Attempt to make our markup respect the docbook specification(!), major changes

[helm.git] / helm / software / matita / help / C / sec_terms.xml

diff --git a/helm/software/matita/help/C/sec_terms.xml b/helm/software/matita/help/C/sec_terms.xml
index e9c1c054cc0201704491cbc5bc09cc56dc309842..fbf8dd4ef9cb614c7dfb52eb4c2fa80e1ab210b2 100644 (file)
--- a/helm/software/matita/help/C/sec_terms.xml
+++ b/helm/software/matita/help/C/sec_terms.xml
@@ -5,62 +5,67 @@
   <title>Syntax</title>
   <para>To describe syntax in this manual we use the following conventions:</para>
   <orderedlist>
-   <listitem>Non terminal symbols are emphasized and have a link to their definition. E.g.: &term;</listitem>
-   <listitem>Terminal symbols are in bold. E.g.: <emphasis role="bold">theorem</emphasis></listitem>
-   <listitem>Optional sequences of elements are put in square brackets.
-    E.g.: [<emphasis role="bold">in</emphasis> &term;]</listitem>
-   <listitem>Alternatives are put in square brakets and they are separated
-    by vertical bars. E.g.: [<emphasis role="bold">&lt;</emphasis>|<emphasis role="bold">&gt;</emphasis>]</listitem>
-   <listitem>Repetition of sequences of elements are given by putting the
+    <listitem><para>Non terminal symbols are emphasized and have a link to their
+       definition. E.g.: &term;</para></listitem>
+    <listitem><para>Terminal symbols are in bold. E.g.:
+       <emphasis role="bold">theorem</emphasis></para></listitem>
+    <listitem><para>Optional sequences of elements are put in square brackets.
+       E.g.: [<emphasis role="bold">in</emphasis> &term;]</para></listitem>
+    <listitem><para>Alternatives are put in square brakets and they are
+       separated by vertical bars. E.g.: [<emphasis role="bold">&lt;</emphasis>|<emphasis role="bold">&gt;</emphasis>]</para></listitem>
+    <listitem><para>Repetition of sequences of elements are given by putting the
     first sequence in square brackets, that are followed by three dots.
-    E.g.: [<emphasis role="bold">and</emphasis> &term;]…</listitem>
+    E.g.: [<emphasis role="bold">and</emphasis> &term;]…</para></listitem>
   </orderedlist>
   <sect1 id="terms_and_co">
   <title>Terms &amp; co.</title>
   <sect2 id="lexical">
   <title>Lexical conventions</title>
-  <table>
-    <tgroup cols="4">
-     <thead />
-    <tbody>
-     <row>
-      <entry id="id">&id;</entry>
-      <entry>::=</entry>
-      <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
-     </row>
-    </tbody>
-   </tgroup>
-  </table>
-  <table>
-    <tgroup cols="4">
-     <thead />
-    <tbody>
-     <row>
-      <entry id="nat">&nat;</entry>
-      <entry>::=</entry>
-      <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
-     </row>
-    </tbody>
-   </tgroup>
-  </table>
-  <table>
-    <tgroup cols="4">
-     <thead />
-    <tbody>
-     <row>
-      <entry id="uri">&uri;</entry>
-      <entry>::=</entry>
-      <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
-     </row>
-    </tbody>
-   </tgroup>
-  </table>
+  <para>
+    <table frame="all" rowsep="0" colsep="0">
+      <title>id</title>
+      <tgroup cols="4">
+      <tbody>
+       <row>
+       <entry id="id">&id;</entry>
+       <entry>::=</entry>
+       <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
+       </row>
+      </tbody>
+     </tgroup>
+    </table>
+    <table frame="all" rowsep="0" colsep="0">
+      <title>nat</title>
+      <tgroup cols="4">
+      <tbody>
+       <row>
+       <entry id="nat">&nat;</entry>
+       <entry>::=</entry>
+       <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
+       </row>
+      </tbody>
+     </tgroup>
+    </table>
+    <table frame="all" rowsep="0" colsep="0">
+      <title>uri</title>
+      <tgroup cols="4">
+      <tbody>
+       <row>
+       <entry id="uri">&uri;</entry>
+       <entry>::=</entry>
+       <entry><emphasis>〈〈&TODO;〉〉</emphasis></entry>
+       </row>
+      </tbody>
+     </tgroup>
+    </table>
+  </para>
   </sect2>
   <sect2 id="terms">
   <title>Terms</title>
-  <table>
+  <para>
+  <table frame="all" rowsep="0" colsep="0">
+    <title>Terms</title>
     <tgroup cols="4">
-     <thead />
     <tbody>
      <row>
       <entry id="term">&term;</entry>
@@ -144,9 +149,9 @@
    </tgroup>
   </table>
 
-  <table>
+  <table frame="all" rowsep="0" colsep="0">
+    <title>Simple terms</title>
     <tgroup cols="4">
-     <thead />
     <tbody>
      <row>
       <entry id="sterm">&sterm;</entry>
@@ -241,9 +246,9 @@
    </tgroup>
   </table>
 
-  <table>
+  <table frame="all" rowsep="0" colsep="0">
+    <title>Arguments</title>
     <tgroup cols="4">
-     <thead />
     <tbody>
      <row>
       <entry id="args">&args;</entry>
@@ -277,9 +282,9 @@
    </tgroup>
   </table>
 
-  <table>
+  <table frame="all" rowsep="0" colsep="0">
+    <title>Miscellaneous arguments</title>
     <tgroup cols="4">
-     <thead />
     <tbody>
      <row>
       <entry id="args2">&args2;</entry>
@@ -297,9 +302,9 @@
    </tgroup>
   </table>
 
-  <table>
+  <table frame="all" rowsep="0" colsep="0">
+    <title>Pattern matching</title>
     <tgroup cols="4">
-     <thead />
     <tbody>
      <row>
       <entry id="match_pattern">&match_pattern;</entry>
@@ -316,6 +321,7 @@
     </tbody>
    </tgroup>
   </table>
+  </para>
 
   </sect2>
   </sect1>
@@ -343,9 +349,30 @@
     <para>Notice that the command is equivalent to <command>theorem f: T ≝ t</command>.</para>
   </sect2>
   <sect2 id="inductive">
-    <title>[co]inductive &id; (of inductive types)</title>
+    <title>[<emphasis role="bold">inductive</emphasis>|<emphasis role="bold">coinductive</emphasis>] &id; [&args2;]… <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis> [<emphasis role="bold">|</emphasis>] [&id;<emphasis role="bold">:</emphasis>&term;] [<emphasis role="bold">|</emphasis> &id;<emphasis role="bold">:</emphasis>&term;]…
+[<emphasis role="bold">with</emphasis> &id; <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis> [<emphasis role="bold">|</emphasis>] [&id;<emphasis role="bold">:</emphasis>&term;] [<emphasis role="bold">|</emphasis> &id;<emphasis role="bold">:</emphasis>&term;]…]…
+</title>
     <titleabbrev>(co)inductive types declaration</titleabbrev>
-    <para> &TODO; </para>
+    <para><userinput>inductive i x y z: S ≝ k1:T1 | … | kn:Tn with i' : S' ≝ k1':T1' | … | km':Tm'</userinput></para>
+    <para>Declares a family of two mutually inductive types
+     <command>i</command> and <command>i'</command> whose types are
+     <command>S</command> and <command>S'</command>, which must be convertible
+     to sorts.</para>
+    <para>The constructors <command>ki</command> of type <command>Ti</command>
+     and <command>ki'</command> of type <command>Ti'</command> are also
+     simultaneously declared. The declared types <command>i</command> and
+     <command>i'</command> may occur in the types of the constructors, but
+     only in strongly positive positions according to the rules of the
+     calculus.</para>
+    <para>The whole family is parameterized over the arguments <command>x,y,z</command>.</para>
+    <para>If the keyword <command>coinductive</command> is used, the declared
+     types are considered mutually coinductive.</para>
+    <para>Elimination principles for the record are automatically generated
+     by Matita, if allowed by the typing rules of the calculus according to
+     the sort <command>S</command>. If generated,
+     they are named <command>i_ind</command>, <command>i_rec</command> and
+     <command>i_rect</command> according to the sort of their induction
+     predicate.</para> 
   </sect2>
   <sect2 id="record">
     <title><emphasis role="bold">record</emphasis> &id; [&args2;]… <emphasis role="bold">:</emphasis> &term; <emphasis role="bold">≝</emphasis><emphasis role="bold">{</emphasis>[&id; [<emphasis role="bold">:</emphasis>|<emphasis role="bold">:&gt;</emphasis>] &term;] [<emphasis role="bold">;</emphasis>&id; [<emphasis role="bold">:</emphasis>|<emphasis role="bold">:&gt;</emphasis>] &term;]…<emphasis role="bold">}</emphasis></title>
@@ -360,8 +387,8 @@
     <para>Elimination principles for the record are automatically generated
      by Matita, if allowed by the typing rules of the calculus according to
      the sort <command>S</command>. If generated,
-     they are named <command>id_ind</command>, <command>id_rec</command> and
-     <command>id_rect</command> according to the sort of their induction
+     they are named <command>i_ind</command>, <command>i_rec</command> and
+     <command>i_rect</command> according to the sort of their induction
      predicate.</para> 
     <para>For each field <command>fi</command> a record projection
      <command>fi</command> is also automatically generated if projection