-\documentclass[a4paper,draft]{article}
+\documentclass[a4paper]{article}
\usepackage{a4wide}
\usepackage{pifont}
\newcommand{\POS}[1]{\ensuremath{#1\mbox{\textbf{:}}}}
\newcommand{\MERGE}{\ensuremath{\mbox{\textbf{]}}}}
\newcommand{\FOCUS}[1]{\ensuremath{\mathtt{focus}~#1}}
-\newcommand{\ENDFOCUS}{\ensuremath{\mathtt{unfocus}}}
+\newcommand{\UNFOCUS}{\ensuremath{\mathtt{unfocus}}}
\newcommand{\SKIP}{\MATHTT{skip}}
\newcommand{\TACTIC}[1]{\ensuremath{\mathtt{tactic}~#1}}
\newcommand{\ENTRY}[4]{\langle#1,#2,#3,#4\rangle}
\newcommand{\TSEM}[3]{\TSEMOP{#1}_{#2,#3}}
-\newcommand{\GIN}[1][1]{\ensuremath{[s_{#1};\cdots;s_n]}}
+\newcommand{\GIN}[1][1]{\ensuremath{[l_{#1};\cdots;l_n]}}
\newcommand{\ZEROPOS}{\MATHIT{zero\_pos}}
\newcommand{\INITPOS}{\MATHIT{init\_pos}}
\newcommand{\FILTEROPEN}{\MATHIT{filter\_open}}
\newcommand{\ISOPEN}{\MATHIT{is\_open}}
\newcommand{\DEEPCLOSE}{\MATHIT{deep\_close}}
+\newcommand{\REMOVEGOALS}{\MATHIT{remove\_goals}}
+\newcommand{\GOALS}{\MATHIT{open\_goals}}
\newcommand{\BRANCHTAG}{\ensuremath{\mathtt{B}}}
-\newcommand{\FOCUSTAG}{\ensuremath{\mathtt{S}}}
+\newcommand{\FOCUSTAG}{\ensuremath{\mathtt{F}}}
\newlength{\sidecondlen}
\setlength{\sidecondlen}{2cm}
\begin{document}
\maketitle
-\section{Semantics}
-
-\subsection{Language}
-
-\[
-\begin{array}{rcll}
- S & ::= & & \mbox{(\textbf{continuationals})}\\
- & & \TACTIC{T} & \mbox{(tactic)}\\[2ex]
- & | & \DOT & \mbox{(dot)} \\
- & | & \SEMICOLON & \mbox{(semicolon)} \\
- & | & \BRANCH & \mbox{(branch)} \\
- & | & \SHIFT & \mbox{(shift)} \\
- & | & \POS{i} & \mbox{(relative positioning)} \\
- & | & \MERGE & \mbox{(merge)} \\[2ex]
- & | & \FOCUS{g_1,\dots,g_n} & \mbox{(absolute positioning)} \\
- & | & \ENDFOCUS & \mbox{(unfocus)} \\[2ex]
- T & : := & & \mbox{(\textbf{tactics})}\\
- & & \SKIP & \mbox{(skip)} \\
- & | & \mathtt{reflexivity} & \\
- & | & \mathtt{apply}~t & \\
- & | & \dots &
-\end{array}
-\]
-
-\subsection{Status}
-
-\[
-\begin{array}{rcll}
- \SWITCH & = & \OPEN~\mathit{goal} ~ | ~ \CLOSED~\mathit{goal} & \\
- \mathit{locator} & = & \INT\times\SWITCH & \\
- \mathit{tag} & = & \BRANCHTAG ~ | ~ \FOCUSTAG \\[2ex]
-
- \xi & = & (\INT\times\alpha)~\LIST& \mbox{(metasenv)} \\
- \Gamma & = & \mathit{locator}~\LIST & \mbox{(context)} \\
- \tau & = & \SWITCH~\LIST & \mbox{(todo)} \\
- \kappa & = & \SWITCH~\LIST & \mbox{(dot's future)} \\[2ex]
-
- \mathit{stack} & = & (\Gamma\times\tau\times\kappa\times\mathit{tag})~\LIST
- \\[2ex]
-
- \mathit{status} & = & \xi\times\mathit{stack} \\
-\end{array}
-\]
-
-\paragraph{Utilities}
-\begin{itemize}
- \item \ZEROPOS: map $g -> 0, \OPEN~g$
- \item \INITPOS: map $g -> i, \OPEN~g$
- \item \ISFRESH: $\OPEN~g, 0 -> true | \_ -> false$
- \item \FILTEROPEN: $G -> \FILTER(\ISOPEN,G)$
- \item \DEEPCLOSE: prende uno stack ed un insieme di goal da chiudere, traversa
- lo stack rimuovendo le occorrenze dei goal da $\tau$ e $\kappa$ e marcandole
- chiuse in $\Gamma$
-\end{itemize}
-
-\paragraph{Invariants}
-\begin{itemize}
- \item $\forall \ENTRY{\Gamma}{\tau}{\kappa}{t}, \forall s \in\tau\cup\kappa,
- \exists g, s = \OPEN~g$ (i goal in $\tau$ e $\kappa$ sono aperti)
- \item la lista dei goal nel metasenv contiene tutti e soli i goal presenti
- sullo stack
- \item lo stack puo' contenere goal duplicati nel caso di uso della select
-\end{itemize}
-
-\subsection{Semantics}
-
-\[
-\begin{array}{rcll}
- \SEMOP{\cdot} & : & C -> \mathit{status} -> \mathit{status} &
- \mbox{(continuationals semantics)} \\
- \TSEMOP{\cdot} & : & T -> \xi -> \SWITCH ->
- \xi\times\GOAL~\LIST\times\GOAL~\LIST & \mbox{(tactics semantics)} \\
-\end{array}
-\]
-
-\[
-\begin{array}{rcl}
- \mathit{apply\_tac} & : & T -> \xi -> \GOAL ->
- \xi\times\GOAL~\LIST\times\GOAL~\LIST
-\end{array}
-\]
-
-\[
-\begin{array}{rlcc}
- \TSEM{T}{\xi}{\OPEN~g} & = & \mathit{apply\_tac}(T,\xi,n) & T\neq\SKIP\\
- \TSEM{\SKIP}{\xi}{\CLOSED~g} & = & \langle \xi, [], [g]\rangle &
-\end{array}
-\]
-
-\[
-\begin{array}{rcl}
-
- \SEM{\TACTIC{T}}{\ENTRY{\GIN}{\tau}{\kappa}{t}::S}
- & =
- & \langle
- \xi_n,
- \ENTRY{\ZEROPOS(G^o_n)}{\tau\setminus G^c_n}{\kappa\setminus G^o_n}{t}
- :: \DEEPCLOSE(G^c_n,S)
- \rangle
- \\[1ex]
-
- \multicolumn{3}{l}{\hspace{\sidecondlen}\mathit{where} ~
- \left\{
- \begin{array}{rcll}
- \langle\xi_0, G^o_0, G^c_0\rangle & = & \langle\xi, [], []\rangle \\
- \langle\xi_{i+1}, G^o_{i+1}, G^c_{i+1}\rangle
- & =
- & \langle\xi_i, G^o_i, G^c_i\rangle
- & s_{i+1}\in G^c_i \\
- \langle\xi_{i+1}, G^o_{i+1}, G^c_{i+1}\rangle
- & =
- & \langle\xi, (G^o_i\setminus G^c)\cup G^o, G^c_i\cup G^c\rangle
- & s_{i+1}\not\in G^c_i \\[1ex]
- & & \mathit{where} ~ \langle\xi,G^o,G^c\rangle=\TSEM{T}{\xi_i}{s_{i+1}}
- \\
- \end{array}
- \right.
- }
- \\[2ex]
-
- \SEM{~\DOT~}{\ENTRY{\Gamma}{\tau}{\kappa}{t}::S}
- & =
- & \langle \xi, \ENTRY{s_1}{\tau}{\GIN[2]\cup\kappa}{t}::S \rangle
- \\[1ex]
- & & \mathrm{where} ~ \FILTEROPEN(\Gamma)=\GIN
- \\[2ex]
-
- \SEM{~\DOT~}{\ENTRY{[]}{\tau}{s::\kappa}{t}::S}
- & =
- & \langle \xi, \ENTRY{\Gamma}{\tau}{\kappa}{t}::S \rangle
- \\[2ex]
-
- \SEM{~\SEMICOLON~}{S} & = & \langle \xi, S \rangle \\[1ex]
-
- \SEM{~\BRANCH~}{\ENTRY{\GIN}{\tau}{\kappa}{t}::S}
- \quad
- & =
- & \langle\xi, \ENTRY{s_1'}{[]}{[]}{\BRANCHTAG}
- ::\ENTRY{[s_2';\cdots;s_n']}{\tau}{\kappa}{t}::S
- \\[1ex]
- & & \mathrm{where} ~ n\geq 2 ~ \land ~ \INITPOS(\GIN)=[s_1';\cdots;s_n']
- \\[2ex]
-
- \SEM{~\SHIFT~}
- {\ENTRY{\Gamma}{\tau}{\kappa}{\BRANCHTAG}::\ENTRY{\GIN}{\tau'}{\kappa'}{t}::S}
- & =
- & \langle
- \xi, \ENTRY{s_1}{[]}{[]}{\BRANCHTAG}
- ::\ENTRY{\GIN[2]}{\tau'\cup\FILTEROPEN(\Gamma)}{\kappa'}{t}::S
- \rangle
- \\[2ex]
-
- \SEM{\POS{i}}
- {\ENTRY{[s]}{[]}{[]}{\BRANCHTAG}::\ENTRY{\Gamma'}{\tau'}{\kappa'}{t'}::S}
- & =
- & \langle \xi, \ENTRY{s_i}{[]}{[]}{\BRANCHTAG}
- ::\ENTRY{s_i :: (\Gamma'\setminus [s_i])}{\tau'}{\kappa'}{t'}::S \rangle
- \\[1ex]
- & & \mathrm{where} ~ \langle i,s'\rangle = s_i\in \Gamma'~\land~\ISFRESH(s)
- \\[2ex]
-
- \SEM{\POS{i}}
- {\ENTRY{\Gamma}{\tau}{\kappa}{\BRANCHTAG}
- ::\ENTRY{\Gamma'}{\tau'}{\kappa'}{t'}::S}
- & =
- & \langle \xi, \ENTRY{s_i}{[]}{[]}{\BRANCHTAG}
- ::\ENTRY{\Gamma'\setminus [s_i]}{\tau'\cup\FILTEROPEN(\Gamma)}{\kappa'}{t'}::S
- \rangle
- \\[1ex]
- & & \mathrm{where} ~ \langle i, s'\rangle = s_i\in \Gamma'
- \\[2ex]
-
- \SEM{~\MERGE~}
- {\ENTRY{\Gamma}{\tau}{\kappa}{\BRANCHTAG}::\ENTRY{\Gamma'}{\tau'}{\kappa'}{t'}
- ::S}
- & =
- & \langle \xi,
- \ENTRY{\tau\cup\FILTEROPEN(\Gamma)\cup\Gamma'\cup\kappa}{\tau'}{\kappa'}{t'}
- :: S
- \rangle
- \\[2ex]
-
- \SEM{\FOCUS{g_1,\dots,g_n}}{S}
- & =
- & \langle \xi, \ENTRY{[\OPEN~g_1;\cdots;\OPEN~g_n]}{[]}{[]}{\FOCUSTAG}::S
- \rangle
- \\[1ex]
- & & \mathrm{where} ~
- \forall ~ i=1,\dots,n,~\exists~\alpha_i,n_i,~\langle n_i,\alpha_i\rangle\in\xi
- \\[2ex]
-
- \SEM{\ENDFOCUS}{\ENTRY{[]}{[]}{[]}{\FOCUSTAG}::S}
- & =
- & \langle \xi, S\rangle \\[2ex]
-
-\end{array}
-\]
+\input{body.tex}
\end{document}
projects / helm.git / blobdiff