Common Lisp reader:
<UL><LI>
All extended tokens are completely uninterpreted. It matters not
whether the token looks like a number, much less like a valid number;
the pattern of package markers also does not matter. An extended token
is simply discarded and treated as if it were <tt>nil</tt>; that is, reading
an extended token when <tt>*read-suppress*</tt> is non-<tt>nil</tt> simply returns <tt>nil</tt>.
(One consequence of this is that the error concerning improper
dotted-list syntax will not be signaled.)
<P>
<LI>
Any standard
<tt>#</tt> macro-character construction that requires, permits, or disallows
an infix numerical argument, such as <tt>#<i>n</i>R</tt>, will not enforce
any constraint on the presence, absence, or value of such an argument.
<P>
<LI>
The <tt>#\</tt> construction always produces the value <tt>nil</tt>.
It will not signal an error even if an unknown character name is seen.
<P>
<LI>
Each of the <tt>#B</tt>, <tt>#O</tt>, <tt>#X</tt>, and <tt>#R</tt>
constructions always scans over a following token and produces the value <tt>nil</tt>.
It will not signal an error even if the token does not have the syntax
of a rational number.
<P>
<LI>
The <tt>#*</tt> construction always scans over a following token and
produces the value <tt>nil</tt>.
It will not signal an error even if the token does not consist solely
of the characters <tt>0</tt> and <tt>1</tt>.
</UL>
<P>
<img align=bottom alt="old_change_begin" src="gif/old_change_begin.gif"><br>
<UL><LI>
Each of the <tt>#.</tt> and <tt>#,</tt> constructions reads the following
form (in suppressed mode, of course) but does not evaluate it.
The form is discarded and <tt>nil</tt> is produced.
</UL>
<img align=bottom alt="old_change_end" src="gif/old_change_end.gif">
<P>
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
<ul>
X3J13 voted in January 1989
(SHARP-COMMA-CONFUSION) <A NAME=20861>&#160;</A> to remove <tt>#,</tt> from the language.
</ul>
<img align=bottom alt="change_end" src="gif/change_end.gif">
<P>
<UL><LI>
Each of the <tt>#A</tt>, <tt>#S</tt>, and <tt>#:</tt>
constructions reads the following
form (in suppressed mode, of course) but does not interpret it in any way;
it need not even be a list in the case of <tt>#S</tt>, or a symbol
in the case of <tt>#:</tt>. The form is discarded and <tt>nil</tt> is produced.
<P>
<LI>
The <tt>#=</tt> construction is totally ignored. It does not read
a following form. It produces no object, but is treated as whitespace.
<P>
<LI>
The <tt>##</tt> construction always produces <tt>nil</tt>.
</UL>
Note that, no matter what the value of <tt>*read-suppress*</tt>,
parentheses still continue to delimit (and construct) lists;
the <tt>#(</tt> construction continues to delimit vectors;
and comments, strings, and the quote and backquote constructions continue to be
interpreted properly. Furthermore, such situations as
<tt>')</tt>,
<tt>#&lt;</tt>, <tt>#)</tt>, and <tt>#<b></b>space<b></b></tt> continue to signal errors.
<P>
In some cases, it may be appropriate for a user-written macro-character
definition to check the value of <tt>*read-suppress*</tt> and to avoid certain
computations or side effects if its value is not <tt>nil</tt>.
<P>
<img align=bottom alt="change_begin" src="gif/change_begin.gif"><br>
<BR><b>[Variable]</b><BR>
<tt>*read-eval*</tt><P>X3J13 voted in June 1989 (DATA-IO) <A NAME=20886>&#160;</A> to add a new reader control variable,
<tt>*read-eval*</tt>, whose default value is <tt>t</tt>.
If <tt>*read-eval*</tt> is false, the <tt>#.</tt> reader macro signals an error.
<P>
Printing is also affected. If
<tt>*read-eval*</tt> is false and <tt>*print-readably*</tt> is true, any <tt>print-object</tt>
method that would otherwise output a <tt>#.</tt> reader macro must either output something
different or signal an error of type <tt>print-not-readable</tt>.
<P>
Binding <tt>*read-eval*</tt> to <tt>nil</tt> is useful when reading data that came from
an untrusted source, such as a network or a user-supplied data file; it
prevents the <tt>#.</tt> reader macro from being exploited as a ``Trojan horse'' to
cause arbitrary forms to be evaluated.
<br><img align=bottom alt="change_end" src="gif/change_end.gif">
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