<entry><emphasis role="bold">Set</emphasis></entry>
<entry>the impredicate sort of datatypes</entry>
</row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><emphasis role="bold">CProp</emphasis></entry>
+ <entry>one fixed predicative sort of constructive propositions</entry>
+ </row>
<row>
<entry/>
<entry>|</entry>
<row>
<entry id="grammar.pattern">&pattern;</entry>
<entry>::=</entry>
- <entry>&TODO;</entry>
+ <entry><emphasis role="bold">in</emphasis>
+ [&id;[<emphasis role="bold">:</emphasis> &path;]]…
+ [<emphasis role="bold">⊢</emphasis> &path;]]</entry>
+ <entry>simple pattern</entry>
+ </row>
+ <row>
+ <entry/>
+ <entry>|</entry>
+ <entry><emphasis role="bold">in match</emphasis> &term;
+ [<emphasis role="bold">in</emphasis>
+ [&id;[<emphasis role="bold">:</emphasis> &path;]]…
+ [<emphasis role="bold">⊢</emphasis> &path;]]</entry>
+ <entry>full pattern</entry>
+ </row>
+ </tbody>
+ </tgroup>
+ </table>
+ <table frame="topbot" rowsep="0" colsep="0" role="grammar">
+ <title>path</title>
+ <tgroup cols="4">
+ <tbody>
+ <row>
+ <entry id="grammar.path">&path;</entry>
+ <entry>::=</entry>
+ <entry><emphasis>〈〈any &sterm; whithout occurrences of <emphasis role="bold">Set</emphasis>, <emphasis role="bold">Prop</emphasis>, <emphasis role="bold">CProp</emphasis>, <emphasis role="bold">Type</emphasis>, &id;, &uri; and user provided notation; however, <emphasis role="bold">%</emphasis> is now an additional production for &sterm;〉〉</emphasis></entry>
</row>
</tbody>
</tgroup>
</table>
- <para>&TODO;</para>
+ <para>A <emphasis>path</emphasis> locates zero or more subterms of a given term by mimicking the term structure up to:</para>
+ <orderedlist>
+ <listitem><para>Occurrences of the subterms to locate that are
+ represented by <emphasis role="bold">%</emphasis>.</para></listitem>
+ <listitem><para>Subterms without any occurrence of subterms to locate
+ that can be represented by <emphasis role="bold">?</emphasis>.
+ </para></listitem>
+ </orderedlist>
+ <para>For instance, the path
+ <userinput>∀_,_:?.(? ? % ?)→(? ? ? %)</userinput>
+ locates at once the subterms
+ <userinput>x+y</userinput> and <userinput>x*y</userinput> in the
+ term <userinput>∀x,y:nat.x+y=1→0=x*y</userinput>
+ (where the notation <userinput>A=B</userinput> hides the term
+ <userinput>(eq T A B)</userinput> for some type <userinput>T</userinput>).
+ </para>
+ <para>A <emphasis>simple pattern</emphasis> extends paths to locate
+ subterms in a whole sequent. In particular, the pattern
+ <userinput>in H: p K: q ⊢ r</userinput> locates at once all the subterms
+ located by the pattern <userinput>r</userinput> in the conclusion of the
+ sequent and by the patterns <userinput>p</userinput> and
+ <userinput>q</userinput> in the hypotheses <userinput>H</userinput>
+ and <userinput>K</userinput> of the sequent.
+ </para>
+ <para>If no list of hypotheses is provided in a simple pattern, no subterm
+ is selected in the hypothesis. If the <userinput>⊢ p</userinput>
+ part of the pattern is not provided, no subterm will be matched in the
+ conclusion if at least one hypothesis is provided; otherwise the whole
+ conclusion is selected.
+ </para>
+ <para>Finally, a <emphasis>full pattern</emphasis> is interpreted in three
+ steps. In the first step the <userinput>match T in</userinput>
+ part is ignored and a set <emphasis>S</emphasis> of subterms is
+ located as for the case of
+ simple patterns. In the second step the term <userinput>T</userinput>
+ is parsed and interpreted in the context of each subterm
+ <emphasis>s ∈ S</emphasis>. In the last term for each
+ <emphasis>s ∈ S</emphasis> the interpreted term <userinput>T</userinput>
+ computed in the previous step is looked for. The final set of subterms
+ located by the full pattern is the set of occurrences of
+ the interpreted <userinput>T</userinput> in the subterms <emphasis>s</emphasis>.
+ </para>
+ <para>A full pattern can always be replaced by a simple pattern,
+ often at the cost of increased verbosity or decreased readability.</para>
+ <para>Example: the pattern
+ <userinput>⊢ in match x+y in ∀_,_:?.(? ? % ?)</userinput>
+ locates only the first occurrence of <userinput>x+y</userinput>
+ in the sequent <userinput>x,y: nat ⊢ ∀z,w:nat. (x+y) * (z+w) =
+ z * (x+y) + w * (x+y)</userinput>. The corresponding simple pattern
+ is <userinput>⊢ ∀_,_:?.(? ? (? % ?) ?)</userinput>.
+ </para>
+ <para>Every tactic that acts on subterms of the selected sequents have
+ a pattern argument for uniformity. To automatically generate a simple
+ pattern:</para>
+ <orderedlist>
+ <listitem><para>Select in the current goal the subterms to pass to the
+ tactic by using the mouse. In order to perform a multiple selection of
+ subterms, hold the Ctrl key while selecting every subterm after the
+ first one.</para></listitem>
+ <listitem><para>From the contextual menu select "Copy".</para></listitem>
+ <listitem><para>From the "Edit" or the contextual menu select
+ "Paste as pattern"</para></listitem>
+ </orderedlist>
</sect2>
<sect2 id="reduction-kind">
projects / helm.git / commitdiff