commit ff20abb7979b296f637475caae5b187109c50cc1
parent 4b21b2d7ab8effb2c75e9a6eb920c2edaddaa239
Author: Andres Navarro <canavarro82@gmail.com>
Date: Fri, 10 Jun 2011 20:17:52 -0300
Completed module numbers in the manual.
Diffstat:
7 files changed, 1572 insertions(+), 133 deletions(-)
diff --git a/manual/html/Characters.html b/manual/html/Characters.html
@@ -34,7 +34,7 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<!-- node-name, next, previous, up -->
<h2 class="chapter">15 Characters</h2>
-<p><a name="index-characters-175"></a>
+<p><a name="index-characters-236"></a>
A character is an object that represents an ASCII character (for
now, only ASCII is supported in klisp, in the future, full UNICODE
will be supported). The external representation of characters
@@ -47,50 +47,50 @@ encapsulated.
features defined here were taken mostly from r5rs scheme.
<div class="defun">
-— Applicative: <b>char?</b> (<var>char? . objects</var>)<var><a name="index-char_003f-176"></a></var><br>
+— Applicative: <b>char?</b> (<var>char? . objects</var>)<var><a name="index-char_003f-237"></a></var><br>
<blockquote><p> The primitive type predicate for type character. <code>char?</code>
returns true iff all the objects in <code>objects</code> are of type
character.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>char=?</b> (<var>char=? . chars</var>)<var><a name="index-char_003d_003f-177"></a></var><br>
-— Applicative: <b>char<?</b> (<var>char<? . chars</var>)<var><a name="index-char_003c_003f-178"></a></var><br>
-— Applicative: <b>char<=?</b> (<var>char<=? . chars</var>)<var><a name="index-char_003c_003d_003f-179"></a></var><br>
-— Applicative: <b>char>?</b> (<var>char>? . chars</var>)<var><a name="index-char_003e_003f-180"></a></var><br>
-— Applicative: <b>char>=?</b> (<var>char>=? . chars</var>)<var><a name="index-char_003e_003d_003f-181"></a></var><br>
+— Applicative: <b>char=?</b> (<var>char=? . chars</var>)<var><a name="index-char_003d_003f-238"></a></var><br>
+— Applicative: <b>char<?</b> (<var>char<? . chars</var>)<var><a name="index-char_003c_003f-239"></a></var><br>
+— Applicative: <b>char<=?</b> (<var>char<=? . chars</var>)<var><a name="index-char_003c_003d_003f-240"></a></var><br>
+— Applicative: <b>char>?</b> (<var>char>? . chars</var>)<var><a name="index-char_003e_003f-241"></a></var><br>
+— Applicative: <b>char>=?</b> (<var>char>=? . chars</var>)<var><a name="index-char_003e_003d_003f-242"></a></var><br>
<blockquote><p> These predicates compare any number of characters using their
ASCII value for the comparison.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>char-ci=?</b> (<var>char-ci=? . chars</var>)<var><a name="index-char_002dci_003d_003f-182"></a></var><br>
-— Applicative: <b>char-ci<?</b> (<var>char-ci<? . chars</var>)<var><a name="index-char_002dci_003c_003f-183"></a></var><br>
-— Applicative: <b>char-ci<=?</b> (<var>char-ci<=? . chars</var>)<var><a name="index-char_002dci_003c_003d_003f-184"></a></var><br>
-— Applicative: <b>char-ci>?</b> (<var>char-ci>? . chars</var>)<var><a name="index-char_002dci_003e_003f-185"></a></var><br>
-— Applicative: <b>char-ci>=?</b> (<var>char-ci>=? . chars</var>)<var><a name="index-char_002dci_003e_003d_003f-186"></a></var><br>
+— Applicative: <b>char-ci=?</b> (<var>char-ci=? . chars</var>)<var><a name="index-char_002dci_003d_003f-243"></a></var><br>
+— Applicative: <b>char-ci<?</b> (<var>char-ci<? . chars</var>)<var><a name="index-char_002dci_003c_003f-244"></a></var><br>
+— Applicative: <b>char-ci<=?</b> (<var>char-ci<=? . chars</var>)<var><a name="index-char_002dci_003c_003d_003f-245"></a></var><br>
+— Applicative: <b>char-ci>?</b> (<var>char-ci>? . chars</var>)<var><a name="index-char_002dci_003e_003f-246"></a></var><br>
+— Applicative: <b>char-ci>=?</b> (<var>char-ci>=? . chars</var>)<var><a name="index-char_002dci_003e_003d_003f-247"></a></var><br>
<blockquote><p> These predicates convert the chars to lowercase and then compare
their ASCII values.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>char-alphabetic?</b> (<var>char-alphabetic? . chars</var>)<var><a name="index-char_002dalphabetic_003f-187"></a></var><br>
-— Applicative: <b>char-numeric?</b> (<var>char-numeric? . chars</var>)<var><a name="index-char_002dnumeric_003f-188"></a></var><br>
-— Applicative: <b>char-whitespace?</b> (<var>char-whitespace? . chars</var>)<var><a name="index-char_002dwhitespace_003f-189"></a></var><br>
+— Applicative: <b>char-alphabetic?</b> (<var>char-alphabetic? . chars</var>)<var><a name="index-char_002dalphabetic_003f-248"></a></var><br>
+— Applicative: <b>char-numeric?</b> (<var>char-numeric? . chars</var>)<var><a name="index-char_002dnumeric_003f-249"></a></var><br>
+— Applicative: <b>char-whitespace?</b> (<var>char-whitespace? . chars</var>)<var><a name="index-char_002dwhitespace_003f-250"></a></var><br>
<blockquote><p> These predicates return true iff all of their arguments are
respectively “alphabetic”, “numeric”, or “whitespace”.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>char-upper-case?</b> (<var>char-upper-case? . chars</var>)<var><a name="index-char_002dupper_002dcase_003f-190"></a></var><br>
-— Applicative: <b>char-lower-case?</b> (<var>char-lower-case? . chars</var>)<var><a name="index-char_002dlower_002dcase_003f-191"></a></var><br>
+— Applicative: <b>char-upper-case?</b> (<var>char-upper-case? . chars</var>)<var><a name="index-char_002dupper_002dcase_003f-251"></a></var><br>
+— Applicative: <b>char-lower-case?</b> (<var>char-lower-case? . chars</var>)<var><a name="index-char_002dlower_002dcase_003f-252"></a></var><br>
<blockquote><p> These predicates return true iff all of their arguments are
respectively “upper case, or “lower case”.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>char-upcase</b> (<var>char-upcase char</var>)<var><a name="index-char_002dupcase-192"></a></var><br>
-— Applicative: <b>char-downcase</b> (<var>char-downcase char</var>)<var><a name="index-char_002ddowncase-193"></a></var><br>
+— Applicative: <b>char-upcase</b> (<var>char-upcase char</var>)<var><a name="index-char_002dupcase-253"></a></var><br>
+— Applicative: <b>char-downcase</b> (<var>char-downcase char</var>)<var><a name="index-char_002ddowncase-254"></a></var><br>
<blockquote><p> These applicatives return a character <code>char2</code> so that:
<pre class="example"> (char-ci=? char char2) ⇒ #t
</pre>
@@ -102,8 +102,8 @@ respectively “upper case, or “lower case”.
</blockquote></div>
<div class="defun">
-— Applicative: <b>char->integer</b> (<var>char->integer char</var>)<var><a name="index-char_002d_003einteger-194"></a></var><br>
-— Applicative: <b>integer->char</b> (<var>integer->char k</var>)<var><a name="index-integer_002d_003echar-195"></a></var><br>
+— Applicative: <b>char->integer</b> (<var>char->integer char</var>)<var><a name="index-char_002d_003einteger-255"></a></var><br>
+— Applicative: <b>integer->char</b> (<var>integer->char k</var>)<var><a name="index-integer_002d_003echar-256"></a></var><br>
<blockquote><p> These applicatives convert between ASCII values (as exact integers
between 0 and 127) and characters. If an integer that is out of range
for ASCII characters is passed to <code>integer->char</code>, an error is
diff --git a/manual/html/Index.html b/manual/html/Index.html
@@ -55,9 +55,20 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Control.html#index-g_t_0024sequence-30"><code>$sequence</code></a>: <a href="Control.html#Control">Control</a></li>
<li><a href="Environments.html#index-g_t_0024set_0021-111"><code>$set!</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Combiners.html#index-g_t_0024vau-119"><code>$vau</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
-<li><a href="Ports.html#index-g_t_0028-200"><code>(</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-g_t_0028-261"><code>(</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-g_t_0028-179"><code>(</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Continuations.html#index-g_t_0028-135"><code>(</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Environments.html#index-g_t_0028-110"><code>(</code></a>: <a href="Environments.html#Environments">Environments</a></li>
+<li><a href="Numbers.html#index-g_t_002a-166"><code>*</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_002b-165"><code>+</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_002d-167"><code>-</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_002f-193"><code>/</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_003c_003d_003f-162"><code><=?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_003c_003f-161"><code><?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_003d_003f-160"><code>=?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_003e_003d_003f-164"><code>>=?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-g_t_003e_003f-163"><code>>?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-acos-208"><code>acos</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Booleans.html#index-and_003f-15"><code>and?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-append-81"><code>append</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-append_0021-89"><code>append!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -66,8 +77,10 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Combiners.html#index-applicatives-115">applicatives</a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Combiners.html#index-apply-123"><code>apply</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Continuations.html#index-apply_002dcontinuation-134"><code>apply-continuation</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
+<li><a href="Numbers.html#index-asin-207"><code>asin</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-assoc-84"><code>assoc</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-assq-91"><code>assq</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-atan-209"><code>atan</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Booleans.html#index-boolean_003f-13"><code>boolean?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Booleans.html#index-booleans-12">booleans</a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-caaaar-59"><code>caaaar</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -84,8 +97,8 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Pairs-and-lists.html#index-cadddr-66"><code>cadddr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-caddr-54"><code>caddr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-cadr-48"><code>cadr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Ports.html#index-call_002dwith_002dinput_002dfile-210"><code>call-with-input-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
-<li><a href="Ports.html#index-call_002dwith_002doutput_002dfile-211"><code>call-with-output-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-call_002dwith_002dinput_002dfile-271"><code>call-with-input-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-call_002dwith_002doutput_002dfile-272"><code>call-with-output-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
<li><a href="Continuations.html#index-call_002fcc-128"><code>call/cc</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Pairs-and-lists.html#index-car-45"><code>car</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-cdaaar-67"><code>cdaaar</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -103,26 +116,27 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Pairs-and-lists.html#index-cdddr-58"><code>cdddr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-cddr-50"><code>cddr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-cdr-46"><code>cdr</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Characters.html#index-char_002d_003einteger-194"><code>char->integer</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dalphabetic_003f-187"><code>char-alphabetic?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dci_003c_003d_003f-184"><code>char-ci<=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dci_003c_003f-183"><code>char-ci<?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dci_003d_003f-182"><code>char-ci=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dci_003e_003d_003f-186"><code>char-ci>=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dci_003e_003f-185"><code>char-ci>?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002ddowncase-193"><code>char-downcase</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dlower_002dcase_003f-191"><code>char-lower-case?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dnumeric_003f-188"><code>char-numeric?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dupcase-192"><code>char-upcase</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dupper_002dcase_003f-190"><code>char-upper-case?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_002dwhitespace_003f-189"><code>char-whitespace?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003c_003d_003f-179"><code>char<=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003c_003f-178"><code>char<?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003d_003f-177"><code>char=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003e_003d_003f-181"><code>char>=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003e_003f-180"><code>char>?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-char_003f-176"><code>char?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
-<li><a href="Characters.html#index-characters-175">characters</a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Numbers.html#index-ceiling-197"><code>ceiling</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Characters.html#index-char_002d_003einteger-255"><code>char->integer</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dalphabetic_003f-248"><code>char-alphabetic?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dci_003c_003d_003f-245"><code>char-ci<=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dci_003c_003f-244"><code>char-ci<?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dci_003d_003f-243"><code>char-ci=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dci_003e_003d_003f-247"><code>char-ci>=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dci_003e_003f-246"><code>char-ci>?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002ddowncase-254"><code>char-downcase</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dlower_002dcase_003f-252"><code>char-lower-case?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dnumeric_003f-249"><code>char-numeric?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dupcase-253"><code>char-upcase</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dupper_002dcase_003f-251"><code>char-upper-case?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_002dwhitespace_003f-250"><code>char-whitespace?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003c_003d_003f-240"><code>char<=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003c_003f-239"><code>char<?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003d_003f-238"><code>char=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003e_003d_003f-242"><code>char>=?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003e_003f-241"><code>char>?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-char_003f-237"><code>char?</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Characters.html#index-characters-236">characters</a>: <a href="Characters.html#Characters">Characters</a></li>
<li><a href="Combiners.html#index-combiner_003f-125"><code>combiner?</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Combiners.html#index-combiners-114">combiners</a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Pairs-and-lists.html#index-cons-39"><code>cons</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
@@ -132,15 +146,21 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Control.html#index-control-26">control</a>: <a href="Control.html#Control">Control</a></li>
<li><a href="Pairs-and-lists.html#index-copy_002des-90"><code>copy-es</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-copy_002des_002dimmutable_0021-42"><code>copy-es-immutable!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-cos-205"><code>cos</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-countable_002dlist_003f-87"><code>countable-list?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-denominator-195"><code>denominator</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Format-of-Descriptions.html#index-description-format-7">description format</a>: <a href="Format-of-Descriptions.html#Format-of-Descriptions">Format of Descriptions</a></li>
+<li><a href="Numbers.html#index-div-169"><code>div</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-div_002dand_002dmod-171"><code>div-and-mod</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-div0-172"><code>div0</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-div0_002dand_002dmod0-174"><code>div0-and-mod0</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Evaluation-Notation.html#index-documentation-notation-4">documentation notation</a>: <a href="Evaluation-Notation.html#Evaluation-Notation">Evaluation Notation</a></li>
<li><a href="Pairs-and-lists.html#index-empty-list-35">empty list</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Encapsulations.html#index-encapsulations-138">encapsulations</a>: <a href="Encapsulations.html#Encapsulations">Encapsulations</a></li>
<li><a href="Pairs-and-lists.html#index-encycle_0021-77"><code>encycle!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Environments.html#index-environment_003f-95"><code>environment?</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Environments.html#index-environments-93">environments</a>: <a href="Environments.html#Environments">Environments</a></li>
-<li><a href="Ports.html#index-eof_002dobject_003f-214"><code>eof-object?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-eof_002dobject_003f-275"><code>eof-object?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
<li><a href="Equivalence.html#index-eq_003f-20"><code>eq?</code></a>: <a href="Equivalence.html#Equivalence">Equivalence</a></li>
<li><a href="Equivalence.html#index-equal_003f-21"><code>equal?</code></a>: <a href="Equivalence.html#Equivalence">Equivalence</a></li>
<li><a href="Equivalence.html#index-equivalence-19">equivalence</a>: <a href="Equivalence.html#Equivalence">Equivalence</a></li>
@@ -148,101 +168,142 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<li><a href="Continuations.html#index-error_002dcontinuation-133"><code>error-continuation</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Environments.html#index-eval-97"><code>eval</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Evaluation-Notation.html#index-evaluation-notation-3">evaluation notation</a>: <a href="Evaluation-Notation.html#Evaluation-Notation">Evaluation Notation</a></li>
+<li><a href="Numbers.html#index-even_003f-178"><code>even?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-exact_003f-156"><code>exact?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Continuations.html#index-exit-137"><code>exit</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
+<li><a href="Numbers.html#index-exp-202"><code>exp</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-expt-211"><code>expt</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Continuations.html#index-extend_002dcontinuation-129"><code>extend-continuation</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Pairs-and-lists.html#index-filter-83"><code>filter</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-finite_002dlist_003f-86"><code>finite-list?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-finite_003f-155"><code>finite?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-floor-196"><code>floor</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Some-Terms.html#index-fonts-2">fonts</a>: <a href="Some-Terms.html#Some-Terms">Some Terms</a></li>
<li><a href="A-Sample-Applicative-Description.html#index-foo-11"><code>foo</code></a>: <a href="A-Sample-Applicative-Description.html#A-Sample-Applicative-Description">A Sample Applicative Description</a></li>
<li><a href="Control.html#index-for_002deach-32"><code>for-each</code></a>: <a href="Control.html#Control">Control</a></li>
<li><a href="Promises.html#index-force-142"><code>force</code></a>: <a href="Promises.html#Promises">Promises</a></li>
+<li><a href="Numbers.html#index-gcd-183"><code>gcd</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Environments.html#index-get_002dcurrent_002denvironment-102"><code>get-current-environment</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Pairs-and-lists.html#index-get_002dlist_002dmetrics-75"><code>get-list-metrics</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Ports.html#index-get_002dmodule-213"><code>get-module</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-get_002dmodule-274"><code>get-module</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-get_002dreal_002dexact_002dbounds-185"><code>get-real-exact-bounds</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-get_002dreal_002dexact_002dprimary-187"><code>get-real-exact-primary</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-get_002dreal_002dinternal_002dbounds-184"><code>get-real-internal-bounds</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-get_002dreal_002dinternal_002dprimary-186"><code>get-real-internal-primary</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-get_002dstring_002darithmetic-192"><code>get-string-arithmetic</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Continuations.html#index-guard_002dcontinuation-130"><code>guard-continuation</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Continuations.html#index-guard_002ddynamic_002dextent-136"><code>guard-dynamic-extent</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
<li><a href="Environments.html#index-ignore-94">ignore</a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Environments.html#index-ignore_003f-96"><code>ignore?</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Control.html#index-inert-27">inert</a>: <a href="Control.html#Control">Control</a></li>
<li><a href="Control.html#index-inert_003f-28"><code>inert?</code></a>: <a href="Control.html#Control">Control</a></li>
-<li><a href="Ports.html#index-input_002dport_003f-198"><code>input-port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
-<li><a href="Characters.html#index-integer_002d_003echar-195"><code>integer->char</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Numbers.html#index-inexact_003f-157"><code>inexact?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Ports.html#index-input_002dport_003f-259"><code>input-port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Characters.html#index-integer_002d_003echar-256"><code>integer->char</code></a>: <a href="Characters.html#Characters">Characters</a></li>
+<li><a href="Numbers.html#index-integer_003f-152"><code>integer?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Kernel-History.html#index-Kernel-history-1">Kernel history</a>: <a href="Kernel-History.html#Kernel-History">Kernel History</a></li>
<li><a href="Keyed-Variables.html#index-keyed-dynamic-variables-146">keyed dynamic variables</a>: <a href="Keyed-Variables.html#Keyed-Variables">Keyed Variables</a></li>
<li><a href="Keyed-Variables.html#index-keyed-static-variables-148">keyed static variables</a>: <a href="Keyed-Variables.html#Keyed-Variables">Keyed Variables</a></li>
<li><a href="Keyed-Variables.html#index-keyed-variables-145">keyed variables</a>: <a href="Keyed-Variables.html#Keyed-Variables">Keyed Variables</a></li>
+<li><a href="Numbers.html#index-lcm-182"><code>lcm</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-length-79"><code>length</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list-43"><code>list</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002a-44"><code>list*</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Strings.html#index-list_002d_003estring-174"><code>list->string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-list_002d_003estring-235"><code>list->string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
<li><a href="Pairs-and-lists.html#index-list_002dneighbors-82"><code>list-neighbors</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002dref-80"><code>list-ref</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-list_002dtail-76"><code>list-tail</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-lists-36">lists</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Ports.html#index-load-212"><code>load</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-load-273"><code>load</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-log-203"><code>log</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Encapsulations.html#index-make_002dencapsulation_002dtype-139"><code>make-encapsulation-type</code></a>: <a href="Encapsulations.html#Encapsulations">Encapsulations</a></li>
<li><a href="Environments.html#index-make_002denvironment-98"><code>make-environment</code></a>: <a href="Environments.html#Environments">Environments</a></li>
+<li><a href="Numbers.html#index-make_002dinexact-188"><code>make-inexact</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Environments.html#index-make_002dkernel_002dstandard_002denvironment-103"><code>make-kernel-standard-environment</code></a>: <a href="Environments.html#Environments">Environments</a></li>
<li><a href="Keyed-Variables.html#index-make_002dkeyed_002ddynamic_002dvariable-147"><code>make-keyed-dynamic-variable</code></a>: <a href="Keyed-Variables.html#Keyed-Variables">Keyed Variables</a></li>
<li><a href="Keyed-Variables.html#index-make_002dkeyed_002dstatic_002dvariable-149"><code>make-keyed-static-variable</code></a>: <a href="Keyed-Variables.html#Keyed-Variables">Keyed Variables</a></li>
-<li><a href="Strings.html#index-make_002dstring-163"><code>make-string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-make_002dstring-224"><code>make-string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
<li><a href="Combiners.html#index-map-124"><code>map</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Pairs-and-lists.html#index-map-78"><code>map</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-max-180"><code>max</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-member_003f-85"><code>member?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Promises.html#index-memoize-144"><code>memoize</code></a>: <a href="Promises.html#Promises">Promises</a></li>
<li><a href="Pairs-and-lists.html#index-memq_003f-92"><code>memq?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-min-181"><code>min</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-mod-170"><code>mod</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-mod0-173"><code>mod0</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-negative_003f-176"><code>negative?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-nil-34">nil</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Booleans.html#index-not_003f-14"><code>not?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
<li><a href="Pairs-and-lists.html#index-null_003f-38"><code>null?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-number_003f-151"><code>number?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Numbers.html#index-numbers-150">numbers</a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-numerator-194"><code>numerator</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="A-Sample-Applicative-Description.html#index-object-descriptions-10">object descriptions</a>: <a href="A-Sample-Applicative-Description.html#A-Sample-Applicative-Description">A Sample Applicative Description</a></li>
-<li><a href="Ports.html#index-open_002dinput_002dfile-204"><code>open-input-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
-<li><a href="Ports.html#index-open_002doutput_002dfile-205"><code>open-output-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-odd_003f-177"><code>odd?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Ports.html#index-open_002dinput_002dfile-265"><code>open-input-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-open_002doutput_002dfile-266"><code>open-output-file</code></a>: <a href="Ports.html#Ports">Ports</a></li>
<li><a href="A-Sample-Applicative-Description.html#index-operative-descriptions-9">operative descriptions</a>: <a href="A-Sample-Applicative-Description.html#A-Sample-Applicative-Description">A Sample Applicative Description</a></li>
<li><a href="Combiners.html#index-operative_003f-117"><code>operative?</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Combiners.html#index-operatives-116">operatives</a>: <a href="Combiners.html#Combiners">Combiners</a></li>
<li><a href="Booleans.html#index-or_003f-16"><code>or?</code></a>: <a href="Booleans.html#Booleans">Booleans</a></li>
-<li><a href="Ports.html#index-output_002dport_003f-199"><code>output-port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-output_002dport_003f-260"><code>output-port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
<li><a href="Pairs-and-lists.html#index-pair_003f-37"><code>pair?</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-pairs-33">pairs</a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Ports.html#index-port_003f-197"><code>port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
-<li><a href="Ports.html#index-ports-196">ports</a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-port_003f-258"><code>port?</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Ports.html#index-ports-257">ports</a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-positive_003f-175"><code>positive?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Printing-Notation.html#index-printing-notation-5">printing notation</a>: <a href="Printing-Notation.html#Printing-Notation">Printing Notation</a></li>
<li><a href="Promises.html#index-promise_003f-141"><code>promise?</code></a>: <a href="Promises.html#Promises">Promises</a></li>
<li><a href="Promises.html#index-promises-140">promises</a>: <a href="Promises.html#Promises">Promises</a></li>
-<li><a href="Ports.html#index-read-208"><code>read</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-rational_003f-153"><code>rational?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-rationalize-200"><code>rationalize</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Ports.html#index-read-269"><code>read</code></a>: <a href="Ports.html#Ports">Ports</a></li>
+<li><a href="Numbers.html#index-real_002d_003eexact-190"><code>real->exact</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-real_002d_003einexact-189"><code>real->inexact</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-real_003f-154"><code>real?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-reduce-88"><code>reduce</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
+<li><a href="Numbers.html#index-robust_003f-158"><code>robust?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Continuations.html#index-root_002dcontinuation-132"><code>root-continuation</code></a>: <a href="Continuations.html#Continuations">Continuations</a></li>
+<li><a href="Numbers.html#index-round-199"><code>round</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Pairs-and-lists.html#index-set_002dcar_0021-40"><code>set-car!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
<li><a href="Pairs-and-lists.html#index-set_002dcdr_0021-41"><code>set-cdr!</code></a>: <a href="Pairs-and-lists.html#Pairs-and-lists">Pairs and lists</a></li>
-<li><a href="Strings.html#index-string-164"><code>string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002d_003eimmutable_002dstring-172"><code>string->immutable-string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002d_003elist-173"><code>string->list</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Numbers.html#index-simplest_002drational-201"><code>simplest-rational</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-sin-204"><code>sin</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-sqrt-210"><code>sqrt</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Strings.html#index-string-225"><code>string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002d_003eimmutable_002dstring-233"><code>string->immutable-string</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002d_003elist-234"><code>string->list</code></a>: <a href="Strings.html#Strings">Strings</a></li>
<li><a href="Symbols.html#index-string_002d_003esymbol-25"><code>string->symbol</code></a>: <a href="Symbols.html#Symbols">Symbols</a></li>
-<li><a href="Strings.html#index-string_002dappend-170"><code>string-append</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dci_003c_003d_003f-160"><code>string-ci<=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dci_003c_003f-159"><code>string-ci<?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dci_003d_003f-158"><code>string-ci=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dci_003e_003d_003f-162"><code>string-ci>=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dci_003e_003f-161"><code>string-ci>?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dcopy-171"><code>string-copy</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dfill_0021-168"><code>string-fill!</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dlength-165"><code>string-length</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dref-166"><code>string-ref</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_002dset_0021-167"><code>string-set!</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003c_003d_003f-155"><code>string<=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003c_003f-154"><code>string<?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003d_003f-153"><code>string=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003e_003d_003f-157"><code>string>=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003e_003f-156"><code>string>?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-string_003f-152"><code>string?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-strings-151">strings</a>: <a href="Strings.html#Strings">Strings</a></li>
-<li><a href="Strings.html#index-substring-169"><code>substring</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dappend-231"><code>string-append</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dci_003c_003d_003f-221"><code>string-ci<=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dci_003c_003f-220"><code>string-ci<?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dci_003d_003f-219"><code>string-ci=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dci_003e_003d_003f-223"><code>string-ci>=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dci_003e_003f-222"><code>string-ci>?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dcopy-232"><code>string-copy</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dfill_0021-229"><code>string-fill!</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dlength-226"><code>string-length</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dref-227"><code>string-ref</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_002dset_0021-228"><code>string-set!</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003c_003d_003f-216"><code>string<=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003c_003f-215"><code>string<?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003d_003f-214"><code>string=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003e_003d_003f-218"><code>string>=?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003e_003f-217"><code>string>?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-string_003f-213"><code>string?</code></a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-strings-212">strings</a>: <a href="Strings.html#Strings">Strings</a></li>
+<li><a href="Strings.html#index-substring-230"><code>substring</code></a>: <a href="Strings.html#Strings">Strings</a></li>
<li><a href="Symbols.html#index-symbol_002d_003estring-24"><code>symbol->string</code></a>: <a href="Symbols.html#Symbols">Symbols</a></li>
<li><a href="Symbols.html#index-symbol_003f-23"><code>symbol?</code></a>: <a href="Symbols.html#Symbols">Symbols</a></li>
<li><a href="Symbols.html#index-symbols-22">symbols</a>: <a href="Symbols.html#Symbols">Symbols</a></li>
+<li><a href="Numbers.html#index-tan-206"><code>tan</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-truncate-198"><code>truncate</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
+<li><a href="Numbers.html#index-undefined_003f-159"><code>undefined?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Combiners.html#index-unwrap-121"><code>unwrap</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
+<li><a href="Numbers.html#index-with_002dstrict_002darithmetic-191"><code>with-strict-arithmetic</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
<li><a href="Combiners.html#index-wrap-120"><code>wrap</code></a>: <a href="Combiners.html#Combiners">Combiners</a></li>
+<li><a href="Numbers.html#index-zero_003f-168"><code>zero?</code></a>: <a href="Numbers.html#Numbers">Numbers</a></li>
</ul><!-- Print the tables of contents -->
<div class="shortcontents">
diff --git a/manual/html/Numbers.html b/manual/html/Numbers.html
@@ -35,6 +35,479 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<h2 class="chapter">13 Numbers</h2>
<p><a name="index-numbers-150"></a>
+All numbers are immutable, and <code>equal?</code> iff <code>eq?</code>. The
+number type is encapsulated.
+
+<!-- TODO add more content on numbers -->
+ <p>The external representation of an undefined number is
+<code>#undefined</code>. The external representation of a real with no
+primary value is <code>#real</code> (but this may change in the future, the
+report is missing the output representation for reals with no primary
+values). All other rules for externally representing numbers pertain
+only to defined numbers with primary values.
+
+ <p>An external representation of a real number consists of optional
+radix and/or exactness prefixes, optional sign (<code>+</code> or <code>-</code>),
+and magnitude. The radix prefixes are <code>#b</code> (binary), <code>#o</code>
+(octal), <code>#d</code> (decimal), and <code>#x</code> (hexadecimal); the default
+is decimal. The exactness prefixes are <code>#e</code> (exact) and
+<code>#i</code> (inexact); by default, the number is inexact iff the
+magnitude representation uses floating point. If both kinds of
+prefixes are used, they may occur in either order. The magnitude is
+either <code>infinity</code>; an unsigned integer (nonempty sequence of
+digits); a ratio of unsigned integers (two unsigned integers with a
+<code>/</code> between, of which the second is non-zero); or a floating
+point representation. If the magnitude is <code>infinity</code>, there must
+be an exactness prefix and a sign, and no radix prefix. Floating
+point representation can only be used with decimal radix; it consists
+of nonempty integer part, point (<code>.</code>), nonempty fraction part,
+and optional exponent part. The optional exponent part consists of an
+exponent letter, and an (optionally signed) integer indicating a power
+of ten by which to multiply the magnitude. The choice of exponent
+letter makes no difference in what mathematical number is indicated by
+the external representation, but does indicate internal representation
+precision. Exponent letters <code>s</code>, <code>f</code>, <code>d</code>, <code>f</code>
+indicate preference for successively higher internal precision -
+short, float, double, long. When reading an inexact real number,
+exponent letter <code>e</code> accepts the default internal precision, which
+must be at least double. When writeing an inexact real number,
+exponent letter <code>e</code> may be used for the default internal
+precision, and must be used for any internal number format not
+indicated by any of the other exponent letters. Float and double must
+provide, respectively, at least as much precision as IEEE 32-bit and
+64-bit floating point standards [IE85]. For example, <code>#i#xa/c</code>
+represents an inexact number using hexadecimal notation, with signed
+magnitude positive five sixths (ten over twelve). <code>-3.5l-2</code>
+represents an inexact number using decimal notation, with signed
+magnitude negative thirty five thousandths, and requested long
+precision (which must be at least IEEE 64-bit floating point). When
+reading an external representation of an inexact real, the bounds on
+the resulting inexact number are chosen in accordance with the
+<!-- TODO add xref -->
+narrow-arithmetic keyed dynamic variable.
+
+ <p>NOTE: in klisp, all inexact numbers are stored as IEEE 64-bit floating
+point. No bounding or robustness info is kept.
+
+<div class="defun">
+— Applicative: <b>number?</b> (<var>number? . objects</var>)<var><a name="index-number_003f-151"></a></var><br>
+<blockquote><p> The primitive type predicate for type number. <code>number?</code>
+returns true iff all the objects in <code>objects</code> are of type number.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>integer?</b> (<var>integer? . objects</var>)<var><a name="index-integer_003f-152"></a></var><br>
+<blockquote><p> The primitive type predicate for number subtype integer.
+<code>integer?</code> returns true iff all the objects in <code>objects</code>
+are of type integer.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>rational?</b> (<var>rational? . objects</var>)<var><a name="index-rational_003f-153"></a></var><br>
+<blockquote><p> The primitive type predicate for number subtype rational.
+<code>rational?</code> returns true iff all the objects in <code>objects</code>
+are of type rational.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>real?</b> (<var>real? . objects</var>)<var><a name="index-real_003f-154"></a></var><br>
+<blockquote><p> The primitive type predicate for number subtype real.
+<code>real?</code> returns true iff all the objects in <code>objects</code>
+are of type real.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>finite?</b> (<var>finite? . numbers</var>)<var><a name="index-finite_003f-155"></a></var><br>
+<blockquote><p> Predicate <code>finite?</code> returns true iff all the numbers in
+<code>numbers</code> are finite.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>exact?</b> (<var>exact? . numbers</var>)<var><a name="index-exact_003f-156"></a></var><br>
+<blockquote><p> Predicate <code>exact?</code> returns true iff all the numbers in
+<code>numbers</code> are exact.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>inexact?</b> (<var>inexact? . numbers</var>)<var><a name="index-inexact_003f-157"></a></var><br>
+<blockquote><p> Predicate <code>inexact?</code> returns true iff all the numbers in
+<code>numbers</code> are inexact.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>robust?</b> (<var>robust? . numbers</var>)<var><a name="index-robust_003f-158"></a></var><br>
+<blockquote><p> Predicate <code>robust?</code> returns true iff all the numbers in
+<code>numbers</code> are robust.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>undefined?</b> (<var>undefined? . numbers</var>)<var><a name="index-undefined_003f-159"></a></var><br>
+<blockquote><p> Predicate <code>undefined?</code> returns true iff all the numbers in
+<code>numbers</code> are undefined.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>=?</b> (<var>=? . numbers</var>)<var><a name="index-g_t_003d_003f-160"></a></var><br>
+<blockquote><p> Applicative <code>=?</code> is a predicate that returns true iff all its
+arguments are numerically equal to each other. If any of its
+arguments has no primary value, an error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b><?</b> (<var><? . reals</var>)<var><a name="index-g_t_003c_003f-161"></a></var><br>
+— Applicative: <b><=?</b> (<var><=? . reals</var>)<var><a name="index-g_t_003c_003d_003f-162"></a></var><br>
+— Applicative: <b>>?</b> (<var>>? . reals</var>)<var><a name="index-g_t_003e_003f-163"></a></var><br>
+— Applicative: <b>>=?</b> (<var>>=? . reals</var>)<var><a name="index-g_t_003e_003d_003f-164"></a></var><br>
+<blockquote><p> Each of these applicatives is a predicate that returns true iff
+every two consecutive elements of <code>reals</code> have primary values in
+the order indicated by the name of the applicative. If any element of
+<code>reals</code> has no primary value, an error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>+</b> (<var>+ . numbers</var>)<var><a name="index-g_t_002b-165"></a></var><br>
+<blockquote><p> Applicative <code>+</code> returns the sum of the elements of numbers. If
+numbers is empty, the sum of its elements is exact zero. If a
+positive infinity is added to a negative infinity, the result has no
+primary value. If all the elements of a cycle are zero, the sum of
+the cycle is zero. If the acyclic sum of the elements of a cycle
+(i.e., the sum of an acyclic list containing just those elements) is
+non-zero, the sum of the cycle is positive infinity times the acyclic
+sum of the elements. If the acyclic sum of the elements of a cycle is
+zero, but some of the elements of the cycle are non-zero, the sum of
+the cycle has no primary value.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>*</b> (<var>* . numbers</var>)<var><a name="index-g_t_002a-166"></a></var><br>
+<blockquote><p> Applicative <code>*</code> returns the product of the elements of numbers.
+If numbers is empty, the product of its elements is exact one. If an
+infinity is multiplied by zero, the result has no primary value. If
+the acyclic product of the elements of a cycle is real greater than
+one, the product of the cycle is positive infinity. If all the
+elements of a cycle are positive one, the product of the cycle is
+positive one. If the acyclic product of the elements of a cycle is
+positive one, but some of the elements of the cycle are not positive
+one, the product of the cycle has no primary value. If the acyclic
+product of the elements of a cycle has magnitude less than one, the
+product of the cycle is zero. If the acyclic product of the elements
+of a cycle has magnitude greater than or equal to one, and is not
+positive real, the product of the cycle has no primary value.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>-</b> (<var>- number . numbers</var>)<var><a name="index-g_t_002d-167"></a></var><br>
+<blockquote><p> <code>numbers</code> should be a nonempty list of numbers.
+
+ <p>Applicative <code>-</code> returns the sum of <code>number</code> with the
+negation of the sum of <code>numbers</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>zero?</b> (<var>zero? . numbers</var>)<var><a name="index-zero_003f-168"></a></var><br>
+<blockquote><p> Applicative <code>zero?</code> is a predicate that returns true iff every
+element of <code>numbers</code> is zero. For this purpose, a real number is
+zero if its primary value is zero. If any element of numbers has no
+primary value an error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>div</b> (<var>div real1 real2</var>)<var><a name="index-div-169"></a></var><br>
+— Applicative: <b>mod</b> (<var>mod real1 real2</var>)<var><a name="index-mod-170"></a></var><br>
+— Applicative: <b>div-and-mod</b> (<var>div-and-mod real1 real2</var>)<var><a name="index-div_002dand_002dmod-171"></a></var><br>
+<blockquote><p> For all three applicatives, if <code>real1</code> is infinite or
+<code>real2</code> is zero, an error is signaled.
+
+ <p>Let <code>n</code> be the greatest integer such that <code>real2 * n <=
+real1</code>. Applicative <code>div</code> returns <code>n</code>. Applicative
+<code>mod</code> returns <code>real1 - (real2 * n)</code>. Applicative
+<code>div-and-mod</code> returns a freshly allocated list of length two,
+whose first element is <code>n</code> and whose second element is
+<code>real1 - (real2 * n)</code>.
+
+ <p>NOTE: I'm not really sure about this description...
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>div0</b> (<var>div0 real1 real2</var>)<var><a name="index-div0-172"></a></var><br>
+— Applicative: <b>mod0</b> (<var>mod0 real1 real2</var>)<var><a name="index-mod0-173"></a></var><br>
+— Applicative: <b>div0-and-mod0</b> (<var>div0-and-mod0 real1 real2</var>)<var><a name="index-div0_002dand_002dmod0-174"></a></var><br>
+<blockquote><p> For all three applicatives, if <code>real1</code> is infinite or
+<code>real2</code> is zero, an error is signaled.
+
+ <p>Let <code>n</code> be the greatest integer such that <code>real2 * n <=
+real1 + |real2/2|</code>. Applicative <code>div0</code> returns <code>n</code>.
+Applicative <code>mod0</code> returns <code>real1 - (real2 * n)</code>.
+Applicative <code>div0-and-mod0</code> returns a freshly allocated list of
+length two, whose first element is <code>n</code> and whose second element
+is <code>real1 - (real2 * n)</code>.
+
+ <p>NOTE: I'm not really sure about this description...
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>positive?</b> (<var>positive? . reals</var>)<var><a name="index-positive_003f-175"></a></var><br>
+— Applicative: <b>negative?</b> (<var>negative? . reals</var>)<var><a name="index-negative_003f-176"></a></var><br>
+<blockquote><p> Applicative <code>positive?</code> is a predicate that returns true iff
+every element of <code>reals</code> is greater than zero. Applicative
+<code>negative?</code> is a predicate that returns true iff every element of
+<code>reals</code> is less than zero. If any argument to either applicative
+has no primary value an error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>odd?</b> (<var>odd? . integers</var>)<var><a name="index-odd_003f-177"></a></var><br>
+— Applicative: <b>even?</b> (<var>even? . integers</var>)<var><a name="index-even_003f-178"></a></var><br>
+<blockquote><p> Applicative <code>odd?</code> is a predicate that returns true iff every
+element of <code>integers</code> is odd. Applicative <code>even?</code> is a
+predicate that returns true iff every element of <code>integers</code> is
+even. If any argument to either applicative has no primary value an
+error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>(</b><var>abs real</var>)<var><a name="index-g_t_0028-179"></a></var><br>
+<blockquote><p> Applicative <code>abs</code> returns the nonnegative real number with the
+same magnitude as <code>real</code>; that is, if <code>real</code> is nonnegative
+it returns <code>real</code>, otherwise it returns the negation of
+<code>real</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>max</b> (<var>max . reals</var>)<var><a name="index-max-180"></a></var><br>
+— Applicative: <b>min</b> (<var>min . reals</var>)<var><a name="index-min-181"></a></var><br>
+<blockquote><p> If <code>reals</code> is nil, applicative <code>max</code> returns exact
+negative infinity, and applicative <code>min</code> returns exact positive
+infinity. If <code>reals</code> is non-nil, applicative <code>max</code> returns
+the largest number in <code>reals</code>, and applicative <code>min</code> returns
+the smallest number in <code>reals</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>lcm</b> (<var>lcm . impints</var>)<var><a name="index-lcm-182"></a></var><br>
+— Applicative: <b>gcd</b> (<var>gcd . impints</var>)<var><a name="index-gcd-183"></a></var><br>
+<blockquote><p> <code>impints</code> should be a list of improper integers, that is, real
+numbers each of which is either an integer or an infinity.
+
+ <p>Applicative <code>lcm</code> returns the smallest positive improper
+integer that is an improper0integer multiple of every element of
+<code>impints</code> (that is, smallest <code>n >= 1</code> such that for every
+argument <code>nk</code> there exists <code>n'k</code> with <code>nk * n'k = n</code>).
+If any of the arguments is zero, the result of <code>lcm</code> has no
+primary value. According to these rules, <code>lcm</code> with nil argument
+list returns <code>1</code>, and <code>lcm</code> with any infinite argument
+returns positive infinity.
+
+ <p>Applicative <code>gcd</code> returns the largest positive improper integer
+such that every element of <code>impints</code> is an improper-integer
+multiple of it (that is, largest <code>n >= 1</code> such that for every
+argument <code>nk</code> there exists <code>n'k</code> with <code>n * n'k = nk</code>).
+<code>gcd</code> with nil argument list returns exact positive infinity. If
+<code>gcd</code> is called with one or more arguments, and at least one of
+the arguments is zero, but none of the arguments is a non-zero finite
+integer, its result has no primary value. According to these rules,
+if <code>gcd</code> is called with at least one finite non-zero argument,
+its result is the same as if all zero and infinite arguments were
+deleted.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>get-real-internal-bounds</b> (<var>get-real-internal-bounds real</var>)<var><a name="index-get_002dreal_002dinternal_002dbounds-184"></a></var><br>
+— Applicative: <b>get-real-exact-bounds</b> (<var>get-real-exact-bounds real</var>)<var><a name="index-get_002dreal_002dexact_002dbounds-185"></a></var><br>
+<blockquote><p> Applicative <code>get-real-internal-bounds</code> returns a freshly
+allocated list of reals <code>(x1 x2)</code>, where the primary value of
+<code>x1</code> is the lower bound of <code>real</code>, using the same internal
+representation as the primary value of <code>real</code>, and the primary
+value of <code>x2</code> is the upper bound of <code>real</code>, using the same
+internal representation as the primary value of <code>real</code>. The
+<code>xk</code> are inexact iff real is inexact. The <code>xk</code> are robust
+(i.e., tagged if the implementation supports such), and the bounds of
+each <code>xk</code> are only required to contain its primary value (i.e.,
+the implementation is allowed to make the bounds equal to the primary
+value).
+
+ <p>Applicative <code>get-real-exact-bounds</code> returns a freshly allocated
+list of exact reals <code>(x1 x2)</code>, where <code>x1</code> is not greater
+than the lower bound of <code>real</code>, and <code>x2</code> is not less than
+the upper bound of <code>real</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>get-real-internal-primary</b> (<var>get-real-internal-primary real</var>)<var><a name="index-get_002dreal_002dinternal_002dprimary-186"></a></var><br>
+— Applicative: <b>get-real-exact-primary</b> (<var>get-real-exact-primary real</var>)<var><a name="index-get_002dreal_002dexact_002dprimary-187"></a></var><br>
+<blockquote><p> If <code>real</code> is exact, both applicatives return <code>real</code>. If
+<code>real</code> has no primary value, both applicatives signal an error.
+
+ <p>If <code>real</code> is inexact with a primary value, applicative
+<code>get-real-internal-primary</code> returns a real number <code>x0</code> whose
+primary value is the same as, and has the same internal format as, the
+primary value of <code>real</code>. <code>x0</code> is robust, and its bounds are
+only required to contain its primary value.
+
+ <!-- TODO add xref to get-real-exact-bounds -->
+ <p>If <code>real</code> is inexact with a primary value, applicative
+<code>get-real-exact-primary</code> returns an exact real number <code>x0</code>
+within the exact bounds that would be returned for <code>real</code> by
+applicative <code>get-real-exact-bounds</code>. Preferably, <code>x0</code>
+should be as close to the primary value of <code>real</code> as the
+implementation can reasonably arrange. If the implementation does not
+support any exact <code>real</code> that reasonably approximates
+<code>real</code>, an error may be signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>make-inexact</b> (<var>make-inexact real1 real2 real3</var>)<var><a name="index-make_002dinexact-188"></a></var><br>
+<blockquote><p> Applicative <code>make-inexact</code> returns an inexact real number, as
+follows. If <code>real2</code> is inexact, the result has the same primary
+value as <code>real2</code>; and if <code>real2</code> has no primary value, the
+result has no primary value. The result has the same robustness as
+<code>real2</code>. If possible, the result uses the same internal
+representation as <code>real2</code>. If <code>real2</code> is exact, the primary
+value of the result is as close to <code>real2</code> as the implementation
+can reasonably arrange; overflow and underflow are handled as
+<!-- TODO add xref to overflow -->
+described in .... The lower bound of the result is no greater than
+the lower bound of <code>real1</code>, the primary value of <code>real2</code>,
+and the primary value of the result. The upper bound of the result is
+no less than the upper bound of <code>real3</code>, the primary value of
+<code>real2</code>, and the primary value of the result.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>real->inexact</b> (<var>real->inexact real</var>)<var><a name="index-real_002d_003einexact-189"></a></var><br>
+— Applicative: <b>real->exact</b> (<var>real->exact real</var>)<var><a name="index-real_002d_003eexact-190"></a></var><br>
+<blockquote><!-- TODO add xref to get-real-exact-primary -->
+ <p>Applicative <code>real->exact</code> behaves just as
+<code>get-real-exact-primary</code>.
+
+ <p>If <code>real</code> is inexact, applicative <code>real->inexact</code> returns
+<code>real</code>. If <code>real</code> is exact, applicative
+<code>real->inexact</code> returns an inexact real <code>x0</code> such that
+<code>real</code> would be a permissible result of passing <code>x0</code> to
+<code>real->exact</code>. If the implementation does not support any such
+<code>x0</code>, an error may be signaled. Otherwise, <code>x0</code> is robust,
+and its bounds are only required to contain its primary value and
+<code>real</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>with-strict-arithmetic</b> (<var>with-strict-arithmetic boolean combiner</var>)<var><a name="index-with_002dstrict_002darithmetic-191"></a></var><br>
+— Applicative: <b>get-string-arithmetic</b> (<var>get-strict-arithmetic?</var>)<var><a name="index-get_002dstring_002darithmetic-192"></a></var><br>
+<blockquote><!-- TODO add xref to dynamic keys and under/over flow, no prim value -->
+ <p>These applicatives are the binder and accessor of the
+<code>strict-arithmetic</code> keyed dynamic variable. When this keyed
+variable is true, various survivable but dubious arithmetic events
+signal an error - notably, operation results with no primary value,
+and over- and underflows.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>/</b> (<var>/ number . numbers</var>)<var><a name="index-g_t_002f-193"></a></var><br>
+<blockquote><p> <code>numbers</code> should be a nonempty list of numbers.
+
+ <p>Applicative <code>/</code> returns <code>number</code> divided by the product of
+<code>numbers</code>. If the product of <code>numbers</code> is zero, an error is
+signaled. If <code>number</code> is infinite and the product of <code>numbers</code> is
+infinite, an error is signaled.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>numerator</b> (<var>numerator rational</var>)<var><a name="index-numerator-194"></a></var><br>
+— Applicative: <b>denominator</b> (<var>denominator rational</var>)<var><a name="index-denominator-195"></a></var><br>
+<blockquote><p> These applicatives return the numerator and denominator of
+<code>rational</code>, in least terms (i.e., chosen for the least positive
+denominator). Note that if <code>rational</code> is inexact, and either of
+its bounds is not its primary value, the denominator has upper bound
+positive infinity, and the numerator must have at least one infinite
+bound (two infinite bounds if the bounds of rational allow values of
+both signs).
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>floor</b> (<var>floor real</var>)<var><a name="index-floor-196"></a></var><br>
+— Applicative: <b>ceiling</b> (<var>ceiling real</var>)<var><a name="index-ceiling-197"></a></var><br>
+— Applicative: <b>truncate</b> (<var>truncate real</var>)<var><a name="index-truncate-198"></a></var><br>
+— Applicative: <b>round</b> (<var>round real</var>)<var><a name="index-round-199"></a></var><br>
+<blockquote><p> Applicative <code>floor</code> returns the largest integer not greater
+than <code>real</code>.
+
+ <p>Applicative <code>ceiling</code> returns the smallest integer not less
+than <code>real</code>.
+
+ <p>Applicative <code>truncate</code> returns the integer closest to
+<code>real</code> whose absolute value is not greater than that of
+<code>real</code>.
+
+ <p>Applicative <code>round</code> returns the closest integer to <code>real</code>,
+rounding to even when <code>real</code> is halfway between two integers.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>rationalize</b> (<var>rationalize real1 real2</var>)<var><a name="index-rationalize-200"></a></var><br>
+— Applicative: <b>simplest-rational</b> (<var>simplest-rational real1 real2</var>)<var><a name="index-simplest_002drational-201"></a></var><br>
+<blockquote><p> A rational number <code>r1</code> is simpler than another rational
+<code>r2</code> if <code>r1 = p1 / q1</code> and <code>r2 = p2 / q2</code>, both in
+lowest terms, and <code>|p1| <= |p2|</code> and <code>|q1| <= |q2|</code>. Thus
+<code>3/5</code> is simpler than <code>4/7</code>. Not all rationals are
+comparable in this ordering, as for example <code>2/7</code> and <code>3/5</code>.
+However, any interval (that contains rational numbers) contains a
+rational number that is simpler than every other rational number in
+that interval. Note that <code>0 = 0/1</code> is simpler than any other
+rational (so that one never has to choose between <code>p/q</code> and
+<code>−p/q</code>).
+
+ <p>For applicative <code>simplest-rational</code>, let <code>x0</code> be the
+simplest rational mathematically not less than the primary value of
+<code>real1</code> and not greater than the primary value of <code>real2</code>.
+If no such <code>x0</code> exists (because the primary value of <code>real1</code>
+is greater, or because the primary values of the arguments are equal
+and irrational), or if either argument does not have a primary value,
+an error is signaled.
+
+ <p>For applicative <code>rationalize</code>, let <code>x0</code> be the simplest
+rational mathematical number within the interval bounded by the
+primary value of <code>real1</code> plus and minus the primary value of
+<code>real2</code>. If no such <code>x0</code> exists (because the primary value
+of <code>real1</code> is irrational and the primary value <code>real2</code> is
+zero), or if either argument does not have a primary value, an error
+is signaled.
+
+ <!-- TODO add xref to real->inexact -->
+ <p>If <code>real1</code> and <code>real2</code> are exact, the applicative
+(whichever it is) returns exact <code>x0</code>. If one or both of
+<code>real1</code> and <code>real2</code> are inexact, the applicative returns an
+inexact rational approximating <code>x0</code> (as by <code>real->inexact</code>.
+Note that an inexact result returned is not necessarily bounded by the
+primary values of the arguments; but the result is an approximation of
+<code>x0</code>, which is so bounded, and the bounds of the result include
+<code>x0</code>.
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>exp</b> (<var>exp number</var>)<var><a name="index-exp-202"></a></var><br>
+— Applicative: <b>log</b> (<var>log number</var>)<var><a name="index-log-203"></a></var><br>
+<blockquote><p>TODO
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>sin</b> (<var>sin number</var>)<var><a name="index-sin-204"></a></var><br>
+— Applicative: <b>cos</b> (<var>cos number</var>)<var><a name="index-cos-205"></a></var><br>
+— Applicative: <b>tan</b> (<var>tan number</var>)<var><a name="index-tan-206"></a></var><br>
+<blockquote><p>TODO
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>asin</b> (<var>asin number</var>)<var><a name="index-asin-207"></a></var><br>
+— Applicative: <b>acos</b> (<var>acos number</var>)<var><a name="index-acos-208"></a></var><br>
+— Applicative: <b>atan</b> (<var>atan number1 </var>[<var>number2</var>])<var><a name="index-atan-209"></a></var><br>
+<blockquote><p>TODO
+</p></blockquote></div>
+
+<div class="defun">
+— Applicative: <b>sqrt</b> (<var>sqrt number</var>)<var><a name="index-sqrt-210"></a></var><br>
+— Applicative: <b>expt</b> (<var>expt number1 number2</var>)<var><a name="index-expt-211"></a></var><br>
+<blockquote><p>TODO
+</p></blockquote></div>
<!-- *-texinfo-*- -->
</body></html>
diff --git a/manual/html/Ports.html b/manual/html/Ports.html
@@ -34,7 +34,7 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<!-- node-name, next, previous, up -->
<h2 class="chapter">16 Ports</h2>
-<p><a name="index-ports-196"></a>
+<p><a name="index-ports-257"></a>
A port is an object that mediates character-based input from a
source or character-based output to a destination. In the former case,
the port is an input port, in the latter case, an output port.
@@ -53,14 +53,14 @@ normal result of a call to read). The eof type is encapsulated.
klisp and was taken from Scheme.
<div class="defun">
-— Applicative: <b>port?</b> (<var>port? . objects</var>)<var><a name="index-port_003f-197"></a></var><br>
+— Applicative: <b>port?</b> (<var>port? . objects</var>)<var><a name="index-port_003f-258"></a></var><br>
<blockquote><p> The primitive type predicate for type port. <code>port?</code>
returns true iff all the objects in <code>objects</code> are of type port.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>input-port?</b> (<var>input-port? . objects</var>)<var><a name="index-input_002dport_003f-198"></a></var><br>
-— Applicative: <b>output-port?</b> (<var>output-port? . objects</var>)<var><a name="index-output_002dport_003f-199"></a></var><br>
+— Applicative: <b>input-port?</b> (<var>input-port? . objects</var>)<var><a name="index-input_002dport_003f-259"></a></var><br>
+— Applicative: <b>output-port?</b> (<var>output-port? . objects</var>)<var><a name="index-output_002dport_003f-260"></a></var><br>
<blockquote><p> Applicative <code>input-port?</code> is a predicate that returns true
unless one or more of its arguments is not an input port. Applicative
output-port? is a predicate that returns true unless one or more of
@@ -70,8 +70,8 @@ its arguments is not an output port.
</p></blockquote></div>
<div class="defun">
-— with-input-from-file: <b>(</b><var>with-input-from-file string combiner</var>)<var><a name="index-g_t_0028-200"></a></var><br>
-— with-output-to-file: <b>(</b><var>with-output-to-file string combiner</var>)<var><a name="index-g_t_0028-201"></a></var><br>
+— with-input-from-file: <b>(</b><var>with-input-from-file string combiner</var>)<var><a name="index-g_t_0028-261"></a></var><br>
+— with-output-to-file: <b>(</b><var>with-output-to-file string combiner</var>)<var><a name="index-g_t_0028-262"></a></var><br>
<blockquote><!-- add xref get-current-input-port/get-current-output-port -->
<p>These two applicatives open the file named in <code>string</code> for
input or output, an invoke the binder of the input-port & output-port
@@ -88,8 +88,8 @@ klisp implementation in the near future.
</p></blockquote></div>
<div class="defun">
-— get-current-input-port: <b>(</b><var>get-current-input-port</var>)<var><a name="index-g_t_0028-202"></a></var><br>
-— get-current-output-port: <b>(</b><var>get-current-output-port</var>)<var><a name="index-g_t_0028-203"></a></var><br>
+— get-current-input-port: <b>(</b><var>get-current-input-port</var>)<var><a name="index-g_t_0028-263"></a></var><br>
+— get-current-output-port: <b>(</b><var>get-current-output-port</var>)<var><a name="index-g_t_0028-264"></a></var><br>
<blockquote><p> These are the accessors for the input-port and output-port keyed
dynamic variables repectively.
<!-- add xref to with-input-from-file, etc -->
@@ -102,7 +102,7 @@ klisp implementation in the near future.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>open-input-file</b> (<var>open-input-file string</var>)<var><a name="index-open_002dinput_002dfile-204"></a></var><br>
+— Applicative: <b>open-input-file</b> (<var>open-input-file string</var>)<var><a name="index-open_002dinput_002dfile-265"></a></var><br>
<blockquote><p> <code>string</code> should be the name/path for an existing file.
<p>Applicative <code>open-input-file</code> creates and returns an input port
@@ -115,7 +115,7 @@ still missing.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>open-output-file</b> (<var>open-output-file string</var>)<var><a name="index-open_002doutput_002dfile-205"></a></var><br>
+— Applicative: <b>open-output-file</b> (<var>open-output-file string</var>)<var><a name="index-open_002doutput_002dfile-266"></a></var><br>
<blockquote><p> <code>string</code> should be the name/path for an existing file.
<p>Applicative <code>open-output-file</code> creates and returns an output
@@ -132,8 +132,8 @@ still missing.
</p></blockquote></div>
<div class="defun">
-— close-input-file: <b>(</b><var>close-input-file input-port</var>)<var><a name="index-g_t_0028-206"></a></var><br>
-— close-output-file: <b>(</b><var>close-output-file output-port</var>)<var><a name="index-g_t_0028-207"></a></var><br>
+— close-input-file: <b>(</b><var>close-input-file input-port</var>)<var><a name="index-g_t_0028-267"></a></var><br>
+— close-output-file: <b>(</b><var>close-output-file output-port</var>)<var><a name="index-g_t_0028-268"></a></var><br>
<blockquote><p> These applicatives close the port argument, so that no more
input/output may be performed on them, and the resources can be
freed. If the port was already closed these applicatives have no
@@ -148,7 +148,7 @@ probably be called close-input-port & close-output-port.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>read</b> (<var>read </var>[<var>input-port</var>])<var><a name="index-read-208"></a></var><br>
+— Applicative: <b>read</b> (<var>read </var>[<var>input-port</var>])<var><a name="index-read-269"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>input-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -164,7 +164,7 @@ still missing.
</p></blockquote></div>
<div class="defun">
-— write: <b>(</b><var>write object </var>[<var>port</var>])<var><a name="index-g_t_0028-209"></a></var><br>
+— write: <b>(</b><var>write object </var>[<var>port</var>])<var><a name="index-g_t_0028-270"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>output-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -182,8 +182,8 @@ still missing.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>call-with-input-file</b> (<var>call-with-input-file string combiner</var>)<var><a name="index-call_002dwith_002dinput_002dfile-210"></a></var><br>
-— Applicative: <b>call-with-output-file</b> (<var>call-with-output-file string combiner</var>)<var><a name="index-call_002dwith_002doutput_002dfile-211"></a></var><br>
+— Applicative: <b>call-with-input-file</b> (<var>call-with-input-file string combiner</var>)<var><a name="index-call_002dwith_002dinput_002dfile-271"></a></var><br>
+— Applicative: <b>call-with-output-file</b> (<var>call-with-output-file string combiner</var>)<var><a name="index-call_002dwith_002doutput_002dfile-272"></a></var><br>
<blockquote><p> These applicatives open file named in <code>string</code> and call their
<code>combiner</code> argument in a fresh empty environment passing it as a
sole operand the opened port. When/if the combiner normally returns a
@@ -195,7 +195,7 @@ still missing.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>load</b> (<var>load string</var>)<var><a name="index-load-212"></a></var><br>
+— Applicative: <b>load</b> (<var>load string</var>)<var><a name="index-load-273"></a></var><br>
<blockquote><!-- TODO add xref, open/input, read -->
<p>Applicative <code>load</code> opens for input a file named <code>string</code>;
reads objects from the file until the end of the file is reached;
@@ -211,7 +211,7 @@ return the value of the last evaluation.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>get-module</b> (<var>get-module string </var>[<var>environment</var>])<var><a name="index-get_002dmodule-213"></a></var><br>
+— Applicative: <b>get-module</b> (<var>get-module string </var>[<var>environment</var>])<var><a name="index-get_002dmodule-274"></a></var><br>
<blockquote><!-- TODO add xref standard-environment, open/input, read -->
<p>Applicative <code>get-module</code> creates a fresh standard environment;
opens for input a file named <code>string</code>; reads objects from the
@@ -224,7 +224,7 @@ prior to evaluating read expressions, by binding symbol
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>eof-object?</b> (<var>eof-object? . objects</var>)<var><a name="index-eof_002dobject_003f-214"></a></var><br>
+— Applicative: <b>eof-object?</b> (<var>eof-object? . objects</var>)<var><a name="index-eof_002dobject_003f-275"></a></var><br>
<blockquote><p> The primitive type predicate for type eof. <code>eof-object?</code>
returns true iff all the objects in <code>objects</code> are of type eof.
@@ -235,7 +235,7 @@ primitive type predicates.
</p></blockquote></div>
<div class="defun">
-— read-char: <b>(</b><var>read-char </var>[<var>port</var>])<var><a name="index-g_t_0028-215"></a></var><br>
+— read-char: <b>(</b><var>read-char </var>[<var>port</var>])<var><a name="index-g_t_0028-276"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>input-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -248,7 +248,7 @@ an eof if the end of file was reached.
</p></blockquote></div>
<div class="defun">
-— peek-char: <b>(</b><var>peek-char </var>[<var>port</var>])<var><a name="index-g_t_0028-216"></a></var><br>
+— peek-char: <b>(</b><var>peek-char </var>[<var>port</var>])<var><a name="index-g_t_0028-277"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>input-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -263,7 +263,7 @@ remains unchanged so that new call to <code>peek-char</code> or
</p></blockquote></div>
<div class="defun">
-— char-ready?: <b>(</b><var>char-ready? </var>[<var>port</var>])<var><a name="index-g_t_0028-217"></a></var><br>
+— char-ready?: <b>(</b><var>char-ready? </var>[<var>port</var>])<var><a name="index-g_t_0028-278"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>input-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -278,7 +278,7 @@ the code to do this is non-portable.
</p></blockquote></div>
<div class="defun">
-— write-char: <b>(</b><var>write-char char </var>[<var>port</var>])<var><a name="index-g_t_0028-218"></a></var><br>
+— write-char: <b>(</b><var>write-char char </var>[<var>port</var>])<var><a name="index-g_t_0028-279"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>output-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -291,7 +291,7 @@ The result returned by <code>write-char</code> is inert.
</p></blockquote></div>
<div class="defun">
-— newline: <b>(</b><var>newline </var>[<var>port</var>])<var><a name="index-g_t_0028-219"></a></var><br>
+— newline: <b>(</b><var>newline </var>[<var>port</var>])<var><a name="index-g_t_0028-280"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>output-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
@@ -303,7 +303,7 @@ The result returned by <code>newline</code> is inert.
</p></blockquote></div>
<div class="defun">
-— display: <b>(</b><var>display object </var>[<var>port</var>])<var><a name="index-g_t_0028-220"></a></var><br>
+— display: <b>(</b><var>display object </var>[<var>port</var>])<var><a name="index-g_t_0028-281"></a></var><br>
<blockquote><p> If the <code>port</code> optional argument is not specified, then the
value of the <code>output-port</code> keyed dynamic variable is used. If the
port is closed, an error is signaled.
diff --git a/manual/html/Strings.html b/manual/html/Strings.html
@@ -34,7 +34,7 @@ Up: <a rel="up" accesskey="u" href="index.html#Top">Top</a>
<!-- node-name, next, previous, up -->
<h2 class="chapter">14 Strings</h2>
-<p><a name="index-strings-151"></a>
+<p><a name="index-strings-212"></a>
A string is an object that represent a sequence of characters (for
now, only ASCII is supported in klisp, in the future, full UNICODE
will be supported). The external representation of strings consists
@@ -68,34 +68,34 @@ to a new type (like Java's StringBuilder/StringBuffer). But for now,
compatibility with r5rs was preferred/simpler.
<div class="defun">
-— Applicative: <b>string?</b> (<var>string? . objects</var>)<var><a name="index-string_003f-152"></a></var><br>
+— Applicative: <b>string?</b> (<var>string? . objects</var>)<var><a name="index-string_003f-213"></a></var><br>
<blockquote><p> The primitive type predicate for type string. <code>string?</code>
returns true iff all the objects in <code>objects</code> are of type
string.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string=?</b> (<var>string=? . strings</var>)<var><a name="index-string_003d_003f-153"></a></var><br>
-— Applicative: <b>string<?</b> (<var>string<? . strings</var>)<var><a name="index-string_003c_003f-154"></a></var><br>
-— Applicative: <b>string<=?</b> (<var>string<=? . strings</var>)<var><a name="index-string_003c_003d_003f-155"></a></var><br>
-— Applicative: <b>string>?</b> (<var>string>? . strings</var>)<var><a name="index-string_003e_003f-156"></a></var><br>
-— Applicative: <b>string>=?</b> (<var>string>=? . strings</var>)<var><a name="index-string_003e_003d_003f-157"></a></var><br>
+— Applicative: <b>string=?</b> (<var>string=? . strings</var>)<var><a name="index-string_003d_003f-214"></a></var><br>
+— Applicative: <b>string<?</b> (<var>string<? . strings</var>)<var><a name="index-string_003c_003f-215"></a></var><br>
+— Applicative: <b>string<=?</b> (<var>string<=? . strings</var>)<var><a name="index-string_003c_003d_003f-216"></a></var><br>
+— Applicative: <b>string>?</b> (<var>string>? . strings</var>)<var><a name="index-string_003e_003f-217"></a></var><br>
+— Applicative: <b>string>=?</b> (<var>string>=? . strings</var>)<var><a name="index-string_003e_003d_003f-218"></a></var><br>
<blockquote><p> These predicates compare any number of strings by their
lexicographic order.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-ci=?</b> (<var>string-ci=? . strings</var>)<var><a name="index-string_002dci_003d_003f-158"></a></var><br>
-— Applicative: <b>string-ci<?</b> (<var>string-ci<? . strings</var>)<var><a name="index-string_002dci_003c_003f-159"></a></var><br>
-— Applicative: <b>string-ci<=?</b> (<var>string-ci<=? . strings</var>)<var><a name="index-string_002dci_003c_003d_003f-160"></a></var><br>
-— Applicative: <b>string-ci>?</b> (<var>string-ci>? . strings</var>)<var><a name="index-string_002dci_003e_003f-161"></a></var><br>
-— Applicative: <b>string-ci>=?</b> (<var>string-ci>=? . strings</var>)<var><a name="index-string_002dci_003e_003d_003f-162"></a></var><br>
+— Applicative: <b>string-ci=?</b> (<var>string-ci=? . strings</var>)<var><a name="index-string_002dci_003d_003f-219"></a></var><br>
+— Applicative: <b>string-ci<?</b> (<var>string-ci<? . strings</var>)<var><a name="index-string_002dci_003c_003f-220"></a></var><br>
+— Applicative: <b>string-ci<=?</b> (<var>string-ci<=? . strings</var>)<var><a name="index-string_002dci_003c_003d_003f-221"></a></var><br>
+— Applicative: <b>string-ci>?</b> (<var>string-ci>? . strings</var>)<var><a name="index-string_002dci_003e_003f-222"></a></var><br>
+— Applicative: <b>string-ci>=?</b> (<var>string-ci>=? . strings</var>)<var><a name="index-string_002dci_003e_003d_003f-223"></a></var><br>
<blockquote><p> These predicates convert the strings to lowercase and then compare
them using their lexicographic order.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>make-string</b> (<var>make-string k </var>[<var>char</var>])<var><a name="index-make_002dstring-163"></a></var><br>
+— Applicative: <b>make-string</b> (<var>make-string k </var>[<var>char</var>])<var><a name="index-make_002dstring-224"></a></var><br>
<blockquote><p> Applicative <code>make-string</code> constructs and returns a new mutable
string of length <code>k</code>. If <code>char</code> is specified, then all
characters in the returned string are <code>char</code>, otherwise the
@@ -103,19 +103,19 @@ content of the string is unspecified.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string</b> (<var>string . chars</var>)<var><a name="index-string-164"></a></var><br>
+— Applicative: <b>string</b> (<var>string . chars</var>)<var><a name="index-string-225"></a></var><br>
<blockquote><p> Applicative <code>string</code> contructs and return a new mutable string
composed of the character arguments.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-length</b> (<var>string-length string</var>)<var><a name="index-string_002dlength-165"></a></var><br>
+— Applicative: <b>string-length</b> (<var>string-length string</var>)<var><a name="index-string_002dlength-226"></a></var><br>
<blockquote><p> Applicative <code>string-length</code> returns the length of
<code>string</code>.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-ref</b> (<var>string-ref string k</var>)<var><a name="index-string_002dref-166"></a></var><br>
+— Applicative: <b>string-ref</b> (<var>string-ref string k</var>)<var><a name="index-string_002dref-227"></a></var><br>
<blockquote><p> Applicative <code>string-ref</code> returns the character of <code>string</code>
at position <code>k</code>. If <code>k</code> is out of bounds (i.e. less than
<code>0</code> or greater or equal than <code>(length string)</code>) an error is
@@ -123,21 +123,21 @@ signaled.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-set!</b> (<var>string-set! string k char</var>)<var><a name="index-string_002dset_0021-167"></a></var><br>
+— Applicative: <b>string-set!</b> (<var>string-set! string k char</var>)<var><a name="index-string_002dset_0021-228"></a></var><br>
<blockquote><p> Applicative <code>string-set!</code> replaces the character with index
<code>k</code> in <code>string</code> with character <code>char</code>. If <code>k</code> is
out of bounds, or <code>string</code> is immutable, an error is signaled.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-fill!</b> (<var>string-fill! string char</var>)<var><a name="index-string_002dfill_0021-168"></a></var><br>
+— Applicative: <b>string-fill!</b> (<var>string-fill! string char</var>)<var><a name="index-string_002dfill_0021-229"></a></var><br>
<blockquote><p> Applicative <code>string-fill!</code> replaces all the characters in
<code>string</code> with character <code>char</code>. If <code>string</code> is an
immutable string, an error is signaled.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>substring</b> (<var>substring string k1 k2</var>)<var><a name="index-substring-169"></a></var><br>
+— Applicative: <b>substring</b> (<var>substring string k1 k2</var>)<var><a name="index-substring-230"></a></var><br>
<blockquote><p> Both <code>k1</code> & <code>k2</code> should be valid indexes in
<code>string</code>. Also it should be the case that <code>k1 <= k2</code>.
@@ -148,27 +148,27 @@ index <code>k2</code> (exclusive).
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-append</b> (<var>string-append . strings</var>)<var><a name="index-string_002dappend-170"></a></var><br>
+— Applicative: <b>string-append</b> (<var>string-append . strings</var>)<var><a name="index-string_002dappend-231"></a></var><br>
<blockquote><p> Applicative <code>string-append</code> constructs and returns a new
mutable string consisting of the concatenation of all its arguments.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string-copy</b> (<var>string-copy string</var>)<var><a name="index-string_002dcopy-171"></a></var><br>
+— Applicative: <b>string-copy</b> (<var>string-copy string</var>)<var><a name="index-string_002dcopy-232"></a></var><br>
<blockquote><p> Applicative <code>string-copy</code> constructs and returns a new mutable
string with the same length and characters as <code>string</code>.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string->immutable-string</b> (<var>string->immutable-string string</var>)<var><a name="index-string_002d_003eimmutable_002dstring-172"></a></var><br>
+— Applicative: <b>string->immutable-string</b> (<var>string->immutable-string string</var>)<var><a name="index-string_002d_003eimmutable_002dstring-233"></a></var><br>
<blockquote><p> Applicative <code>string->immutable-string</code> constructs and returns a
new immutable string with the same length and characters as
<code>string</code>.
</p></blockquote></div>
<div class="defun">
-— Applicative: <b>string->list</b> (<var>string->list string</var>)<var><a name="index-string_002d_003elist-173"></a></var><br>
-— Applicative: <b>list->string</b> (<var>list->string chars</var>)<var><a name="index-list_002d_003estring-174"></a></var><br>
+— Applicative: <b>string->list</b> (<var>string->list string</var>)<var><a name="index-string_002d_003elist-234"></a></var><br>
+— Applicative: <b>list->string</b> (<var>list->string chars</var>)<var><a name="index-list_002d_003estring-235"></a></var><br>
<blockquote><p> Applicatives <code>string->list</code> and <code>list->string</code> convert
between strings and list of characters. The strings returned by
<code>list->string</code> are mutable.
diff --git a/manual/klisp.info b/manual/klisp.info
@@ -1565,6 +1565,392 @@ File: klisp.info, Node: Numbers, Next: Strings, Prev: Keyed Variables, Up: T
13 Numbers
**********
+All numbers are immutable, and `equal?' iff `eq?'. The number type is
+encapsulated.
+
+ The external representation of an undefined number is `#undefined'.
+The external representation of a real with no primary value is `#real'
+(but this may change in the future, the report is missing the output
+representation for reals with no primary values). All other rules for
+externally representing numbers pertain only to defined numbers with
+primary values.
+
+ An external representation of a real number consists of optional
+radix and/or exactness prefixes, optional sign (`+' or `-'), and
+magnitude. The radix prefixes are `#b' (binary), `#o' (octal), `#d'
+(decimal), and `#x' (hexadecimal); the default is decimal. The
+exactness prefixes are `#e' (exact) and `#i' (inexact); by default, the
+number is inexact iff the magnitude representation uses floating point.
+If both kinds of prefixes are used, they may occur in either order. The
+magnitude is either `infinity'; an unsigned integer (nonempty sequence
+of digits); a ratio of unsigned integers (two unsigned integers with a
+`/' between, of which the second is non-zero); or a floating point
+representation. If the magnitude is `infinity', there must be an
+exactness prefix and a sign, and no radix prefix. Floating point
+representation can only be used with decimal radix; it consists of
+nonempty integer part, point (`.'), nonempty fraction part, and
+optional exponent part. The optional exponent part consists of an
+exponent letter, and an (optionally signed) integer indicating a power
+of ten by which to multiply the magnitude. The choice of exponent
+letter makes no difference in what mathematical number is indicated by
+the external representation, but does indicate internal representation
+precision. Exponent letters `s', `f', `d', `f' indicate preference for
+successively higher internal precision - short, float, double, long.
+When reading an inexact real number, exponent letter `e' accepts the
+default internal precision, which must be at least double. When
+writeing an inexact real number, exponent letter `e' may be used for
+the default internal precision, and must be used for any internal
+number format not indicated by any of the other exponent letters.
+Float and double must provide, respectively, at least as much precision
+as IEEE 32-bit and 64-bit floating point standards [IE85]. For
+example, `#i#xa/c' represents an inexact number using hexadecimal
+notation, with signed magnitude positive five sixths (ten over twelve).
+`-3.5l-2' represents an inexact number using decimal notation, with
+signed magnitude negative thirty five thousandths, and requested long
+precision (which must be at least IEEE 64-bit floating point). When
+reading an external representation of an inexact real, the bounds on
+the resulting inexact number are chosen in accordance with the
+narrow-arithmetic keyed dynamic variable.
+
+ NOTE: in klisp, all inexact numbers are stored as IEEE 64-bit
+floating point. No bounding or robustness info is kept.
+
+ -- Applicative: number? (number? . objects)
+ The primitive type predicate for type number. `number?' returns
+ true iff all the objects in `objects' are of type number.
+
+ -- Applicative: integer? (integer? . objects)
+ The primitive type predicate for number subtype integer.
+ `integer?' returns true iff all the objects in `objects' are of
+ type integer.
+
+ -- Applicative: rational? (rational? . objects)
+ The primitive type predicate for number subtype rational.
+ `rational?' returns true iff all the objects in `objects' are of
+ type rational.
+
+ -- Applicative: real? (real? . objects)
+ The primitive type predicate for number subtype real. `real?'
+ returns true iff all the objects in `objects' are of type real.
+
+ -- Applicative: finite? (finite? . numbers)
+ Predicate `finite?' returns true iff all the numbers in `numbers'
+ are finite.
+
+ -- Applicative: exact? (exact? . numbers)
+ Predicate `exact?' returns true iff all the numbers in `numbers'
+ are exact.
+
+ -- Applicative: inexact? (inexact? . numbers)
+ Predicate `inexact?' returns true iff all the numbers in `numbers'
+ are inexact.
+
+ -- Applicative: robust? (robust? . numbers)
+ Predicate `robust?' returns true iff all the numbers in `numbers'
+ are robust.
+
+ -- Applicative: undefined? (undefined? . numbers)
+ Predicate `undefined?' returns true iff all the numbers in
+ `numbers' are undefined.
+
+ -- Applicative: =? (=? . numbers)
+ Applicative `=?' is a predicate that returns true iff all its
+ arguments are numerically equal to each other. If any of its
+ arguments has no primary value, an error is signaled.
+
+ -- Applicative: <? (<? . reals)
+ -- Applicative: <=? (<=? . reals)
+ -- Applicative: >? (>? . reals)
+ -- Applicative: >=? (>=? . reals)
+ Each of these applicatives is a predicate that returns true iff
+ every two consecutive elements of `reals' have primary values in
+ the order indicated by the name of the applicative. If any
+ element of `reals' has no primary value, an error is signaled.
+
+ -- Applicative: + (+ . numbers)
+ Applicative `+' returns the sum of the elements of numbers. If
+ numbers is empty, the sum of its elements is exact zero. If a
+ positive infinity is added to a negative infinity, the result has
+ no primary value. If all the elements of a cycle are zero, the
+ sum of the cycle is zero. If the acyclic sum of the elements of a
+ cycle (i.e., the sum of an acyclic list containing just those
+ elements) is non-zero, the sum of the cycle is positive infinity
+ times the acyclic sum of the elements. If the acyclic sum of the
+ elements of a cycle is zero, but some of the elements of the cycle
+ are non-zero, the sum of the cycle has no primary value.
+
+ -- Applicative: * (* . numbers)
+ Applicative `*' returns the product of the elements of numbers.
+ If numbers is empty, the product of its elements is exact one. If
+ an infinity is multiplied by zero, the result has no primary
+ value. If the acyclic product of the elements of a cycle is real
+ greater than one, the product of the cycle is positive infinity.
+ If all the elements of a cycle are positive one, the product of
+ the cycle is positive one. If the acyclic product of the elements
+ of a cycle is positive one, but some of the elements of the cycle
+ are not positive one, the product of the cycle has no primary
+ value. If the acyclic product of the elements of a cycle has
+ magnitude less than one, the product of the cycle is zero. If the
+ acyclic product of the elements of a cycle has magnitude greater
+ than or equal to one, and is not positive real, the product of the
+ cycle has no primary value.
+
+ -- Applicative: - (- number . numbers)
+ `numbers' should be a nonempty list of numbers.
+
+ Applicative `-' returns the sum of `number' with the negation of
+ the sum of `numbers'.
+
+ -- Applicative: zero? (zero? . numbers)
+ Applicative `zero?' is a predicate that returns true iff every
+ element of `numbers' is zero. For this purpose, a real number is
+ zero if its primary value is zero. If any element of numbers has
+ no primary value an error is signaled.
+
+ -- Applicative: div (div real1 real2)
+ -- Applicative: mod (mod real1 real2)
+ -- Applicative: div-and-mod (div-and-mod real1 real2)
+ For all three applicatives, if `real1' is infinite or `real2' is
+ zero, an error is signaled.
+
+ Let `n' be the greatest integer such that `real2 * n <= real1'.
+ Applicative `div' returns `n'. Applicative `mod' returns `real1 -
+ (real2 * n)'. Applicative `div-and-mod' returns a freshly
+ allocated list of length two, whose first element is `n' and whose
+ second element is `real1 - (real2 * n)'.
+
+ NOTE: I'm not really sure about this description...
+
+ -- Applicative: div0 (div0 real1 real2)
+ -- Applicative: mod0 (mod0 real1 real2)
+ -- Applicative: div0-and-mod0 (div0-and-mod0 real1 real2)
+ For all three applicatives, if `real1' is infinite or `real2' is
+ zero, an error is signaled.
+
+ Let `n' be the greatest integer such that `real2 * n <= real1 +
+ |real2/2|'. Applicative `div0' returns `n'. Applicative `mod0'
+ returns `real1 - (real2 * n)'. Applicative `div0-and-mod0'
+ returns a freshly allocated list of length two, whose first
+ element is `n' and whose second element is `real1 - (real2 * n)'.
+
+ NOTE: I'm not really sure about this description...
+
+ -- Applicative: positive? (positive? . reals)
+ -- Applicative: negative? (negative? . reals)
+ Applicative `positive?' is a predicate that returns true iff every
+ element of `reals' is greater than zero. Applicative `negative?'
+ is a predicate that returns true iff every element of `reals' is
+ less than zero. If any argument to either applicative has no
+ primary value an error is signaled.
+
+ -- Applicative: odd? (odd? . integers)
+ -- Applicative: even? (even? . integers)
+ Applicative `odd?' is a predicate that returns true iff every
+ element of `integers' is odd. Applicative `even?' is a predicate
+ that returns true iff every element of `integers' is even. If any
+ argument to either applicative has no primary value an error is
+ signaled.
+
+ -- Applicative: (abs real)
+ Applicative `abs' returns the nonnegative real number with the
+ same magnitude as `real'; that is, if `real' is nonnegative it
+ returns `real', otherwise it returns the negation of `real'.
+
+ -- Applicative: max (max . reals)
+ -- Applicative: min (min . reals)
+ If `reals' is nil, applicative `max' returns exact negative
+ infinity, and applicative `min' returns exact positive infinity.
+ If `reals' is non-nil, applicative `max' returns the largest
+ number in `reals', and applicative `min' returns the smallest
+ number in `reals'.
+
+ -- Applicative: lcm (lcm . impints)
+ -- Applicative: gcd (gcd . impints)
+ `impints' should be a list of improper integers, that is, real
+ numbers each of which is either an integer or an infinity.
+
+ Applicative `lcm' returns the smallest positive improper integer
+ that is an improper0integer multiple of every element of `impints'
+ (that is, smallest `n >= 1' such that for every argument `nk'
+ there exists `n'k' with `nk * n'k = n'). If any of the arguments
+ is zero, the result of `lcm' has no primary value. According to
+ these rules, `lcm' with nil argument list returns `1', and `lcm'
+ with any infinite argument returns positive infinity.
+
+ Applicative `gcd' returns the largest positive improper integer
+ such that every element of `impints' is an improper-integer
+ multiple of it (that is, largest `n >= 1' such that for every
+ argument `nk' there exists `n'k' with `n * n'k = nk'). `gcd' with
+ nil argument list returns exact positive infinity. If `gcd' is
+ called with one or more arguments, and at least one of the
+ arguments is zero, but none of the arguments is a non-zero finite
+ integer, its result has no primary value. According to these
+ rules, if `gcd' is called with at least one finite non-zero
+ argument, its result is the same as if all zero and infinite
+ arguments were deleted.
+
+ -- Applicative: get-real-internal-bounds (get-real-internal-bounds
+ real)
+ -- Applicative: get-real-exact-bounds (get-real-exact-bounds real)
+ Applicative `get-real-internal-bounds' returns a freshly allocated
+ list of reals `(x1 x2)', where the primary value of `x1' is the
+ lower bound of `real', using the same internal representation as
+ the primary value of `real', and the primary value of `x2' is the
+ upper bound of `real', using the same internal representation as
+ the primary value of `real'. The `xk' are inexact iff real is
+ inexact. The `xk' are robust (i.e., tagged if the implementation
+ supports such), and the bounds of each `xk' are only required to
+ contain its primary value (i.e., the implementation is allowed to
+ make the bounds equal to the primary value).
+
+ Applicative `get-real-exact-bounds' returns a freshly allocated
+ list of exact reals `(x1 x2)', where `x1' is not greater than the
+ lower bound of `real', and `x2' is not less than the upper bound
+ of `real'.
+
+ -- Applicative: get-real-internal-primary (get-real-internal-primary
+ real)
+ -- Applicative: get-real-exact-primary (get-real-exact-primary real)
+ If `real' is exact, both applicatives return `real'. If `real'
+ has no primary value, both applicatives signal an error.
+
+ If `real' is inexact with a primary value, applicative
+ `get-real-internal-primary' returns a real number `x0' whose
+ primary value is the same as, and has the same internal format as,
+ the primary value of `real'. `x0' is robust, and its bounds are
+ only required to contain its primary value.
+
+ If `real' is inexact with a primary value, applicative
+ `get-real-exact-primary' returns an exact real number `x0' within
+ the exact bounds that would be returned for `real' by applicative
+ `get-real-exact-bounds'. Preferably, `x0' should be as close to
+ the primary value of `real' as the implementation can reasonably
+ arrange. If the implementation does not support any exact `real'
+ that reasonably approximates `real', an error may be signaled.
+
+ -- Applicative: make-inexact (make-inexact real1 real2 real3)
+ Applicative `make-inexact' returns an inexact real number, as
+ follows. If `real2' is inexact, the result has the same primary
+ value as `real2'; and if `real2' has no primary value, the result
+ has no primary value. The result has the same robustness as
+ `real2'. If possible, the result uses the same internal
+ representation as `real2'. If `real2' is exact, the primary value
+ of the result is as close to `real2' as the implementation can
+ reasonably arrange; overflow and underflow are handled as
+ described in .... The lower bound of the result is no greater than
+ the lower bound of `real1', the primary value of `real2', and the
+ primary value of the result. The upper bound of the result is no
+ less than the upper bound of `real3', the primary value of
+ `real2', and the primary value of the result.
+
+ -- Applicative: real->inexact (real->inexact real)
+ -- Applicative: real->exact (real->exact real)
+ Applicative `real->exact' behaves just as `get-real-exact-primary'.
+
+ If `real' is inexact, applicative `real->inexact' returns `real'.
+ If `real' is exact, applicative `real->inexact' returns an inexact
+ real `x0' such that `real' would be a permissible result of
+ passing `x0' to `real->exact'. If the implementation does not
+ support any such `x0', an error may be signaled. Otherwise, `x0'
+ is robust, and its bounds are only required to contain its primary
+ value and `real'.
+
+ -- Applicative: with-strict-arithmetic (with-strict-arithmetic boolean
+ combiner)
+ -- Applicative: get-string-arithmetic (get-strict-arithmetic?)
+ These applicatives are the binder and accessor of the
+ `strict-arithmetic' keyed dynamic variable. When this keyed
+ variable is true, various survivable but dubious arithmetic events
+ signal an error - notably, operation results with no primary value,
+ and over- and underflows.
+
+ -- Applicative: / (/ number . numbers)
+ `numbers' should be a nonempty list of numbers.
+
+ Applicative `/' returns `number' divided by the product of
+ `numbers'. If the product of `numbers' is zero, an error is
+ signaled. If `number' is infinite and the product of `numbers' is
+ infinite, an error is signaled.
+
+ -- Applicative: numerator (numerator rational)
+ -- Applicative: denominator (denominator rational)
+ These applicatives return the numerator and denominator of
+ `rational', in least terms (i.e., chosen for the least positive
+ denominator). Note that if `rational' is inexact, and either of
+ its bounds is not its primary value, the denominator has upper
+ bound positive infinity, and the numerator must have at least one
+ infinite bound (two infinite bounds if the bounds of rational
+ allow values of both signs).
+
+ -- Applicative: floor (floor real)
+ -- Applicative: ceiling (ceiling real)
+ -- Applicative: truncate (truncate real)
+ -- Applicative: round (round real)
+ Applicative `floor' returns the largest integer not greater than
+ `real'.
+
+ Applicative `ceiling' returns the smallest integer not less than
+ `real'.
+
+ Applicative `truncate' returns the integer closest to `real' whose
+ absolute value is not greater than that of `real'.
+
+ Applicative `round' returns the closest integer to `real',
+ rounding to even when `real' is halfway between two integers.
+
+ -- Applicative: rationalize (rationalize real1 real2)
+ -- Applicative: simplest-rational (simplest-rational real1 real2)
+ A rational number `r1' is simpler than another rational `r2' if
+ `r1 = p1 / q1' and `r2 = p2 / q2', both in lowest terms, and `|p1|
+ <= |p2|' and `|q1| <= |q2|'. Thus `3/5' is simpler than `4/7'. Not
+ all rationals are comparable in this ordering, as for example
+ `2/7' and `3/5'. However, any interval (that contains rational
+ numbers) contains a rational number that is simpler than every
+ other rational number in that interval. Note that `0 = 0/1' is
+ simpler than any other rational (so that one never has to choose
+ between `p/q' and `−p/q').
+
+ For applicative `simplest-rational', let `x0' be the simplest
+ rational mathematically not less than the primary value of `real1'
+ and not greater than the primary value of `real2'. If no such
+ `x0' exists (because the primary value of `real1' is greater, or
+ because the primary values of the arguments are equal and
+ irrational), or if either argument does not have a primary value,
+ an error is signaled.
+
+ For applicative `rationalize', let `x0' be the simplest rational
+ mathematical number within the interval bounded by the primary
+ value of `real1' plus and minus the primary value of `real2'. If
+ no such `x0' exists (because the primary value of `real1' is
+ irrational and the primary value `real2' is zero), or if either
+ argument does not have a primary value, an error is signaled.
+
+ If `real1' and `real2' are exact, the applicative (whichever it
+ is) returns exact `x0'. If one or both of `real1' and `real2' are
+ inexact, the applicative returns an inexact rational approximating
+ `x0' (as by `real->inexact'. Note that an inexact result returned
+ is not necessarily bounded by the primary values of the arguments;
+ but the result is an approximation of `x0', which is so bounded,
+ and the bounds of the result include `x0'.
+
+ -- Applicative: exp (exp number)
+ -- Applicative: log (log number)
+ TODO
+
+ -- Applicative: sin (sin number)
+ -- Applicative: cos (cos number)
+ -- Applicative: tan (tan number)
+ TODO
+
+ -- Applicative: asin (asin number)
+ -- Applicative: acos (acos number)
+ -- Applicative: atan (atan number1 [number2])
+ TODO
+
+ -- Applicative: sqrt (sqrt number)
+ -- Applicative: expt (expt number1 number2)
+ TODO
+
File: klisp.info, Node: Strings, Next: Characters, Prev: Numbers, Up: Top
@@ -2017,8 +2403,19 @@ Index
* $set!: Environments. (line 182)
* $vau: Combiners. (line 26)
* ( <1>: Ports. (line 37)
-* ( <2>: Continuations. (line 143)
+* ( <2>: Numbers. (line 193)
+* ( <3>: Continuations. (line 143)
* (: Environments. (line 174)
+* *: Numbers. (line 121)
+* +: Numbers. (line 109)
+* -: Numbers. (line 137)
+* /: Numbers. (line 306)
+* <=?: Numbers. (line 101)
+* <?: Numbers. (line 100)
+* =?: Numbers. (line 95)
+* >=?: Numbers. (line 103)
+* >?: Numbers. (line 102)
+* acos: Numbers. (line 385)
* and?: Booleans. (line 20)
* append: Pairs and lists. (line 208)
* append!: Pairs and lists. (line 306)
@@ -2028,8 +2425,10 @@ Index
* applicatives: Combiners. (line 6)
* apply: Combiners. (line 83)
* apply-continuation: Continuations. (line 134)
+* asin: Numbers. (line 384)
* assoc: Pairs and lists. (line 252)
* assq: Pairs and lists. (line 333)
+* atan: Numbers. (line 386)
* boolean?: Booleans. (line 12)
* booleans: Booleans. (line 6)
* caaaar: Pairs and lists. (line 101)
@@ -2065,6 +2464,7 @@ Index
* cdddr: Pairs and lists. (line 100)
* cddr: Pairs and lists. (line 92)
* cdr: Pairs and lists. (line 86)
+* ceiling: Numbers. (line 325)
* char->integer: Characters. (line 58)
* char-alphabetic?: Characters. (line 37)
* char-ci<=?: Characters. (line 31)
@@ -2094,9 +2494,15 @@ Index
* control: Control. (line 6)
* copy-es: Pairs and lists. (line 321)
* copy-es-immutable!: Pairs and lists. (line 49)
+* cos: Numbers. (line 380)
* countable-list?: Pairs and lists. (line 265)
+* denominator: Numbers. (line 315)
* description format: Format of Descriptions.
(line 6)
+* div: Numbers. (line 149)
+* div-and-mod: Numbers. (line 151)
+* div0: Numbers. (line 163)
+* div0-and-mod0: Numbers. (line 165)
* documentation notation: Evaluation Notation. (line 6)
* empty list: Pairs and lists. (line 6)
* encapsulations: Encapsulations. (line 6)
@@ -2111,30 +2517,45 @@ Index
* error-continuation: Continuations. (line 110)
* eval: Environments. (line 32)
* evaluation notation: Evaluation Notation. (line 6)
+* even?: Numbers. (line 186)
+* exact?: Numbers. (line 79)
* exit: Continuations. (line 162)
+* exp: Numbers. (line 375)
+* expt: Numbers. (line 390)
* extend-continuation: Continuations. (line 50)
* filter: Pairs and lists. (line 239)
* finite-list?: Pairs and lists. (line 261)
+* finite?: Numbers. (line 75)
+* floor: Numbers. (line 324)
* fonts: Some Terms. (line 13)
* foo: A Sample Applicative Description.
(line 15)
* for-each: Control. (line 42)
* force: Promises. (line 35)
+* gcd: Numbers. (line 207)
* get-current-environment: Environments. (line 114)
* get-list-metrics: Pairs and lists. (line 123)
* get-module: Ports. (line 156)
+* get-real-exact-bounds: Numbers. (line 233)
+* get-real-exact-primary: Numbers. (line 252)
+* get-real-internal-bounds: Numbers. (line 232)
+* get-real-internal-primary: Numbers. (line 251)
+* get-string-arithmetic: Numbers. (line 299)
* guard-continuation: Continuations. (line 63)
* guard-dynamic-extent: Continuations. (line 156)
* ignore: Environments. (line 6)
* ignore?: Environments. (line 28)
* inert: Control. (line 6)
* inert?: Control. (line 11)
+* inexact?: Numbers. (line 83)
* input-port?: Ports. (line 27)
* integer->char: Characters. (line 59)
+* integer?: Numbers. (line 61)
* Kernel history: Kernel History. (line 6)
* keyed dynamic variables: Keyed Variables. (line 15)
* keyed static variables: Keyed Variables. (line 40)
* keyed variables: Keyed Variables. (line 6)
+* lcm: Numbers. (line 206)
* length: Pairs and lists. (line 191)
* list: Pairs and lists. (line 72)
* list*: Pairs and lists. (line 78)
@@ -2144,23 +2565,33 @@ Index
* list-tail: Pairs and lists. (line 147)
* lists: Pairs and lists. (line 6)
* load: Ports. (line 143)
+* log: Numbers. (line 376)
* make-encapsulation-type: Encapsulations. (line 12)
* make-environment: Environments. (line 36)
+* make-inexact: Numbers. (line 270)
* make-kernel-standard-environment: Environments. (line 119)
* make-keyed-dynamic-variable: Keyed Variables. (line 21)
* make-keyed-static-variable: Keyed Variables. (line 44)
* make-string: Strings. (line 57)
* map <1>: Combiners. (line 96)
* map: Pairs and lists. (line 169)
+* max: Numbers. (line 198)
* member?: Pairs and lists. (line 257)
* memoize: Promises. (line 74)
* memq?: Pairs and lists. (line 338)
+* min: Numbers. (line 199)
+* mod: Numbers. (line 150)
+* mod0: Numbers. (line 164)
+* negative?: Numbers. (line 178)
* nil: Pairs and lists. (line 6)
* not?: Booleans. (line 16)
* null?: Pairs and lists. (line 31)
+* number?: Numbers. (line 57)
* numbers: Numbers. (line 6)
+* numerator: Numbers. (line 314)
* object descriptions: A Sample Applicative Description.
(line 6)
+* odd?: Numbers. (line 185)
* open-input-file: Ports. (line 62)
* open-output-file: Ports. (line 73)
* operative descriptions: A Sample Applicative Description.
@@ -2173,14 +2604,25 @@ Index
* pairs: Pairs and lists. (line 6)
* port?: Ports. (line 23)
* ports: Ports. (line 6)
+* positive?: Numbers. (line 177)
* printing notation: Printing Notation. (line 6)
* promise?: Promises. (line 31)
* promises: Promises. (line 6)
+* rational?: Numbers. (line 66)
+* rationalize: Numbers. (line 340)
* read: Ports. (line 102)
+* real->exact: Numbers. (line 286)
+* real->inexact: Numbers. (line 285)
+* real?: Numbers. (line 71)
* reduce: Pairs and lists. (line 270)
+* robust?: Numbers. (line 87)
* root-continuation: Continuations. (line 104)
+* round: Numbers. (line 327)
* set-car!: Pairs and lists. (line 41)
* set-cdr!: Pairs and lists. (line 42)
+* simplest-rational: Numbers. (line 341)
+* sin: Numbers. (line 379)
+* sqrt: Numbers. (line 389)
* string: Strings. (line 63)
* string->immutable-string: Strings. (line 103)
* string->list: Strings. (line 108)
@@ -2207,8 +2649,13 @@ Index
* symbol->string: Symbols. (line 16)
* symbol?: Symbols. (line 12)
* symbols: Symbols. (line 6)
+* tan: Numbers. (line 381)
+* truncate: Numbers. (line 326)
+* undefined?: Numbers. (line 91)
* unwrap: Combiners. (line 72)
+* with-strict-arithmetic: Numbers. (line 298)
* wrap: Combiners. (line 68)
+* zero?: Numbers. (line 143)
@@ -2238,9 +2685,9 @@ Node: Encapsulations63984
Node: Promises65437
Node: Keyed Variables69360
Node: Numbers72131
-Node: Strings72240
-Node: Characters77587
-Node: Ports80297
-Node: Index91582
+Node: Strings91630
+Node: Characters96977
+Node: Ports99687
+Node: Index110972
End Tag Table
diff --git a/manual/src/numbers.texi b/manual/src/numbers.texi
@@ -6,3 +6,461 @@
@chapter Numbers
@cindex numbers
+
+All numbers are immutable, and @code{equal?} iff @code{eq?}. The
+number type is encapsulated.
+
+@c TODO add more content on numbers
+
+ The external representation of an undefined number is
+@code{#undefined}. The external representation of a real with no
+primary value is @code{#real} (but this may change in the future, the
+report is missing the output representation for reals with no primary
+values). All other rules for externally representing numbers pertain
+only to defined numbers with primary values.
+
+ An external representation of a real number consists of optional
+radix and/or exactness prefixes, optional sign (@code{+} or @code{-}),
+and magnitude. The radix prefixes are @code{#b} (binary), @code{#o}
+(octal), @code{#d} (decimal), and @code{#x} (hexadecimal); the default
+is decimal. The exactness prefixes are @code{#e} (exact) and
+@code{#i} (inexact); by default, the number is inexact iff the
+magnitude representation uses floating point. If both kinds of
+prefixes are used, they may occur in either order. The magnitude is
+either @code{infinity}; an unsigned integer (nonempty sequence of
+digits); a ratio of unsigned integers (two unsigned integers with a
+@code{/} between, of which the second is non-zero); or a floating
+point representation. If the magnitude is @code{infinity}, there must
+be an exactness prefix and a sign, and no radix prefix. Floating
+point representation can only be used with decimal radix; it consists
+of nonempty integer part, point (@code{.}), nonempty fraction part,
+and optional exponent part. The optional exponent part consists of an
+exponent letter, and an (optionally signed) integer indicating a power
+of ten by which to multiply the magnitude. The choice of exponent
+letter makes no difference in what mathematical number is indicated by
+the external representation, but does indicate internal representation
+precision. Exponent letters @code{s}, @code{f}, @code{d}, @code{f}
+indicate preference for successively higher internal precision -
+short, float, double, long. When reading an inexact real number,
+exponent letter @code{e} accepts the default internal precision, which
+must be at least double. When writeing an inexact real number,
+exponent letter @code{e} may be used for the default internal
+precision, and must be used for any internal number format not
+indicated by any of the other exponent letters. Float and double must
+provide, respectively, at least as much precision as IEEE 32-bit and
+64-bit floating point standards [IE85]. For example, @code{#i#xa/c}
+represents an inexact number using hexadecimal notation, with signed
+magnitude positive five sixths (ten over twelve). @code{-3.5l-2}
+represents an inexact number using decimal notation, with signed
+magnitude negative thirty five thousandths, and requested long
+precision (which must be at least IEEE 64-bit floating point). When
+reading an external representation of an inexact real, the bounds on
+the resulting inexact number are chosen in accordance with the
+@c TODO add xref
+narrow-arithmetic keyed dynamic variable.
+
+NOTE: in klisp, all inexact numbers are stored as IEEE 64-bit floating
+point. No bounding or robustness info is kept.
+
+@deffn Applicative number? (number? . objects)
+ The primitive type predicate for type number. @code{number?}
+returns true iff all the objects in @code{objects} are of type number.
+@end deffn
+
+@deffn Applicative integer? (integer? . objects)
+ The primitive type predicate for number subtype integer.
+@code{integer?} returns true iff all the objects in @code{objects}
+are of type integer.
+@end deffn
+
+@deffn Applicative rational? (rational? . objects)
+ The primitive type predicate for number subtype rational.
+@code{rational?} returns true iff all the objects in @code{objects}
+are of type rational.
+@end deffn
+
+@deffn Applicative real? (real? . objects)
+ The primitive type predicate for number subtype real.
+@code{real?} returns true iff all the objects in @code{objects}
+are of type real.
+@end deffn
+
+@deffn Applicative finite? (finite? . numbers)
+ Predicate @code{finite?} returns true iff all the numbers in
+@code{numbers} are finite.
+@end deffn
+
+@deffn Applicative exact? (exact? . numbers)
+ Predicate @code{exact?} returns true iff all the numbers in
+@code{numbers} are exact.
+@end deffn
+
+@deffn Applicative inexact? (inexact? . numbers)
+ Predicate @code{inexact?} returns true iff all the numbers in
+@code{numbers} are inexact.
+@end deffn
+
+@deffn Applicative robust? (robust? . numbers)
+ Predicate @code{robust?} returns true iff all the numbers in
+@code{numbers} are robust.
+@end deffn
+
+@deffn Applicative undefined? (undefined? . numbers)
+ Predicate @code{undefined?} returns true iff all the numbers in
+@code{numbers} are undefined.
+@end deffn
+
+@deffn Applicative =? (=? . numbers)
+ Applicative @code{=?} is a predicate that returns true iff all its
+arguments are numerically equal to each other. If any of its
+arguments has no primary value, an error is signaled.
+@end deffn
+
+@deffn Applicative <? (<? . reals)
+@deffnx Applicative <=? (<=? . reals)
+@deffnx Applicative >? (>? . reals)
+@deffnx Applicative >=? (>=? . reals)
+ Each of these applicatives is a predicate that returns true iff
+every two consecutive elements of @code{reals} have primary values in
+the order indicated by the name of the applicative. If any element of
+@code{reals} has no primary value, an error is signaled.
+@end deffn
+
+@deffn Applicative + (+ . numbers)
+ Applicative @code{+} returns the sum of the elements of numbers. If
+numbers is empty, the sum of its elements is exact zero. If a
+positive infinity is added to a negative infinity, the result has no
+primary value. If all the elements of a cycle are zero, the sum of
+the cycle is zero. If the acyclic sum of the elements of a cycle
+(i.e., the sum of an acyclic list containing just those elements) is
+non-zero, the sum of the cycle is positive infinity times the acyclic
+sum of the elements. If the acyclic sum of the elements of a cycle is
+zero, but some of the elements of the cycle are non-zero, the sum of
+the cycle has no primary value.
+@end deffn
+
+@deffn Applicative * (* . numbers)
+ Applicative @code{*} returns the product of the elements of numbers.
+If numbers is empty, the product of its elements is exact one. If an
+infinity is multiplied by zero, the result has no primary value. If
+the acyclic product of the elements of a cycle is real greater than
+one, the product of the cycle is positive infinity. If all the
+elements of a cycle are positive one, the product of the cycle is
+positive one. If the acyclic product of the elements of a cycle is
+positive one, but some of the elements of the cycle are not positive
+one, the product of the cycle has no primary value. If the acyclic
+product of the elements of a cycle has magnitude less than one, the
+product of the cycle is zero. If the acyclic product of the elements
+of a cycle has magnitude greater than or equal to one, and is not
+positive real, the product of the cycle has no primary value.
+@end deffn
+
+@deffn Applicative - (- number . numbers)
+ @code{numbers} should be a nonempty list of numbers.
+
+ Applicative @code{-} returns the sum of @code{number} with the
+negation of the sum of @code{numbers}.
+@end deffn
+
+@deffn Applicative zero? (zero? . numbers)
+ Applicative @code{zero?} is a predicate that returns true iff every
+element of @code{numbers} is zero. For this purpose, a real number is
+zero if its primary value is zero. If any element of numbers has no
+primary value an error is signaled.
+@end deffn
+
+@deffn Applicative div (div real1 real2)
+@deffnx Applicative mod (mod real1 real2)
+@deffnx Applicative div-and-mod (div-and-mod real1 real2)
+ For all three applicatives, if @code{real1} is infinite or
+@code{real2} is zero, an error is signaled.
+
+ Let @code{n} be the greatest integer such that @code{real2 * n <=
+real1}. Applicative @code{div} returns @code{n}. Applicative
+@code{mod} returns @code{real1 - (real2 * n)}. Applicative
+@code{div-and-mod} returns a freshly allocated list of length two,
+whose first element is @code{n} and whose second element is
+@code{real1 - (real2 * n)}.
+
+ NOTE: I'm not really sure about this description...
+@end deffn
+
+@deffn Applicative div0 (div0 real1 real2)
+@deffnx Applicative mod0 (mod0 real1 real2)
+@deffnx Applicative div0-and-mod0 (div0-and-mod0 real1 real2)
+ For all three applicatives, if @code{real1} is infinite or
+@code{real2} is zero, an error is signaled.
+
+ Let @code{n} be the greatest integer such that @code{real2 * n <=
+real1 + |real2/2|}. Applicative @code{div0} returns @code{n}.
+Applicative @code{mod0} returns @code{real1 - (real2 * n)}.
+Applicative @code{div0-and-mod0} returns a freshly allocated list of
+length two, whose first element is @code{n} and whose second element
+is @code{real1 - (real2 * n)}.
+
+ NOTE: I'm not really sure about this description...
+@end deffn
+
+@deffn Applicative positive? (positive? . reals)
+@deffnx Applicative negative? (negative? . reals)
+ Applicative @code{positive?} is a predicate that returns true iff
+every element of @code{reals} is greater than zero. Applicative
+@code{negative?} is a predicate that returns true iff every element of
+@code{reals} is less than zero. If any argument to either applicative
+has no primary value an error is signaled.
+@end deffn
+
+@deffn Applicative odd? (odd? . integers)
+@deffnx Applicative even? (even? . integers)
+ Applicative @code{odd?} is a predicate that returns true iff every
+element of @code{integers} is odd. Applicative @code{even?} is a
+predicate that returns true iff every element of @code{integers} is
+even. If any argument to either applicative has no primary value an
+error is signaled.
+@end deffn
+
+@deffn Applicative (abs real)
+ Applicative @code{abs} returns the nonnegative real number with the
+same magnitude as @code{real}; that is, if @code{real} is nonnegative
+it returns @code{real}, otherwise it returns the negation of
+@code{real}.
+@end deffn
+
+@deffn Applicative max (max . reals)
+@deffnx Applicative min (min . reals)
+ If @code{reals} is nil, applicative @code{max} returns exact
+negative infinity, and applicative @code{min} returns exact positive
+infinity. If @code{reals} is non-nil, applicative @code{max} returns
+the largest number in @code{reals}, and applicative @code{min} returns
+the smallest number in @code{reals}.
+@end deffn
+
+
+@deffn Applicative lcm (lcm . impints)
+@deffnx Applicative gcd (gcd . impints)
+ @code{impints} should be a list of improper integers, that is, real
+numbers each of which is either an integer or an infinity.
+
+ Applicative @code{lcm} returns the smallest positive improper
+integer that is an improper0integer multiple of every element of
+@code{impints} (that is, smallest @code{n >= 1} such that for every
+argument @code{nk} there exists @code{n'k} with @code{nk * n'k = n}).
+If any of the arguments is zero, the result of @code{lcm} has no
+primary value. According to these rules, @code{lcm} with nil argument
+list returns @code{1}, and @code{lcm} with any infinite argument
+returns positive infinity.
+
+ Applicative @code{gcd} returns the largest positive improper integer
+such that every element of @code{impints} is an improper-integer
+multiple of it (that is, largest @code{n >= 1} such that for every
+argument @code{nk} there exists @code{n'k} with @code{n * n'k = nk}).
+@code{gcd} with nil argument list returns exact positive infinity. If
+@code{gcd} is called with one or more arguments, and at least one of
+the arguments is zero, but none of the arguments is a non-zero finite
+integer, its result has no primary value. According to these rules,
+if @code{gcd} is called with at least one finite non-zero argument,
+its result is the same as if all zero and infinite arguments were
+deleted.
+@end deffn
+
+@deffn Applicative get-real-internal-bounds (get-real-internal-bounds real)
+@deffnx Applicative get-real-exact-bounds (get-real-exact-bounds real)
+ Applicative @code{get-real-internal-bounds} returns a freshly
+allocated list of reals @code{(x1 x2)}, where the primary value of
+@code{x1} is the lower bound of @code{real}, using the same internal
+representation as the primary value of @code{real}, and the primary
+value of @code{x2} is the upper bound of @code{real}, using the same
+internal representation as the primary value of @code{real}. The
+@code{xk} are inexact iff real is inexact. The @code{xk} are robust
+(i.e., tagged if the implementation supports such), and the bounds of
+each @code{xk} are only required to contain its primary value (i.e.,
+the implementation is allowed to make the bounds equal to the primary
+value).
+
+ Applicative @code{get-real-exact-bounds} returns a freshly allocated
+list of exact reals @code{(x1 x2)}, where @code{x1} is not greater
+than the lower bound of @code{real}, and @code{x2} is not less than
+the upper bound of @code{real}.
+@end deffn
+
+@deffn Applicative get-real-internal-primary (get-real-internal-primary real)
+@deffnx Applicative get-real-exact-primary (get-real-exact-primary real)
+ If @code{real} is exact, both applicatives return @code{real}. If
+@code{real} has no primary value, both applicatives signal an error.
+
+ If @code{real} is inexact with a primary value, applicative
+@code{get-real-internal-primary} returns a real number @code{x0} whose
+primary value is the same as, and has the same internal format as, the
+primary value of @code{real}. @code{x0} is robust, and its bounds are
+only required to contain its primary value.
+
+@c TODO add xref to get-real-exact-bounds
+ If @code{real} is inexact with a primary value, applicative
+@code{get-real-exact-primary} returns an exact real number @code{x0}
+within the exact bounds that would be returned for @code{real} by
+applicative @code{get-real-exact-bounds}. Preferably, @code{x0}
+should be as close to the primary value of @code{real} as the
+implementation can reasonably arrange. If the implementation does not
+support any exact @code{real} that reasonably approximates
+@code{real}, an error may be signaled.
+@end deffn
+
+@deffn Applicative make-inexact (make-inexact real1 real2 real3)
+ Applicative @code{make-inexact} returns an inexact real number, as
+follows. If @code{real2} is inexact, the result has the same primary
+value as @code{real2}; and if @code{real2} has no primary value, the
+result has no primary value. The result has the same robustness as
+@code{real2}. If possible, the result uses the same internal
+representation as @code{real2}. If @code{real2} is exact, the primary
+value of the result is as close to @code{real2} as the implementation
+can reasonably arrange; overflow and underflow are handled as
+@c TODO add xref to overflow
+described in .... The lower bound of the result is no greater than
+the lower bound of @code{real1}, the primary value of @code{real2},
+and the primary value of the result. The upper bound of the result is
+no less than the upper bound of @code{real3}, the primary value of
+@code{real2}, and the primary value of the result.
+@end deffn
+
+@deffn Applicative real->inexact (real->inexact real)
+@deffnx Applicative real->exact (real->exact real)
+@c TODO add xref to get-real-exact-primary
+ Applicative @code{real->exact} behaves just as
+@code{get-real-exact-primary}.
+
+ If @code{real} is inexact, applicative @code{real->inexact} returns
+@code{real}. If @code{real} is exact, applicative
+@code{real->inexact} returns an inexact real @code{x0} such that
+@code{real} would be a permissible result of passing @code{x0} to
+@code{real->exact}. If the implementation does not support any such
+@code{x0}, an error may be signaled. Otherwise, @code{x0} is robust,
+and its bounds are only required to contain its primary value and
+@code{real}.
+@end deffn
+
+@deffn Applicative with-strict-arithmetic (with-strict-arithmetic boolean combiner)
+@deffnx Applicative get-string-arithmetic (get-strict-arithmetic?)
+@c TODO add xref to dynamic keys and under/over flow, no prim value
+ These applicatives are the binder and accessor of the
+@code{strict-arithmetic} keyed dynamic variable. When this keyed
+variable is true, various survivable but dubious arithmetic events
+signal an error - notably, operation results with no primary value,
+and over- and underflows.
+@end deffn
+
+@deffn Applicative / (/ number . numbers)
+ @code{numbers} should be a nonempty list of numbers.
+
+ Applicative @code{/} returns @code{number} divided by the product of
+@code{numbers}. If the product of @code{numbers} is zero, an error is
+signaled. If @code{number} is infinite and the product of @code{numbers} is
+infinite, an error is signaled.
+@end deffn
+
+@deffn Applicative numerator (numerator rational)
+@deffnx Applicative denominator (denominator rational)
+ These applicatives return the numerator and denominator of
+@code{rational}, in least terms (i.e., chosen for the least positive
+denominator). Note that if @code{rational} is inexact, and either of
+its bounds is not its primary value, the denominator has upper bound
+positive infinity, and the numerator must have at least one infinite
+bound (two infinite bounds if the bounds of rational allow values of
+both signs).
+@end deffn
+
+
+@deffn Applicative floor (floor real)
+@deffnx Applicative ceiling (ceiling real)
+@deffnx Applicative truncate (truncate real)
+@deffnx Applicative round (round real)
+ Applicative @code{floor} returns the largest integer not greater
+than @code{real}.
+
+ Applicative @code{ceiling} returns the smallest integer not less
+than @code{real}.
+
+ Applicative @code{truncate} returns the integer closest to
+@code{real} whose absolute value is not greater than that of
+@code{real}.
+
+ Applicative @code{round} returns the closest integer to @code{real},
+rounding to even when @code{real} is halfway between two integers.
+@end deffn
+
+@deffn Applicative rationalize (rationalize real1 real2)
+@deffnx Applicative simplest-rational (simplest-rational real1 real2)
+ A rational number @code{r1} is simpler than another rational
+@code{r2} if @code{r1 = p1 / q1} and @code{r2 = p2 / q2}, both in
+lowest terms, and @code{|p1| <= |p2|} and @code{|q1| <= |q2|}. Thus
+@code{3/5} is simpler than @code{4/7}. Not all rationals are
+comparable in this ordering, as for example @code{2/7} and @code{3/5}.
+However, any interval (that contains rational numbers) contains a
+rational number that is simpler than every other rational number in
+that interval. Note that @code{0 = 0/1} is simpler than any other
+rational (so that one never has to choose between @code{p/q} and
+@code{−p/q}).
+
+ For applicative @code{simplest-rational}, let @code{x0} be the
+simplest rational mathematically not less than the primary value of
+@code{real1} and not greater than the primary value of @code{real2}.
+If no such @code{x0} exists (because the primary value of @code{real1}
+is greater, or because the primary values of the arguments are equal
+and irrational), or if either argument does not have a primary value,
+an error is signaled.
+
+ For applicative @code{rationalize}, let @code{x0} be the simplest
+rational mathematical number within the interval bounded by the
+primary value of @code{real1} plus and minus the primary value of
+@code{real2}. If no such @code{x0} exists (because the primary value
+of @code{real1} is irrational and the primary value @code{real2} is
+zero), or if either argument does not have a primary value, an error
+is signaled.
+
+@c TODO add xref to real->inexact
+ If @code{real1} and @code{real2} are exact, the applicative
+(whichever it is) returns exact @code{x0}. If one or both of
+@code{real1} and @code{real2} are inexact, the applicative returns an
+inexact rational approximating @code{x0} (as by @code{real->inexact}.
+Note that an inexact result returned is not necessarily bounded by the
+primary values of the arguments; but the result is an approximation of
+@code{x0}, which is so bounded, and the bounds of the result include
+@code{x0}.
+@end deffn
+
+@deffn Applicative exp (exp number)
+@deffnx Applicative log (log number)
+TODO
+@end deffn
+
+
+@deffn Applicative sin (sin number)
+@deffnx Applicative cos (cos number)
+@deffnx Applicative tan (tan number)
+TODO
+@end deffn
+
+@deffn Applicative asin (asin number)
+@deffnx Applicative acos (acos number)
+@deffnx Applicative atan (atan number1 [number2])
+TODO
+@end deffn
+
+@deffn Applicative sqrt (sqrt number)
+@deffnx Applicative expt (expt number1 number2)
+TODO
+@end deffn
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
