</tgroup>
</table>
+ <table>
+ <tgroup cols="4">
+ <thead />
+ <tbody>
+ <row>
+ <entry id="args2">&args2;</entry>
+ <entry>::=</entry>
+ <entry>&id;</entry>
+ <entry/>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><emphasis role="bold">(</emphasis>&id;[<emphasis role="bold">,</emphasis>&id;]…<emphasis role="bold">:</emphasis> &term;<emphasis role="bold">)</emphasis></entry>
+ <entry/>
+ </row>
+ </tbody>
+ </tgroup>
+ </table>
+
<table>
<tgroup cols="4">
<thead />
<sect1 id="axiom_definition_declaration">
<title>Definitions and declarations</title>
<sect2 id="axiom">
- <title>axiom &id;: &term;</title>
+ <title><emphasis role="bold">axiom</emphasis> &id;<emphasis role="bold">:</emphasis> &term;</title>
<titleabbrev>axiom</titleabbrev>
<para><userinput>axiom H: P</userinput></para>
<para><command>H</command> is declared as an axiom that states <command>P</command></para>
</sect2>
<sect2 id="definition">
- <title>definition &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">definition</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>definition</titleabbrev>
<para><userinput>definition f: T ≝ t</userinput></para>
<para><command>f</command> is defined as <command>t</command>;
<titleabbrev>(co)inductive types declaration</titleabbrev>
<para> &TODO; </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">:></emphasis>] &term;] [<emphasis role="bold">;</emphasis>&id; [<emphasis role="bold">:</emphasis>|<emphasis role="bold">:></emphasis>] &term;]…<emphasis role="bold">}</emphasis></title>
+ <titleabbrev>record</titleabbrev>
+ <para><userinput>record id x y z: S ≝ { f1: T1; …; fn:Tn }</userinput></para>
+ <para>Declares a new record family <command>id</command> parameterized over
+ <command>x,y,z</command>.</para>
+ <para><command>S</command> is the type of the record
+ and it must be convertible to a sort.</para>
+ <para>Each field <command>fi</command> is declared by giving its type
+ <command>Ti</command>. A record without any field is admitted.</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>id_ind</command>, <command>id_rec</command> and
+ <command>id_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
+ is allowed by the typing rules of the calculus according to the
+ sort <command>S</command>, the type <command>T1</command> and
+ the definability of depending record projections.</para>
+ <para>If the type of a field is declared with <command>:></command>,
+ the corresponding record projection becomes an implicit coercion.
+ This is just syntactic sugar and it has the same effect of declaring the
+ record projection as a coercion later on.</para>
+ </sect2>
</sect1>
<sect1 id="proofs">
<title>Proofs</title>
<sect2 id="theorem">
- <title>theorem &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">theorem</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>theorem</titleabbrev>
<para><userinput>theorem f: P ≝ p</userinput></para>
<para>Proves a new theorem <command>f</command> whose thesis is
<para>Notice that the command is equivalent to <command>definition f: T ≝ t</command>.</para>
</sect2>
<sect2 id="variant">
- <title>variant &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">variant</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>variant</titleabbrev>
<para><userinput>variant f: T ≝ t</userinput></para>
<para>Same as <command>theorem f: T ≝ t</command>, but it does not
an alternative name or proof to a theorem.</para>
</sect2>
<sect2 id="lemma">
- <title>lemma &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">lemma</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>lemma</titleabbrev>
<para><userinput>lemma f: T ≝ t</userinput></para>
<para>Same as <command>theorem f: T ≝ t</command></para>
</sect2>
<sect2 id="fact">
- <title>fact &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">fact</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>fact</titleabbrev>
<para><userinput>fact f: T ≝ t</userinput></para>
<para>Same as <command>theorem f: T ≝ t</command></para>
</sect2>
<sect2 id="remark">
- <title>remark &id;[: &term;] [≝ &term;]</title>
+ <title><emphasis role="bold">remark</emphasis> &id;[<emphasis role="bold">:</emphasis> &term;] [<emphasis role="bold">≝</emphasis> &term;]</title>
<titleabbrev>remark</titleabbrev>
<para><userinput>remark f: T ≝ t</userinput></para>
<para>Same as <command>theorem f: T ≝ t</command></para>