helm/software/matita/help/C/sec_commands.xml

   1
   2 <!-- ============ Commands ====================== -->
   3 <chapter id="sec_commands">
   4  <title>Other commands</title>
   5  <sect1 id="command_alias">
   6    <title>alias</title>
   7    <para><userinput>alias id &quot;s&quot; = &quot;def&quot;</userinput></para>
   8    <para><userinput>alias symbol &quot;s&quot; (instance n) = &quot;def&quot;</userinput></para>
   9    <para><userinput>alias num (instance n) = &quot;def&quot;</userinput></para>
  10    <para>
  11      <variablelist>
  12        <varlistentry>
  13          <term>Synopsis:</term>
  14          <listitem>
  15            <para><emphasis role="bold">alias</emphasis>
  16             [<emphasis role="bold">id</emphasis> &qstring; <emphasis role="bold">=</emphasis> &qstring;
  17             | <emphasis role="bold">symbol</emphasis> &qstring; [<emphasis role="bold">(instance</emphasis> &nat;<emphasis role="bold">)</emphasis>] <emphasis role="bold">=</emphasis> &qstring;
  18             | <emphasis role="bold">num</emphasis> [<emphasis role="bold">(instance</emphasis> &nat;<emphasis role="bold">)</emphasis>] <emphasis role="bold">=</emphasis> &qstring;
  19             ]
  20            </para>
  21          </listitem>
  22        </varlistentry>
  23        <varlistentry>
  24          <term>Action:</term>
  25          <listitem>
  26            <para>Used to give an hint to the disambiguating parser.
  27             When the parser is faced to the identifier (or symbol)
  28             <command>s</command> or to any number, it will prefer
  29             interpretations that &quot;map <command>s</command> (or the
  30             number) to <command>def</command>&quot;. For identifiers,
  31             &quot;def&quot; is the URI of the interpretation.
  32             E.g.: <command>cic:/matita/nat/nat.ind#xpointer(1/1/1)</command>
  33             for the first constructor of the first inductive type defined
  34             in the block of inductive type(s)
  35             <command>cic:/matita/nat/nat.ind</command>.
  36             For symbols and numbers, &quot;def&quot; is the label used to
  37             mark the wanted
  38             <link linkend="interpretation">interpretation</link>.
  39            </para>
  40           <para>When a symbol or a number occurs several times in the
  41            term to be parsed, it is possible to give an hint only for the
  42            instance <command>n</command>. When the instance is omitted,
  43            the hint is valid for every occurrence.
  44           </para>
  45           <para>
  46            Hints are automatically inserted in the script by Matita every
  47            time the user is interactively asked a question to disambiguate
  48            a term. This way the user won't be posed the same question twice
  49            when the script will be executed again.</para>
  50          </listitem>
  51        </varlistentry>
  52      </variablelist>
  53    </para>
  54  </sect1>
  55  <sect1 id="command_check">
  56    <title>check</title>
  57    <para><userinput>check t</userinput></para>
  58    <para>
  59      <variablelist>
  60        <varlistentry>
  61          <term>Synopsis:</term>
  62          <listitem>
  63            <para><emphasis role="bold">check</emphasis> &term;</para>
  64          </listitem>
  65        </varlistentry>
  66        <varlistentry>
  67          <term>Action:</term>
  68          <listitem>
  69            <para>Opens a CIC browser window that shows <command>t</command>
  70             together with its type. The command is immediately removed from
  71             the script.</para>
  72          </listitem>
  73        </varlistentry>
  74      </variablelist>
  75    </para>
  76  </sect1>
  77  <sect1 id="command_eval">
  78    <title>eval</title>
  79    <para><userinput>eval red on t</userinput></para>
  80    <para>
  81      <variablelist>
  82        <varlistentry>
  83          <term>Synopsis:</term>
  84          <listitem>
  85            <para><emphasis role="bold">eval</emphasis>
  86             &reduction-kind;
  87              <emphasis role="bold">on</emphasis>
  88              &term;</para>
  89          </listitem>
  90        </varlistentry>
  91        <varlistentry>
  92          <term>Action:</term>
  93          <listitem>
  94            <para>Opens a CIC browser window that shows
  95              the reduct of
  96              <command>t</command>
  97              together with its type.</para>
  98          </listitem>
  99        </varlistentry>
 100      </variablelist>
 101    </para>
 102  </sect1>
 103  <sect1 id="command_coercion">
 104    <title>coercion</title>
 105    <para><userinput>coercion u with ariety saturation nocomposites</userinput></para>
 106    <para>
 107      <variablelist>
 108        <varlistentry>
 109          <term>Synopsis:</term>
 110          <listitem>
 111                  <para>
 112                          <emphasis role="bold">coercion</emphasis>
 113                          (&uri; | &term; <emphasis role="bold">with</emphasis>)
 114                          [ &nat; [&nat;]]
 115                          [ <emphasis role="bold">nocomposites</emphasis> ]
 116                  </para>
 117          </listitem>
 118        </varlistentry>
 119        <varlistentry>
 120          <term>Action:</term>
 121          <listitem>
 122                  <para>Declares <command>u</command> as an implicit coercion.
 123                  If the type of <command>u</command> is
 124                  <command>∀x1:T1. … ∀x(n-1):T(n-1).Tn</command> the coercion target is
 125                  <command>T(n - ariety)</command> while its source is
 126                  <command>T(n - ariety - saturation - 1)</command>.
 127             Every time a term <command>x</command>
 128             of type source is used with expected type target, Matita
 129             automatically replaces <command>x</command> with
 130             <command>(u ? … ? x ? … ?)</command> to avoid a typing error.</para>
 131             Note that the number of <command>?</command> added after
 132             <command>x</command> is saturation.
 133            <para>Implicit coercions are not displayed to the user:
 134             <command>(u ? … ? x)</command> is rendered simply
 135             as <command>x</command>.</para>
 136            <para>When a coercion <command>u</command> is declared
 137             from source <command>s</command> to target <command>t</command>
 138             and there is already a coercion <command>u'</command> of
 139             target <command>s</command> or source <command>t</command>,
 140             a composite implicit coercion is automatically computed
 141             by Matita unless <emphasis role="bold">nocomposites</emphasis>
 142             is specified.</para>
 143          </listitem>
 144        </varlistentry>
 145      </variablelist>
 146    </para>
 147  </sect1>
 148  <sect1 id="command_default">
 149    <title>default</title>
 150    <para><userinput>default &quot;s&quot; u<subscript>1</subscript> … u<subscript>n</subscript></userinput></para>
 151    <para>
 152      <variablelist>
 153        <varlistentry>
 154          <term>Synopsis:</term>
 155          <listitem>
 156            <para><emphasis role="bold">default</emphasis>
 157             &qstring; &uri; [&uri;]…
 158            </para>
 159          </listitem>
 160        </varlistentry>
 161        <varlistentry>
 162          <term>Action:</term>
 163          <listitem>
 164            <para>It registers a cluster of related definitions and
 165             theorems to be used by tactics and the rendering engine.
 166             Some functionalities of Matita are not available when some
 167             clusters have not been registered. Overloading a cluster
 168             registration is possible: the last registration will be the
 169             default one, but the previous ones are still in effect.</para>
 170            <para>
 171             <command>s</command> is an identifier of the cluster and
 172             <command>u<subscript>1</subscript> … u<subscript>n</subscript></command>
 173             are the URIs of the definitions and theorems of the cluster.
 174             The number <command>n</command> of required URIs depends on the
 175             cluster. The following clusters are supported.
 176            </para>
 177            <table>
 178             <title>clusters</title>
 179             <tgroup cols="6">
 180             <thead>
 181              <row>
 182               <entry>name</entry>
 183               <entry>expected object for 1st URI</entry>
 184               <entry>expected object for 2nd URI</entry>
 185               <entry>expected object for 3rd URI</entry>
 186               <entry>expected object for 4th URI</entry>
 187               <entry>expected object for 5th URI</entry>
 188               <entry>expected object for 6th URI</entry>
 189               <entry>expected object for 7th URI</entry>
 190               <entry>expected object for 8th URI</entry>
 191               <entry>expected object for 9th URI</entry>
 192               <entry>expected object for 10th URI</entry>
 193               <entry>expected object for 11th URI</entry>
 194              </row>
 195             </thead>
 196             <tbody>
 197              <row>
 198               <entry>equality</entry>
 199               <entry>an inductive type (say, of type <command>eq</command>) of type ∀A:Type.A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis> with one family parameter and one constructor of type ∀x:A.eq A x</entry>
 200               <entry>a theorem of type <emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq A y x</entry>
 201               <entry>a theorem of type <emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>x,y,z:A.eq A x y <emphasis role="bold">→</emphasis> eq A y z <emphasis role="bold">→</emphasis> eq A x z</entry>
 202               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
 203               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Prop</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
 204               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Set</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
 205               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Set</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
 206               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Type</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A x y <emphasis role="bold">→</emphasis> P y</entry>
 207               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>a.<emphasis role="bold">∀</emphasis> P:A <emphasis role="bold">→</emphasis> <emphasis role="bold">Type</emphasis>.P x <emphasis role="bold">→</emphasis> <emphasis role="bold">∀</emphasis>y.eq A y x <emphasis role="bold">→</emphasis> P y</entry>
 208               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>B.<emphasis role="bold">∀</emphasis> f:A <emphasis role="bold">→</emphasis> B.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq B (f x) (f y)</entry>
 209               <entry><emphasis role="bold">∀</emphasis>A.<emphasis role="bold">∀</emphasis>B.<emphasis role="bold">∀</emphasis> f:A <emphasis role="bold">→</emphasis> B.<emphasis role="bold">∀</emphasis>x,y:A.eq A x y <emphasis role="bold">→</emphasis> eq B (f y) (f x)</entry>
 210              </row>
 211              <row>
 212               <entry>true</entry>
 213               <entry>an inductive type of type <emphasis role="bold">Prop</emphasis> with only one constructor that has no arguments</entry>
 214               <entry/>
 215               <entry/>
 216               <entry/>
 217               <entry/>
 218              </row>
 219              <row>
 220               <entry>false</entry>
 221               <entry>an inductive type of type <emphasis role="bold">Prop</emphasis> without constructors</entry>
 222               <entry/>
 223               <entry/>
 224               <entry/>
 225               <entry/>
 226              </row>
 227              <row>
 228               <entry>absurd</entry>
 229               <entry>a theorem of type <emphasis role="bold">∀</emphasis>A:Prop.<emphasis role="bold">∀</emphasis>B:Prop.A <emphasis role="bold">→</emphasis> Not A <emphasis role="bold">→</emphasis> B</entry>
 230               <entry/>
 231               <entry/>
 232               <entry/>
 233               <entry/>
 234              </row>
 235             </tbody>
 236             </tgroup>
 237            </table>
 238          </listitem>
 239        </varlistentry>
 240      </variablelist>
 241    </para>
 242  </sect1>
 243  <sect1 id="command_hint">
 244    <title>hint</title>
 245    <para><userinput>hint</userinput></para>
 246    <para>
 247      <variablelist>
 248        <varlistentry>
 249          <term>Synopsis:</term>
 250          <listitem>
 251            <para><emphasis role="bold">hint</emphasis>
 252            </para>
 253          </listitem>
 254        </varlistentry>
 255        <varlistentry>
 256          <term>Action:</term>
 257          <listitem>
 258            <para>Displays a list of theorems that can be successfully
 259             applied to the current selected sequent. The command is
 260             removed from the script, but the window that displays the
 261             theorems allow to add to the script the application of the
 262             selected theorem.
 263            </para>
 264          </listitem>
 265        </varlistentry>
 266      </variablelist>
 267    </para>
 268  </sect1>
 269  <sect1 id="command_include">
 270    <title>include</title>
 271    <para><userinput>include &quot;s&quot;</userinput></para>
 272    <para>
 273      <variablelist>
 274        <varlistentry>
 275          <term>Synopsis:</term>
 276          <listitem>
 277            <para><emphasis role="bold">include</emphasis> &qstring;</para>
 278          </listitem>
 279        </varlistentry>
 280        <varlistentry>
 281          <term>Action:</term>
 282          <listitem>
 283            <para>Every <link linkend="command_coercion">coercion</link>,
 284             <link linkend="notation">notation</link> and
 285             <link linkend="interpretation">interpretation</link> that was active
 286             when the file <command>s</command> was compiled last time
 287             is made active. The same happens for declarations of
 288             <link linkend="command_default">default definitions and
 289             theorems</link> and disambiguation
 290             hints (<link linkend="command_alias">aliases</link>).
 291             On the contrary, theorem and definitions declared in a file can be
 292            immediately used without including it.</para>
 293           <para>The file <command>s</command> is automatically compiled
 294           if it is not compiled yet.
 295           </para>
 296          </listitem>
 297        </varlistentry>
 298      </variablelist>
 299    </para>
 300  </sect1>
 301  <sect1 id="command_include_first">
 302    <title>include' &quot;s&quot;</title>
 303    <para><userinput></userinput></para>
 304    <para>
 305      <variablelist>
 306        <varlistentry>
 307          <term>Synopsis:</term>
 308          <listitem>
 309            <para><emphasis role="bold">include'</emphasis> &qstring;</para>
 310          </listitem>
 311        </varlistentry>
 312        <varlistentry>
 313          <term>Action:</term>
 314          <listitem>
 315            <para>Not documented (&TODO;), do not use it.</para>
 316          </listitem>
 317        </varlistentry>
 318      </variablelist>
 319    </para>
 320  </sect1>
 321  <sect1 id="command_whelp">
 322    <title>whelp</title>
 323    <para><userinput>whelp locate &quot;s&quot;</userinput></para>
 324    <para><userinput>whelp hint t</userinput></para>
 325    <para><userinput>whelp elim t</userinput></para>
 326    <para><userinput>whelp match t</userinput></para>
 327    <para><userinput>whelp instance t</userinput></para>
 328    <para>
 329      <variablelist>
 330        <varlistentry>
 331          <term>Synopsis:</term>
 332          <listitem>
 333            <para><emphasis role="bold">whelp</emphasis>
 334             [<emphasis role="bold">locate</emphasis> &qstring;
 335             | <emphasis role="bold">hint</emphasis> &term;
 336             | <emphasis role="bold">elim</emphasis> &term;
 337             | <emphasis role="bold">match</emphasis> &term;
 338             | <emphasis role="bold">instance</emphasis> &term;
 339             ]
 340            </para>
 341          </listitem>
 342        </varlistentry>
 343        <varlistentry>
 344          <term>Action:</term>
 345          <listitem>
 346            <para>Performs the corresponding <link linkend="whelp">query</link>,
 347             showing the result in the CIC browser. The command is removed
 348             from the script.
 349            </para>
 350          </listitem>
 351        </varlistentry>
 352      </variablelist>
 353    </para>
 354  </sect1>
 355  <sect1 id="command_qed">
 356    <title>qed</title>
 357    <para><userinput></userinput></para>
 358    <para>
 359      <variablelist>
 360        <varlistentry>
 361          <term>Synopsis:</term>
 362          <listitem>
 363            <para><emphasis role="bold">qed</emphasis>
 364            </para>
 365          </listitem>
 366        </varlistentry>
 367        <varlistentry>
 368          <term>Action:</term>
 369          <listitem>
 370            <para>Saves and indexes the current interactive theorem or
 371             definition.
 372             In order to do this, the set of sequents still to be proved
 373             must be empty.</para>
 374          </listitem>
 375        </varlistentry>
 376      </variablelist>
 377    </para>
 378  </sect1>
 379 </chapter>
 380