-\subsection {The core language}
+\subsection {The core language} \label{OCore}
\subsubsection*{Preliminaries}
-Wih the above background we are able to type the main objects needed in the
+With the above background we are able to type the main objects needed in the
formalization:
\begin{itemize}
\item
-A path $ s $ is a list of strings therefore its type is
+A path $ p $ is a list of strings therefore its type is
$ T_{0a} = \Listof\ \Str $.
\item
-A multiple string value $ V $ is an object of type $ T_{0b} = \Setof\ \Str $.
+The attribute contents $ V $ are an object of type $ T_{0b} = \Setof\ \Str $.
\item
-A attribute group $ G $ is an association set connecting the attribute names
-to their values, therefore its type is
+An attribute group $ G $ is an association set connecting the attribute names
+to their contents, therefore its type is
$ T_1 = \Setof\ (T_{0a} \times T_{0b}) $.
\item
-A subject string $ r $ is an object of type $ \Str $.
+A head string $ r $ is an object of type $ \Str $.
\item
A set $ A $ of attribute groups is an object of type $ T_2 = \Setof\ T_1 $.
\item
-An {\av} is a subject string with its attribute groups, so its type is
+An {\av}, {\ie} a head string with its attribute groups, has type
$ T_3 = \Str \times T_2 $.
\item
When a constant string appearing in a {\MathQL} expression is unquoted, the
surrounding double quotes are deleted and each escaped sequence is translated
-according \figref{EscTS}.
-
+according to \figref{EscTS}.
This operation is formally performed by the function
$ \Unquote $ of type $ \Str \to \Str $.
Moreover $ \Name \oft \GP{path} \to T_{0a} $ is a helper function that
relation $ \daq $ that evaluates a query to an {\av} set.
These expressions are evaluated in a context $ \G = \g $
which is a triple of association sets that connect
-svar's to {\av} sets, avar's to {\av}'s and avar's to attribute groups.
+set variables to {\av} sets, element variables to {\av}'s and element
+variables to attribute groups.
Therefore the type $ K $ of the context $ \G $ is:
\begin{footnotesize} \begin{center}
$
-\Setof\ (\GP{svar} \times T_4) \times
-\Setof\ (\GP{avar} \times T_3)\ \times % $ \\ $ \times\
-\Setof\ (\GP{avar} \times T_1)
+\Setof\ (\GP{svar} \times T_4) \times
+\Setof\ (\GP{evar} \times T_3) \times % $ \\ $ \times\
+\Setof\ (\GP{evar} \times T_1)
$
\end{center} \end{footnotesize}
\end{tabular} \end{center}
\end{footnotesize}
-The context components $ \G_s $ and $ \G_a $ are used to store the contents of
+The context components $ \G_s $ and $ \G_e $ are used to store the contents of
variables, while $ \G_g $ is used by the \TT{ex} operator to be presented
below.
\subsubsection*{Queries}
-The first \GP{query} expressions include explicit {\av} sets and syntactic
-grouping:
+The first group of \GP{query} expressions include the representation of
+explicit {\av} sets and the syntactic grouping facility:
\begin{itemize}
\item
The syntactic grouping is obtained enclosing a \GP{query} between \TT{(}
and \TT{)}.
-An explicit {\av} set can be represented by a single string, which is
+An explicit {\av} set can be represented either by a single string, which is
converted into a single {\av} with no attributes, or by a \GP{xavs}
(extended {\av} set) expression enclosed between \TT{[} and \TT{]}.
Such an expression describes all the components of an {\av} set and is
\begin{center}
%
\irule{x_1, \cdots, x_m \in \GP{xav} \spc
- (\G, TT{[} x_1 \TT{]}) \daq S_1 \spc \cdots \spc (\G, \TT{[} x_m \TT{]}) \daq S_m}{}
- {(\G, \TT{[} x_1 \TT{;} \cdots \TT{;} x_m \TT{]}) \daq S_1 \sum \cdots \sum S_m}
+ (\G, \TT{[} x_1 \TT{]}) \daq S_1 \spc \cdots \spc (\G, \TT{[} x_m \TT{]}) \daq S_m}{}
+ {(\G, \TT{[} x_1 \TT{;} \cdots \TT{;} x_m \TT{]}) \daq S_1 \ssum \cdots \ssum S_m}
%
\end{center}
\begin{center}
%
-\irule{q \in \GP{string} \spc g_1, \cdots, g_m \in \GP{xgroup} \spc
+\irule{q \in \GP{string} \spc g_1, \cdots, g_m \in \GP{xgroup} \icr
(\G, \TT{[} q\ \TT{attr}\ g_1 \TT{]}) \daq S_1 \spc \cdots \spc
(\G, \TT{[} q\ \TT{attr}\ g_m \TT{]}) \daq S_m}{}
- {(\G, \TT{[} q\ \TT{attr}\ g_1 \TT{,} \cdots \TT{,} g_m \TT{]}) \daq S_1 \sum \cdots \sum S_m}
+ {(\G, \TT{[} q\ \TT{attr}\ g_1 \TT{,} \cdots \TT{,} g_m \TT{]}) \daq S_1 \ssum \cdots \ssum S_m}
%
\end{center}
\begin{center}
%
-\irule{q \in \GP{string} \spc a_1, \cdots, a_m \in \GP{xatr} \spc
+\irule{q \in \GP{string} \spc a_1, \cdots, a_m \in \GP{xatr} \icr
(\G, \TT{[} q\ \TT{attr}\ \{ a_1 \} \TT{]}) \daq S_1 \spc \cdots \spc
(\G, \TT{[} q\ \TT{attr}\ \{ a_m \} \TT{]}) \daq S_m}{}
{(\G, \TT{[} q\ \TT{attr}\ \{ a_1 \TT{;} \cdots \TT{;} a_m \} \TT{]}) \daq S_1 \dsum \cdots \dsum S_m}
\end{center}
\end{footnotesize}
-$ \dsum $ and $ \sum $ are helper functions describing the two union operations
-on {\av} sets: with and without attribute distribution respectively.
-$ \dsum $ and $ \sum $ have two rewrite rules each.
+$ \dsum $ and $ \ssum $ are helper functions describing the two union
+operations on {\av} sets: with and without attribute distribution respectively.
\begin{footnotesize}
\begin{center} \begin{tabular}{lrll}
%
1a &
-$ (S_1 \sdor \{(r, A_1)\}) \sum (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
-$ (S_1 \sum S_2) \sor \{(r, A_1 \sor A_2)\} $ \\
-1b & $ S_1 \sum S_2 $ & rewrites to & $ S_1 \sor S_2 $ \\
+$ (S_1 \sdor \{(r, A_1)\}) \ssum (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
+$ (S_1 \ssum S_2) \sor \{(r, A_1 \sor A_2)\} $ \\
+1b & $ S_1 \ssum S_2 $ & rewrites to & $ S_1 \sor S_2 $ \\
2a &
$ (S_1 \sdor \{(r, A_1)\}) \dsum (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
$ (S_1 \dsum S_2) \sor \{(r, A_1 \distr A_2)\} $ \\
\end{tabular} \end{center}
\end{footnotesize}
-Rules 1a, 2a override 1b, 2b respectively and
-$ A_1 \distr A_2 = \{G_1 \sum G_2 \st G_1 \in A_1, G_2 \in A_2\} $.
+Rules 1a, 2a override 1b, 2b and
+$ A_1 \distr A_2 = \{G_1 \ssum G_2 \st G_1 \in A_1, G_2 \in A_2\} $.
\item
-The semantics of \TT{property} operator is described below.
+The semantics of the \TT{property} operator is described below.
In the following rule,
-$s$ is ``$ \TT{property}\ h\ p_1\ \TT{main}\ p_2\ \RM{attr}\ e_1, \cdots,
+$s$ is ``$ \TT{property}\ h\ p_1\ \TT{main}\ p_2\ \TT{attr}\ e_1, \cdots,
e_m\ \TT{in}\ k\ x $'', $P$ is $ \Property\ h $ and
$A_2$ is $ \{ \Exp\ P\ p_1\ r_1\ \{e_1, \cdots, e_m\}\} $:
\begin{center}
%
\irule
-{h \oft \GP{refine} \spc p_1, p_2 \oft \GP{path} \spc
+{h \oft \GP{ref} \spc p_1, p_2 \oft \GP{path} \spc
e_1, \cdots, e_m \oft \GP{exp} \spc k \in \TT{["pattern"]?} \spc
(\G, x) \daq S
}{A}
When the \TT{main} clause is not present, we assume $ p_2 = \TT{/} $.
Here $ \Property\ h $ gives the appropriate access relation according to
-the $ h $ flag (this is the primitive function that inspects the {\RDF} graph,
-see \subsecref{HighAccess}).
+the $ h $ flag (this is the primitive function that inspects the {\RDF}
+graph).
$ \Src\ k\ P\ V $ is a helper function giving the source set
according to the $ k $ flag. $ \Src $ is based on $ \Match $, the helper
-function handling POSIX regular expressions. Formally:
+function handling {\POSIX} regular expressions.
+Here $ \Pattern\ W\ s $ is the primitive function returning the subset of
+$ W \oft \Setof\ \Str $ whose element match the {\POSIX} 1003.2-1992%
+\footnote{In {\POSIX} 1003.1-2001:
+\CURI{http://www.unix-systems.org/version3/ieee\_\,std.html}.}
+regular expression $ \verb+"^"+ \app s \app \TT{"\$"} $.
\begin{footnotesize}
\begin{center} \begin{tabular}{rll}
\end{tabular} \end{center}
\end{footnotesize}
-Here $ \Pattern\ W\ s $ is the primitive function returning the subset of
-$ W \oft \Setof\ \Str $ whose element match the POSIX 1003.2-1992%
-\footnote{Included in POSIX 1003.1-2001:
-\CURI{http://www.unix-systems.org/version3/ieee\_\,std.html}.}
-regular expression $ \verb+"^"+ \app s \app \TT{"\$"} $.
-
-$ \Exp\ P\ \p_1\ r_1\ E $ is the helper function that builds the group of
+$ \Exp\ P\ p_1\ r_1\ E $ is the helper function that builds the group of
attributes specified in the \TT{attr} clause.
-$ \Exp $ is based on $ \Exp\p $ which handles a single attribute. Formally:
+$ \Exp $ is based on $ \Exp\p $ which handles a single attribute. Formally,
+if $ p, p\p \oft \GP{path} $ and $ E \oft \Setof\ \GP{exp} $:
\begin{footnotesize}
-\begin{center} \begin{tabular}{rlll}
+\begin{center} \begin{tabular}{rll}
%
$ f\ P\ r_1\ p_1\ p $ & rewrites to &
-$ \{ r_2 \st (r_1, p_1 \app (\Name\ p), r_2) \in P \} $ &
-with $ p \oft \GP{path} $ \\
+$ \{ r_2 \st (r_1, p_1 \app (\Name\ p), r_2) \in P \} $ \\
$ \Exp\p\ P\ r_1\ p_1\ p $ & rewrites to &
-$ \{ (\Name\ p, f\ P\ r_1\ p_1\ p) \} $ &
-with $ p \oft \GP{path} $ \\
+$ \{ (\Name\ p, f\ P\ r_1\ p_1\ p) \} $ \\
$ \Exp\p\ P\ r_1\ p_1\ (p\ \TT{as}\ p\p) $ & rewrites to &
-$ \{ (\Name\ p\p, f\ P\ r_1\ p_1\ p) \} $ &
-with $ p, p\p \oft \GP{path} $ \\
+$ \{ (\Name\ p\p, f\ P\ r_1\ p_1\ p) \} $ \\
$ \Exp\ P\ r_1\ p_1\ E $ & rewrites to &
-$ \bigsum \{ \Exp\p\ P\ r_1\ p_1\ e \st e \in E \} $ &
-with $ E \oft \Setof\ \GP{exp} $
+$ \bigsum \{ \Exp\p\ P\ r_1\ p_1\ e \st e \in E \} $ \\
\end{tabular} \end{center}
\end{footnotesize}
\end{footnotesize}
For each clause ``\TT{isfalse} $ c_1, \cdots, c_n $'' the set $ P $
-must be replaced with
+must be replaced with \newline
$ \{ (r_1, p, r_2) \in P \st \lnot (\Istrue\ P\ r_1\ p_1\ C) \} $
(using the above notation).
Note that these substitutions and the former must be composed if necessary.
\end{itemize}
-The second group of \GP{query} expressions includes the context manipulation
-facilities:
+The second group of \GP{query} expressions allows the context manipulation:
\begin{itemize}
\begin{footnotesize} \begin{center}
%
\irule{i \oft \GP{svar}}{}{(\g, i) \daq \get{\G_s}{i}} \spc
-\irule{i \oft \GP{avar}}{}{(\g, i) \daq \{\get{\G_a}{i}\}}
+\irule{i \oft \GP{evar}}{}{(\g, i) \daq \{\get{\G_e}{i}\}}
%
\end{center} \end{footnotesize}
-$ \get{\G_s}{i} $ and $ \{\get{\G_a}{i}\} $ mean $ \ES $ if $ i $ is not defined.
+$ \get{\G_s}{i} $ and $ \{\get{\G_e}{i}\} $ mean $ \ES $ if $ i $ is not defined.
\item
-The \TT{let} operator assigns an {\av} set variable (svar):
+The \TT{let} operator assigns a set variable (\GP{svar}):
\begin{footnotesize}
\begin{center}
%
\irule{i \oft \GP{svar} \spc (\G_1, x_1) \daq (\g, S_1) \spc
- ((\set{\G_s}{i}{S_1}, \G_a, \G_g), x_2) \daq (\G_2, S_2)}
+ ((\set{\G_s}{i}{S_1}, \G_e, \G_g), x_2) \daq (\G_2, S_2)}
{}{(\G_1, \TT{let}\ i\ \TT{=}\ x_1\ \TT{in}\ x_2) \daq (\G_2, S_2)}
%
\end{center}
\end{footnotesize}
The sequential composition operator \TT{;;} has the semantics of a \TT{let}
-introducing a fresh variable, so ``$ x_1\ \TT{;;}\ x_2 $'' revrites
+introducing a fresh variable, so ``$ x_1\ \TT{;;}\ x_2 $'' rewrites
to ``$ \TT{let}\ i\ \TT{=}\ x_1\ \TT{in}\ x_2 $'' where $i$ does not occur in
$x_2$.
\item
The \TT{ex} and ``dot'' operators provide a way to read the attributes stored
-in avar's.
-
+in element variables.
The \TT{ex} (exists) operator gives access to the groups of attributes
-associated to the {\av}'s in the $ \G_a $ part of the context and does
+associated to the {\av}'s in the $ \G_e $ part of the context and does
this by loading its $ \G_g $ part, which is used by the ``dot'' operator
described below.
\TT{ex} is true if the query following it is successful for at least one
-pool of attribute groups, one for each {\av} in the $ \G_a $ part of the
+pool of attribute groups, one for each {\av} in the $ \G_e $ part of the
context. Formally we have the rules:
\begin{footnotesize}
\begin{center}
%
-\irule{(\lall \D_g \in \All\ \G_a)\ ((\G_s, \G_a, \G_g + \D_g), y) \daq \F}
+\irule{(\lall \D_g \in \All\ \G_e)\ ((\G_s, \G_e, \G_g + \D_g), y) \daq \F}
{1}{(\G, \TT{ex}\ y) \daq \F} \spc
\irule{\Nop}{2}{(\G, \TT{ex}\ y) \daq \T} \spc
%
\end{center}
\begin{center}
%
-\irule {i \oft \GP{avar} \spc p \oft \GP{path} \spc \get{\get{\G_g}{i}}{\Name\ p} = \{s_1, \cdots, s_m\}}{}
+\irule {i \oft \GP{evar} \spc p \oft \GP{path} \spc \get{\get{\G_g}{i}}{\Name\ p} = \{s_1, \cdots, s_m\}}{}
{(\G, i\TT{.}p) \daq \{(s_1, \ES), \cdots, (s_m, \ES)\}}
%
\end{center}
where%
\footnote{$\D_g$ has the type of $ \G_g $.}
-$ \All\ \G_a = \{\D_g \st \get{\D_g}{i} = G\ \RM{iff}\ G \in \Snd\ \get{\G_a}{i} \} $,
+$ \All\ \G_e = \{\D_g \st \get{\D_g}{i} = G\ \RM{iff}\ G \in \Snd\ \get{\G_e}{i} \} $,
and $ \G = \g $.
Moreover $ \get{\get{\G_g}{i}}{\Name\ p} $ means $ \ES $
if $ i $ or $ \Name\ p $ are not defined where appropriate.
-
Here the first rule has higher precedence than the second one does.
\end{itemize}
-The third group of \GP{query} expressions includes the {\av} set manipulation
-facilities:
+The third group of \GP{query} expressions allows the {\av} set manipulation:
\begin{itemize}
\item
The \TT{add} operator adds a given set of attribute groups to the {\av}'s
of an {\av} set using a union with or without attribute distribution
-according to the \TT{distr} flag.
+according to the setting of the \TT{distr} flag.
\begin{footnotesize}
\begin{center}
%
\irule
-{h \in \TT{["distr"]?} \spc a \in \GP{xgroups} \spc
+{h \in \TT{["distr"]?} \spc a \in \GP{xgroups} \icr
(\G, \TT{[} ""\ \TT{attr}\ a \TT{]}) \daq \{("", A)\} \spc
(\G, x) \daq \{(r_1, A_1), \cdots, (r_m, A_m)\}}{}
{(\G, \TT{add}\ a\ \TT{in}\ x) \daq \{(r_1, A_1 \jolly A), \cdots, (r_m, A_m \jolly A)\}}
\begin{center}
%
\irule
-{h \in \TT{["distr"]?} \spc i \in \GP{avar} \spc
+{h \in \TT{["distr"]?} \spc i \in \GP{evar} \spc
(\g, x) \daq \{(r_1, A_1), \cdots, (r_m, A_m)\}}{}
-{(\g, \TT{add}\ i\ \TT{in}\ x) \daq \{(r_1, A_1 \jolly \Snd\ \get{\G_a}{i}), \cdots, (r_m, A_m \jolly \Snd\ \get{\G_a}{i})\}}
+{(\g, \TT{add}\ i\ \TT{in}\ x) \daq \{(r_1, A_1 \jolly \Snd\ \get{\G_e}{i}), \cdots, (r_m, A_m \jolly \Snd\ \get{\G_e}{i})\}}
%
\end{center}
\end{footnotesize}
Where $ \jolly_{\tt""} = \sor $ and $ \jolly_{\tt"distr"} = \distr $.
-Moreover $ \Snd\ \get{\G_a}{i} = \ES $ if $i$ is not defined.
+Moreover $ \Snd\ \get{\G_e}{i} = \ES $ if $i$ is not defined.
\item
-The semantics of the \TT{for} operator is given in terms of the {\For} helper
+The semantics of the \TT{for} operator is given using the {\For} helper
function:
\begin{footnotesize}
\begin{center}
%
-\irule{i \oft \GP{avar} \spc (\G, x_1) \daq (\G_1, S_1) \spc h \in \TT{["sup"|"inf"]}}
-{}{(\G, \TT{for}\ i\ \TT{in}\ x_1\ h\ x_2) \daq \For\ h\ \G_1\ i\ x_2\ S_1} \spc
-\irule{i \oft \GP{avar} \spc x_2 \oft \GP{query}}{}
+\irule{i \oft \GP{evar} \spc (\G, x_1) \daq (\G_1, S_1) \spc h \in \TT{["sup"|"inf"]}}
+{}{(\G, \TT{for}\ i\ \TT{in}\ x_1\ h\ x_2) \daq \For\ h\ \G_1\ i\ x_2\ S_1}
+%
+\end{center}
+\begin{center}
+%
+\irule{i \oft \GP{evar} \spc x_2 \oft \GP{query}}{}
{\For\ h\ \G\ i\ x_2\ \ES\ \RM{rewrites to}\ (\G, \ES)}
%
\end{center}
\begin{center}
%
-\irule{i \oft \GP{avar} \spc ((\G_s, \set{\G_a}{i}{R}, \G_g), x_2) \daq (\G_2, S_2)}
+\irule{i \oft \GP{evar} \spc ((\G_s, \set{\G_e}{i}{R}, \G_g), x_2) \daq (\G_2, S_2)}
{}{\For\ h\ \G\ i\ x_2\ (S_1 \sdor \{R\})\ \RM{rewrites to}\
(\G_2 ,(\Snd\ (\For\ h\ \G_2\ i\ x_2\ S_1)) \jolly_h S_2)}
%
\end{center}
\end{footnotesize}
-Here we have $ R \oft T_3 $, $ \G = \g $, $ \jolly_{\tt"sup"} = \sum $ and
-$ \jolly_{\tt"inf"} = \prod $.
+Here we have $ R \oft T_3 $, $ \G = \g $, $ \jolly_{\tt"sup"} = \ssum $ and
+$ \jolly_{\tt"inf"} = \sprod $.
-$ \dprod $ and $ \prod $ are helper functions describing the two intersection
+$ \dprod $ and $ \sprod $ are helper functions describing the two intersection
operations on {\av} sets: with and without attribute distribution respectively.
-They are dual to $ \dsum $ and $ \sum $. $ \dprod $ does not appear in this
-version of {\MathQL} but was used in the erlier versions
-\cite{Lor02, GS03, Gui03}.
+They are dual to $ \dsum $ and $ \ssum $. $ \dprod $ does not appear in this
+version of {\MathQL} but was used in the earlier versions
+\cite{Lor02,GS03,Gui03}.
\begin{footnotesize}
\begin{center} \begin{tabular}{lrll}
%
1a &
-$ (S_1 \sdor \{(r, A_1)\}) \prod (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
-$ (S_1 \prod S_2) \sor \{(r, A_1 \sor A_2)\} $ \\
-1b & $ S_1 \prod S_2 $ & rewrites to & $ \ES $ \\
+$ (S_1 \sdor \{(r, A_1)\}) \sprod (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
+$ (S_1 \sprod S_2) \sor \{(r, A_1 \sor A_2)\} $ \\
+1b & $ S_1 \sprod S_2 $ & rewrites to & $ \ES $ \\
2a &
$ (S_1 \sdor \{(r, A_1)\}) \dprod (S_2 \sdor \{(r, A_2)\}) $ & rewrites to &
$ (S_1 \dprod S_2) \sor \{(r, A_1 \distr A_2)\} $ \\
\end{tabular} \end{center}
\end{footnotesize}
-As for $ \sum $ and $ \dsum $, rules 1a, 2a override rules 1b, 2b respectively.
+As for $ \ssum $ and $ \dsum $, rules 1a, 2a override rules 1b, 2b respectively.
\item
The semantics of the \TT{while} operator is given by the rules below:
%
\irule
{h \in \TT{["sup"|"inf"]} \spc (\G, x_1) \daq (\G_1, S_1) \spc
- (\G_1, x_2) \daq (\G_2, S_2) \spc
+ (\G_1, x_2) \daq (\G_2, S_2) \icr
(\G_2, \TT{while}\ x_1\ h\ x_2) \daq (\G_3, S)}{2}
{(\G, \TT{while}\ x_1\ h\ x_2) \daq (\G_3, S_2 \jolly_h S)}
%
\end{center}
\end{footnotesize}
-Again $ \jolly_{\tt"sup"} = \sum $ and $ \jolly_{\tt"inf"} = \prod $.
-Moreover rule 1 takes precedence over rule 2.
+Again $ \jolly_{\tt"sup"} = \ssum $ and $ \jolly_{\tt"inf"} = \sprod $.
+Rule 1 takes precedence over rule 2.
\end{itemize}
-The forth group of \GP{query} constructions make {\MathQL} an extensible
-language.
+The forth group of \GP{query} constructions makes {\MathQL} extensible.
\begin{itemize}
to invoke an undefined function.
\item
-The \TT{gen} construction invokes an external function returning a \GP{query}
+The \TT{gen} construction invokes an external function returning a \GP{query}.
The function is identified by a \GP{path} and its arguments are a set of
\GP{query}'s. It is a mistake to invoke a function with the wrong number of
\GP{query}'s as input (each particular function defines this number
\GP{query} $ is the primitive function performing the low level invocation.
The core language does not include any external function of this kind and it
is a mistake to invoke an undefined function.
-
-The construction ``\TT{gen} p \TT{in} x'' rewrites to ``\TT{gen} p \{x\}''
-for the user's convenience.
+The construction ``\TT{gen} p \TT{in} x'' rewrites to ``\TT{gen} p \verb+{+x\verb+}+''.
\end{itemize}
\subsubsection*{Results}
-An \GP{avs} expression ({\ie} the explicit representation of an {\av} set that
-can denote a query result) is evaluated to an {\av} set according to the
-following rules.
+An \GP{avs} expression (the explicit representation of an {\av} set denoting a
+query result) is evaluated to an {\av} set according to the following rules.
\begin{footnotesize}
\begin{center}
%
\irule{x_1, \cdots, x_m \in \GP{av} \spc
x_1 \dar S_1 \spc \cdots \spc x_m \dar S_m}{}
- {x_1 \TT{;} \cdots \TT{;} x_m \dar S_1 \sum \cdots \sum S_m}
+ {x_1 \TT{;} \cdots \TT{;} x_m \dar S_1 \ssum \cdots \ssum S_m}
%
\end{center}
\begin{center}
\irule{q \in \GP{string} \spc g_1, \cdots, g_m \in \GP{group} \spc
q\ \TT{attr}\ g_1 \dar S_1 \spc \cdots \spc
q\ \TT{attr}\ g_m \dar S_m}{}
- {q\ \TT{attr}\ g_1 \TT{,} \cdots \TT{,} g_m \dar S_1 \sum \cdots \sum S_m}
+ {q\ \TT{attr}\ g_1 \TT{,} \cdots \TT{,} g_m \dar S_1 \ssum \cdots \ssum S_m}
%
\end{center}
\begin{center}
\end{center}
\begin{center}
%
+\irule{q, q_0 \in \GP{string} \spc p \in \GP{path}}{}
+ {q\ \TT{attr}\ \{ p = q_0 \} \dar
+ \{(\Unquote\ q, \{ \{ (\Name\ p, \{ \Unquote\ q_0 \}) \} \})\}}
+%
+\end{center}
+\begin{center}
+%
\irule{q, q_1, \cdots, q_m \in \GP{string} \spc p \in \GP{path}}{}
{q\ \TT{attr}\ \{ p = \{ q_1 \TT{,} \cdots \TT{,} q_m \} \} \dar
\{(\Unquote\ q, \{ \{ (\Name\ p, \{ \Unquote\ q_1, \cdots, \Unquote\ q_m \}) \} \})\}}
projects / helm.git / blobdiff