iclp07 submission
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docs/index/iclp07.tex
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%==============================================================================
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\documentclass{llncs}
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%------------------------------------------------------------------------------
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\usepackage{a4wide}
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\usepackage{float}
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\usepackage{xspace}
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\usepackage{epsfig}
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\usepackage{wrapfig}
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\usepackage{subfigure}
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\renewcommand{\rmdefault}{ptm}
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%------------------------------------------------------------------------------
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\floatstyle{ruled}
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\newfloat{Algorithm}{ht}{lop}
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%------------------------------------------------------------------------------
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\newcommand{\wamcodesize}{scriptsize}
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\newcommand{\code}[1]{\texttt{#1}}
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\newcommand{\instr}[1]{\textsf{#1}}
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\newcommand{\try}{\instr{try}\xspace}
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\newcommand{\retry}{\mbox{\instr{retry}}\xspace}
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\newcommand{\trust}{\instr{trust}\xspace}
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\newcommand{\TryRetryTrust}{\mbox{\instr{try-retry-trust}}\xspace}
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\newcommand{\fail}{\instr{fail}\xspace}
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\newcommand{\jump}{\instr{jump}\xspace}
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\newcommand{\jitiSTAR}{\mbox{\instr{dindex\_on\_*}}\xspace}
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\newcommand{\switchSTAR}{\mbox{\instr{switch\_on\_*}}\xspace}
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\newcommand{\jitiONterm}{\mbox{\instr{dindex\_on\_term}}\xspace}
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\newcommand{\jitiONconstant}{\mbox{\instr{dindex\_on\_constant}}\xspace}
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\newcommand{\jitiONstructure}{\mbox{\instr{dindex\_on\_structure}}\xspace}
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\newcommand{\switchONterm}{\mbox{\instr{switch\_on\_term}}\xspace}
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\newcommand{\switchONconstant}{\mbox{\instr{switch\_on\_constant}}\xspace}
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\newcommand{\switchONstructure}{\mbox{\instr{switch\_on\_structure}}\xspace}
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\newcommand{\getcon}{\mbox{\instr{get\_constant}}\xspace}
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\newcommand{\proceed}{\instr{proceed}\xspace}
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\newcommand{\Cline}{\cline{2-3}}
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\newcommand{\JITI}{demand-driven indexing\xspace}
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%------------------------------------------------------------------------------
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\newenvironment{SmallProg}{\begin{tt}\begin{small}\begin{tabular}[b]{l}}{\end{tabular}\end{small}\end{tt}}
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\newenvironment{ScriptProg}{\begin{tt}\begin{scriptsize}\begin{tabular}[b]{l}}{\end{tabular}\end{scriptsize}\end{tt}}
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\newenvironment{FootProg}{\begin{tt}\begin{footnotesize}\begin{tabular}[c]{l}}{\end{tabular}\end{footnotesize}\end{tt}}
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\newcommand{\TODOcomment}[2]{%
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\stepcounter{TODOcounter#1}%
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{\scriptsize\bf$^{(\arabic{TODOcounter#1})}$}%
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\marginpar[\fbox{
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\parbox{2cm}{\raggedleft
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\scriptsize$^{({\bf{\arabic{TODOcounter#1}{#1}}})}$%
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\scriptsize #2}}]%
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{\fbox{\parbox{2cm}{\raggedright
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\scriptsize$^{({\bf{\arabic{TODOcounter#1}{#1}}})}$%
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\scriptsize #2}}}
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}%
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\newcounter{TODOcounter}
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\newcommand{\TODO}[1]{\TODOcomment{}{#1}}
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%------------------------------------------------------------------------------
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\title{Demand-Driven Indexing of Prolog Clauses}
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\titlerunning{Demand-Driven Indexing of Prolog Clauses}
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\author{V\'{\i}tor Santos Costa\inst{1} \and Konstantinos
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Sagonas\inst{2} \and Ricardo Lopes\inst{1}}
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\authorrunning{V. Santos Costa, K. Sagonas and R. Lopes}
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\institute{
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University of Porto, Portugal
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\and
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National Technical University of Athens, Greece
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}
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\begin{document}
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\maketitle
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\begin{abstract}
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As logic programming applications grow in size, Prolog systems need
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to efficiently access larger and larger data sets and the need for
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any- and multi-argument indexing becomes more and more profound.
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Static generation of multi-argument indexing is one alternative, but
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applications often rely on features that are inherently dynamic
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(e.g., generating hypotheses for ILP data sets during runtime) which
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makes static techniques inapplicable or inaccurate. Another
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alternative, which has not been investigated so far, is to employ
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dynamic schemes for flexible demand-driven indexing of Prolog
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clauses. We propose such schemes and discuss issues that need to be
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addressed for their efficient implementation in the context of
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WAM-based Prolog systems. We have implemented demand-driven indexing
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in two different Prolog systems and have been able to obtain
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non-negligible performance speedups: from a few percent up to orders
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of magnitude. Given these results, we see very little reason for
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Prolog systems not to incorporate some form of dynamic indexing
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based on actual demand. In fact, we see demand-driven indexing as
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the first step towards effective runtime optimization of Prolog
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programs.
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\end{abstract}
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\section{Introduction}
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%=====================
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The WAM~\cite{Warren83}
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\section{Demand-Driven Indexing of Static Predicates} \label{sec:static}
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%=======================================================================
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For static predicates the compiler has complete information about all
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clauses and shapes of their arguments. It is both desirable and
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possible to take advantage of this information at compile time and so
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we treat the case of static predicates separately.
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%
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We will do so with schemes of increasing effectiveness and
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implementation complexity.
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\subsection{A simple WAM extension for any argument indexing}
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%------------------------------------------------------------
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Let us initially consider the case where the predicates to index
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consist only of Datalog facts. This is commonly the case for all
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extensional database predicates where indexing is most effective and
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called for. One such code example is shown in
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Fig.~\ref{fig:carc:facts}. It is a fragment of the well-known machine
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learning dataset \textit{Carcinogenesis}~\cite{SriKinMugSte97-ILP97}.
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These clauses get compiled to the WAM code shown in
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Fig.~\ref{fig:carc:clauses}. Assuming WAM-style, first argument
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indexing, the indexing code that a Prolog compiler generates is shown
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in Fig.~\ref{fig:carc:index}. This code is typically placed before the
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code for the clauses and the \switchONconstant instruction is the
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entry point of predicate. Note that compared to vanilla WAM this
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instruction has an extra argument: the register on the value of which
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we will hash ($r_1$). Also, if the register contains an unbound
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variable instead of a constant then execution will continue with the
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next instruction. The reason for the extra argument and this small
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change in functionality will become apparent soon.
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%------------------------------------------------------------------------------
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\begin{figure}[t]
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\centering
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\subfigure[Some Prolog clauses\label{fig:carc:facts}]{%
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\begin{ScriptProg}
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has\_property(d1,salmonella,p).\\
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has\_property(d1,salmonella\_n,p).\\
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has\_property(d2,salmonella,p). \\
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has\_property(d2,cytogen\_ca,n).\\
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has\_property(d3,cytogen\_ca,p).
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\end{ScriptProg}
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}%
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\subfigure[WAM indexing\label{fig:carc:index}]{%
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\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}[b]{l}
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\switchONconstant $r_1$ 5 $T_1$ \\
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\try $L_1$ \\
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\retry $L_2$ \\
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\retry $L_3$ \\
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\retry $L_4$ \\
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\trust $L_5$ \\
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\\
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\begin{tabular}[b]{r|c@{\ }|l|}
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\Cline
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$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
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\ & d1 & \try $L_1$ \\
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\ & & \trust $L_2$ \\ \Cline
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\ & d2 & \try $L_3$ \\
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\ & & \trust $L_4$ \\ \Cline
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\ & d3 & \jump $L_5$ \\
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\Cline
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\end{tabular}
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\subfigure[Code for the clauses\label{fig:carc:clauses}]{%
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\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}[b]{rl}
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$L_1$: & \getcon $r_1$ d1 \\
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\ & \getcon $r_2$ salmonella \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_2$: & \getcon $r_1$ d1 \\
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\ & \getcon $r_2$ salmonella\_n \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_3$: & \getcon $r_1$ d2 \\
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\ & \getcon $r_2$ salmonella \\
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\ & \getcon $r_3$ p \\
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\ & \proceed \\
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$L_4$: & \getcon $r_1$ d2 \\
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\ & \getcon $r_2$ cytogen\_ca \\
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\ & \getcon $r_3$ n \\
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\ & \proceed \\
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$L_5$: & \getcon $r_1$ d3 \\
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\ & \getcon $r_2$ cytogen\_ca \\
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\ & \getcon $r_3$ p \\
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\ & \proceed
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\subfigure[Any arg indexing\label{fig:carc:jiti_single:before}]{%
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\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}[b]{l}
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\switchONconstant $r_1$ 5 $T_1$ \\
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\jitiONconstant $r_2$ 5 3 \\
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\jitiONconstant $r_3$ 5 3 \\
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\try $L_1$ \\
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\retry $L_2$ \\
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\retry $L_3$ \\
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\retry $L_4$ \\
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\trust $L_5$ \\
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\\
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\begin{tabular}[b]{r|c@{\ }|l|}
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\Cline
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$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
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\ & \code{d1} & \try $L_1$ \\
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\ & & \trust $L_2$ \\ \Cline
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\ & \code{d2} & \try $L_3$ \\
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\ & & \trust $L_4$ \\ \Cline
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\ & \code{d3} & \jump $L_5$ \\
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\Cline
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\end{tabular}
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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}%
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\caption{Part of the Carcinogenesis dataset and WAM code that a byte
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code compiler generates}
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\label{fig:carc}
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\end{figure}
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%------------------------------------------------------------------------------
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The indexing code of Fig.~\ref{fig:carc:index} incurs a small cost for
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the open call (executing the \switchONconstant instruction) but this
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cost pays off for calls where the first argument is bound. On the
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other hand, for calls where the first argument is a free variable and
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some other argument is bound, a choice point will be created, the
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\TryRetryTrust chain will be used, and execution will go through the
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code of all clauses. This is clearly inefficient, more so for larger
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data sets.
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%
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We can do much better with the relatively simple scheme shown in
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Fig.~\ref{fig:carc:jiti_single:before}. Immediately after the
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\switchONconstant instruction, we can generate \jitiONconstant (demand
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indexing) instructions, one for each remaining argument. Recall that
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the entry point of the predicate is the \switchONconstant instruction.
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The \jitiONconstant $r_i$ \instr{N A} instruction works as follows:
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\begin{itemize}
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\item if the argument register $r_i$ is a free variable, then
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execution continues with the next instruction;
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\item otherwise, \JITI kicks in as follows. The abstract machine will
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scan the WAM code of the clauses and create an index table for the
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values of the corresponding argument. It can do so, because the
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instruction takes as arguments the number of clauses \instr{N} to
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index and the arity \instr{A} of the predicate. (In our example, the
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numbers 5 and 3.) For Datalog facts, this information is sufficient.
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Also, because the WAM byte code for the clauses has a very regular
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structure, the index table can be created very quickly. Upon its
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creation, the \jitiONconstant instruction will get transformed to a
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\switchONconstant. Again this is straightforward because of the two
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instructions have similar layouts in memory. Execution will continue
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with the \switchONconstant instruction.
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\end{itemize}
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Figure~\ref{fig:carg:jiti_single:after} shows the index table $T_2$
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which is created for our example and how the indexing code looks after
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the execution of a call with mode \code{(out,in,?)}. Note that the
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\jitiONconstant instruction for argument register $r_2$ has been
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appropriately patched. The call that triggered \JITI and subsequent
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calls of the same mode will use table $T_2$. The index for the second
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argument has been created.
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%------------------------------------------------------------------------------
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\begin{figure}
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\centering
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\begin{sf}
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\begin{\wamcodesize}
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\begin{tabular}{c@{\hspace*{2em}}c@{\hspace*{2em}}c}
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\begin{tabular}{l}
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\switchONconstant $r_1$ 5 $T_1$ \\
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\switchONconstant $r_2$ 5 $T_2$ \\
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\jitiONconstant $r_3$ 5 3 \\
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\try $L_1$ \\
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\retry $L_2$ \\
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\retry $L_3$ \\
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\retry $L_4$ \\
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\trust $L_5$ \\
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\end{tabular}
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&
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\begin{tabular}{r|c@{\ }|l|}
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\Cline
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$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
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\ & \code{d1} & \try $L_1$ \\
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\ & & \trust $L_2$ \\ \Cline
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\ & \code{d2} & \try $L_3$ \\
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\ & & \trust $L_4$ \\ \Cline
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\ & \code{d3} & \jump $L_5$ \\
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\Cline
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\end{tabular}
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&
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\begin{tabular}{r|c@{\ }|l|}
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\Cline
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$T_2$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
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\ & \code{salmonella} & \try $L_1$ \\
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\ & & \trust $L_3$ \\ \Cline
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\ & \code{salmonella\_n} & \jump $L_2$ \\ \Cline
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\ & \code{cytrogen\_ca} & \try $L_4$ \\
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\ & & \trust $L_5$ \\
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\Cline
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\end{tabular}
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\end{tabular}
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\end{\wamcodesize}
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\end{sf}
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\caption{WAM code after demand-driven indexing for argument 2;
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table $T_2$ is generated dynamically}
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\label{fig:carg:jiti_single:after}
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\end{figure}
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%------------------------------------------------------------------------------
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The main advantage of this scheme is its simplicity. The compiled code
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(Fig.~\ref{fig:carc:jiti_single:before}) is not significantly bigger
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than the code which a WAM-based compiler would generate
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(Fig.~\ref{fig:carc:index}) and, even if \JITI turns out unnecessary
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during runtime (e.g. execution encounters only open calls or with only
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the first argument bound), the extra overhead is minimal: the
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execution of some \jitiONconstant instructions for the open call only.
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%
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In short, this is a simple scheme that allows for \JITI on \emph{any
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single} argument. At least for big sets of Datalog facts, we see
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little reason not to use this indexing scheme.
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\paragraph*{Optimizations.}
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Because we are dealing with static code, there are opportunities for
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some easy optimizations. Suppose we statically determine that there
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will never be any calls with \code{in} mode for some arguments or that
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these arguments are not discriminating enough.\footnote{In our example,
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suppose the third argument of \code{has\_property/3} had the atom
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\code{p} as value throughout.} Then we can avoid generating
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\jitiONconstant instructions for them. Also, suppose we detect or
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heuristically decide that some arguments are most likely than others
|
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to be used in the \code{in} mode. Then we can simply place the
|
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\jitiONconstant instructions for these arguments \emph{before} the
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instructions for other arguments. This is possible since all indexing
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instructions take the argument register number as an argument.
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\subsection{From any argument indexing to multi-argument indexing}
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%-----------------------------------------------------------------
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The scheme of the previous section gives us only single argument
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indexing. However, all the infrastructure we need is already in place.
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We can use it to support (fixed-order) multi-argument \JITI in a
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straightforward way.
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Note that the compiler knows exactly the set of clauses that need to
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be tried for each query with a specific symbol in the first argument.
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This information is needed in order to construct, at compile time, the
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||||
hash table $T_1$ of Fig.~\ref{fig:carc:index}. For multi-argument
|
||||
\JITI, instead of generating for each hash bucket only \TryRetryTrust
|
||||
instructions, the compiler can prepend appropriate \JITI instructions.
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We illustrate this on our running example. The table $T_1$ contains
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four \jitiONconstant instructions: two for each of the remaining two
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arguments of hash buckets with more than one alternative. For hash
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buckets with none or only one alternative (e.g., \code{d3}'s bucket)
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there is obviously no need to resort to \JITI for the remaining
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arguments. Figure~\ref{fig:carc:jiti_multi} shows the state of the
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hash tables after the execution of queries
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\code{has\_property(C,salmonella,T)}, which creates table $T_2$, and
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\code{has\_property(d2,P,n)} which creates the $T_3$ table and
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transforms the \jitiONconstant instruction for \code{d2} and register
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$r_3$ to the appropriate \switchONconstant instruction.
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%------------------------------------------------------------------------------
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\begin{figure}[t]
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||||
\centering
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||||
\begin{sf}
|
||||
\begin{\wamcodesize}
|
||||
\begin{tabular}{@{}cccc@{}}
|
||||
\begin{tabular}{l}
|
||||
\switchONconstant $r_1$ 5 $T_1$ \\
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||||
\switchONconstant $r_2$ 5 $T_2$ \\
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||||
\jitiONconstant $r_3$ 5 3 \\
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||||
\try $L_1$ \\
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||||
\retry $L_2$ \\
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||||
\retry $L_3$ \\
|
||||
\retry $L_4$ \\
|
||||
\trust $L_5$ \\
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||||
\end{tabular}
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||||
&
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||||
\begin{tabular}{r|c@{\ }|l|}
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||||
\Cline
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||||
$T_1$: & \multicolumn{2}{c|}{Hash Table Info}\\ \Cline\Cline
|
||||
\ & \code{d1} & \jitiONconstant $r_2$ 2 3 \\
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||||
\ & & \jitiONconstant $r_3$ 2 3 \\
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||||
\ & & \try $L_1$ \\
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||||
\ & & \trust $L_2$ \\ \Cline
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||||
\ & \code{d2} & \jitiONconstant $r_2$ 2 3 \\
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||||
\ & & \switchONconstant $r_3$ 2 $T_3$ \\
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||||
\ & & \try $L_3$ \\
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||||
\ & & \trust $L_4$ \\ \Cline
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||||
\ & \code{d3} & \jump $L_5$ \\
|
||||
\Cline
|
||||
\end{tabular}
|
||||
&
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||||
\begin{tabular}{r|c@{\ }|l|}
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||||
\Cline
|
||||
$T_2$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
|
||||
\ & \code{salmonella} & \jitiONconstant $r_3$ 2 3 \\
|
||||
\ & & \try $L_1$ \\
|
||||
\ & & \trust $L_3$ \\ \Cline
|
||||
\ & \code{salmonella\_n} & \jump $L_2$ \\ \Cline
|
||||
\ & \code{cytrogen\_ca} & \jitiONconstant $r_3$ 2 3 \\
|
||||
\ & & \try $L_4$ \\
|
||||
\ & & \trust $L_5$ \\
|
||||
\Cline
|
||||
\end{tabular}
|
||||
&
|
||||
\begin{tabular}{r|c@{\ }|l|}
|
||||
\Cline
|
||||
$T_3$: & \multicolumn{2}{|c|}{Hash Table Info}\\ \Cline\Cline
|
||||
\ & \code{p} & \jump $L_3$ \\ \Cline
|
||||
\ & \code{n} & \jump $L_4$ \\
|
||||
\Cline
|
||||
\end{tabular}
|
||||
\end{tabular}
|
||||
\end{\wamcodesize}
|
||||
\end{sf}
|
||||
\caption{\JITI for all argument combinations;
|
||||
table $T_1$ is static; $T_2$ and $T_3$ are generated dynamically}
|
||||
\label{fig:carc:jiti_multi}
|
||||
\end{figure}
|
||||
%------------------------------------------------------------------------------
|
||||
|
||||
\paragraph{Implementation issues.}
|
||||
In the \jitiONconstant instructions of Fig.~\ref{fig:carc:jiti_multi}
|
||||
notice the integer 2 which denotes the number of clauses that the
|
||||
instruction will index. Using this number an index table of
|
||||
appropriate size will be created, such as $T_3$. To fill this table we
|
||||
need information about the clauses to index and the symbols to hash
|
||||
on. The clauses can be obtained by scanning the labels of the
|
||||
\TryRetryTrust instructions following \jitiONconstant; the symbols by
|
||||
appropriate byte code offsets (based on the argument register number)
|
||||
from these labels. Thus, multi-argument \JITI is easy to get and the
|
||||
creation of index tables can be extremely fast when indexing Datalog
|
||||
facts.
|
||||
|
||||
\subsection{Beyond Datalog and other implementation issues}
|
||||
%----------------------------------------------------------
|
||||
Indexing on demand clauses with function symbols is not significantly
|
||||
more difficult. The scheme we have described is applicable but
|
||||
requires the following extensions:
|
||||
\begin{enumerate}
|
||||
\item Besides \jitiONconstant we also need \jitiONterm and
|
||||
\jitiONstructure instructions, the \JITI counterparts of the WAM's
|
||||
\switchONterm and \switchONstructure.
|
||||
\item Because the byte code for the clause heads does not necessarily
|
||||
have a regular structure, the abstract machine needs to be able to
|
||||
``walk'' the byte code instructions and recover the symbols on which
|
||||
hashing will be based. Writing such a code walking procedure is not
|
||||
hard.\footnote{In many Prolog systems, a procedure with similar
|
||||
functionality often exists for the disassembler, the debugger, etc.}
|
||||
\item Indexing on an argument that contains unconstrained variables
|
||||
for some clauses can be tricky. Without special treatment, the WAM
|
||||
creates two choice points for this argument (one for the variables
|
||||
and one per each group of clauses). However, this issue is
|
||||
well-known by now. Possible solutions to it are described in a 1987
|
||||
paper by Carlsson~\cite{Carlsson} and can be readily adapted to
|
||||
\JITI. Alternatively, we can skip \JITI for these arguments.
|
||||
\end{enumerate}
|
||||
Before describing \JITI more formally, we remark on the following
|
||||
design decisions whose rationale may not be immediately obvious:
|
||||
\begin{itemize}
|
||||
\item By default, only $T_1$ is generated at compile time (as in the
|
||||
WAM) and the additional index tables $T_2, T_3, \ldots$ are
|
||||
generated dynamically. This is because we do not want to increase
|
||||
compiled code size unnecessarily (i.e., when there is no demand for
|
||||
these indices).
|
||||
\item On the other hand, we generate \jitiSTAR instructions at compile
|
||||
time for the head arguments.\footnote{The \jitiSTAR instructions for
|
||||
the $T_1$ table can be generated either by the compiler or by the
|
||||
loader.} This does not noticeably increase the generated byte code
|
||||
but it greatly simplifies code loading. Notice that a nice property
|
||||
of the scheme we have described is that the loaded byte code can be
|
||||
patched \emph{without} the need to move any instructions.
|
||||
% The indexing tables are typically not intersperced with the byte code.
|
||||
\item Finally, one may wonder why the \jitiSTAR instructions create
|
||||
the dynamic index tables with an additional code walking pass
|
||||
instead of piggy-backing on the pass which examines all clauses via
|
||||
the main \TryRetryTrust chain. Main reasons are: 1) in many cases
|
||||
the code walking can be selective and guided by offsets and 2) by
|
||||
first creating the hash table and then using it we speed up the
|
||||
execution of the queries encountered during runtime and often avoid
|
||||
unnecessary choice point creations.
|
||||
\end{itemize}
|
||||
This is \JITI as we have implemented it.
|
||||
% in one of our Prolog systems.
|
||||
However, we note that these decisions are orthogonal to the main idea
|
||||
and under compiler control. If, for example, analysis determines that
|
||||
some argument sequences will never demand indexing we can simply avoid
|
||||
generation of \jitiSTAR instructions for them. Similarly, if we
|
||||
determine that some argument sequences will definitely demand indexing
|
||||
we can speed up execution by generating the appropriate index tables
|
||||
at compile time instead of dynamically.
|
||||
|
||||
\subsection{Demand-driven index construction and its properties}
|
||||
%---------------------------------------------------------------
|
||||
The idea behind \JITI can be captured in a single sentence: \emph{we
|
||||
can generate every index we need during program execution when this
|
||||
index is demanded}. Subsequent uses of these indices can speed up
|
||||
execution considerably more than the time it takes to construct them
|
||||
(more on this below) so this runtime action makes sense.\footnote{In
|
||||
fact, because choice points are expensive in the WAM, \JITI can speed
|
||||
up even the execution of the query that triggers the process, not only
|
||||
subsequent queries.}
|
||||
%
|
||||
We describe the process of demand-driven index construction.
|
||||
|
||||
% \subsubsection{Demand-driven index construction}
|
||||
%-------------------------------------------------
|
||||
Let $p/k$ be a predicate with $n$ clauses.
|
||||
%
|
||||
At a high level, its indices form a tree whose root is the entry point
|
||||
of the predicate. For simplicity, we assume that the root node of the
|
||||
tree and the interior nodes corresponding to the index table for the
|
||||
first argument have been constructed at compile time. Leaves of this
|
||||
tree are the nodes containing the code for the clauses of the
|
||||
predicate and each clause is identified by a unique label \mbox{$L_i,
|
||||
1 \leq i \leq n$}. Execution always starts at the first instruction of
|
||||
the root node and follows Algorithm~\ref{alg:construction}. The
|
||||
algorithm might look complicated but is actually quite simple.
|
||||
%
|
||||
Each non-leaf node contains a sequence of byte code instructions with
|
||||
groups of the form \mbox{$\langle I_1, \ldots, I_m, T_1, \ldots, T_l
|
||||
\rangle, 0 \leq m \leq k, 1 \leq l \leq n$} where each of the $I$
|
||||
instructions, if any, is either a \switchSTAR or a \jitiSTAR
|
||||
instruction and the $T$ instructions are either a sequence of
|
||||
\TryRetryTrust instructions (if $l > 1$) or a \jump instruction (if
|
||||
\mbox{$l = 1$}). Step~2.2 dynamically constructs an index table $\cal
|
||||
T$ whose buckets are the newly created interior nodes in the tree.
|
||||
Each bucket associated with a single clause contains a \jump
|
||||
instruction to the label of that clause. Each bucket associated with
|
||||
many clauses starts with the $I$ instructions which are yet to be
|
||||
visited and continues with a \TryRetryTrust chain pointing to the
|
||||
clauses. When the index construction is done, the instruction mutates
|
||||
to a \switchSTAR WAM instruction.
|
||||
%-------------------------------------------------------------------------
|
||||
\begin{Algorithm}
|
||||
\caption{Actions of the abstract machine with \JITI}
|
||||
\label{alg:construction}
|
||||
\begin{enumerate}
|
||||
\item if the current instruction $I$ is a \switchSTAR, \try, \retry,
|
||||
\trust or \jump, the action is an in the WAM;
|
||||
\item if the current instruction $I$ is a \jitiSTAR with arguments $r,
|
||||
l$, and $k$ where $r$ is a register then
|
||||
\begin{enumerate}
|
||||
\item[2.1] if register $r$ contains a variable, the action is simply to
|
||||
\instr{goto} the next instruction in the node;
|
||||
\item[2.2] if register $r$ contains a value $v$, the action is to
|
||||
dynamically construct the index as follows:
|
||||
\begin{itemize}
|
||||
\item[2.2.1] collect the subsequent instructions in a list $\cal I$
|
||||
until the next instruction is a \try;\footnote{Note that there
|
||||
will always be a \try following a \jitiSTAR instruction.}
|
||||
\item[2.2.2] for each label $L$ in the \TryRetryTrust chain
|
||||
inspect the code of the clause with label $L$ to find the
|
||||
symbol~$c$ associated with register $r$ in the clause; (This
|
||||
step creates a list of $\langle c, L \rangle$ pairs.)
|
||||
\item[2.2.3] create an index table $\cal T$ out of these pairs as
|
||||
follows:
|
||||
\begin{itemize}
|
||||
\item if $I$ is a \jitiONconstant or a \jitiONstructure then
|
||||
create an index table for the symbols in the list of pairs;
|
||||
each entry of the table is identified by a symbol $c$ and
|
||||
contains:
|
||||
\begin{itemize}
|
||||
\item the instruction \jump $L_c$ if $L_c$ is the only label
|
||||
associated with $c$;
|
||||
\item the sequence of instructions obtained by appending to
|
||||
$\cal I$ a \TryRetryTrust chain for the sequence of labels
|
||||
$L'_1, \ldots, L'_l$ that are associated with $c$
|
||||
\end{itemize}
|
||||
\item if $I$ is a \jitiONterm then
|
||||
\begin{itemize}
|
||||
\item partition the sequence of labels $\cal L$ in the list
|
||||
of pairs into sequences of labels ${\cal L}_c, {\cal L}_l$
|
||||
and ${\cal L}_s$ for constants, lists and structures,
|
||||
respectively;
|
||||
\item for each of the four sequences ${\cal L}, {\cal L}_c,
|
||||
{\cal L}_l, {\cal L}_s$ of labels create code as follows:
|
||||
\begin{itemize}
|
||||
\item the instruction \fail if the sequence is empty;
|
||||
\item the instruction \jump $L$ if $L$ is the only label in
|
||||
the sequence;
|
||||
\item the sequence of instructions obtained by appending to
|
||||
$\cal I$ a \TryRetryTrust chain for the current sequence
|
||||
of labels;
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\end{itemize}
|
||||
\item[2.2.4] transform the \jitiSTAR $r, l, k$ instruction to
|
||||
a \switchSTAR $r, l, \cal T$ instruction; and
|
||||
\item[2.2.5] continue execution with this instruction.
|
||||
\end{itemize}
|
||||
\end{enumerate}
|
||||
\end{enumerate}
|
||||
\end{Algorithm}
|
||||
%-------------------------------------------------------------------------
|
||||
|
||||
Complexity-wise, dynamic index construction does not add any overhead
|
||||
to program execution. First, note that each demanded index table will
|
||||
be constructed at most once. Also, a \jitiSTAR instruction will be
|
||||
encountered only in cases where execution would examine all clauses in
|
||||
the \TryRetryTrust chain.\footnote{This statement is possibly not
|
||||
valid the presence of Prolog cuts.} The construction visits these
|
||||
clauses \emph{once} and then creates the index table in time linear in
|
||||
the number of clauses as one pass over the list of $\langle c, L
|
||||
\rangle$ pairs suffices. After index construction, execution will
|
||||
visit only a subset of these clauses as the index table will be
|
||||
consulted.
|
||||
%% Finally, note that the maximum number of \jitiSTAR instructions
|
||||
%% that will be visited for each query is bounded by the maximum
|
||||
%% number of index positions (symbols) in the clause heads of the
|
||||
%% predicate.
|
||||
Thus, in cases where \JITI is not effective, execution of a query will
|
||||
at most double due to dynamic index construction. In fact, this worst
|
||||
case is extremely unlikely in practice. On the other hand, \JITI can
|
||||
change the complexity of evaluating a predicate call from $O(n)$ to
|
||||
$O(1)$ where $n$ is the number of clauses.
|
||||
|
||||
\subsection{More implementation choices}
|
||||
%---------------------------------------
|
||||
The observant reader has no doubt noticed that
|
||||
Algorithm~\ref{alg:construction} provides multi-argument indexing but
|
||||
only for the outermost symbols of arguments. For clauses with
|
||||
structured terms that require indexing in their subterms we can either
|
||||
employ a compile-time program transformation like \emph{unification
|
||||
factoring}~\cite{Dawson:1995:UFE} or modify the algorithm to consider
|
||||
index positions inside structure symbols. This is relatively easy to
|
||||
do but requires support from the register allocator (passing the
|
||||
subterms of structures in appropriate argument registers) and/or a new
|
||||
set of instructions. Due to space limitations we omit further details.
|
||||
|
||||
Algorithm~\ref{alg:construction} relies on a procedure that inspects
|
||||
the code of a clause and collects the symbols associated with some
|
||||
particular index position (step~2.2.2). At the cost of increased
|
||||
implementation complexity, this step can of course take into account
|
||||
other information that may exist in the body of the clause (e.g., type
|
||||
tests such as \code{var(X)}, \code{atom(X)}, aliasing constraints such
|
||||
as \code{X = Y}, numeric constraints \code{X > 0}, etc).
|
||||
|
||||
A reasonable concern for \JITI is increased memory consumption due to
|
||||
the index tables. In our experience, this does not seem to be a
|
||||
problem in practice since most applications do not have demand for
|
||||
indexing on all argument combinations. In applications where it
|
||||
becomes a problem or when running in an environment where memory is
|
||||
limited, we can easily put a bound on the size of index tables, either
|
||||
globally or for each predicate. The \jitiSTAR instructions can either
|
||||
become inactive when this limit is reached, or better yet we can
|
||||
recover the space of some tables. We can employ any standard recycling
|
||||
algorithm (e.g., least recently used) and reclaim the space for some
|
||||
tables that are no longer in use. This is easy to do by reverting the
|
||||
corresponding \jitiSTAR instructions back to \switchSTAR instructions.
|
||||
If the indices are needed again, they can simply be regenerated.
|
||||
|
||||
|
||||
\section{Demand-Driven Indexing of Dynamic Predicates} \label{sec:dynamic}
|
||||
%=========================================================================
|
||||
|
||||
|
||||
\section{Performance Evaluation} \label{sec:perf}
|
||||
%================================================
|
||||
|
||||
|
||||
\section{Related Work} \label{sec:related}
|
||||
%=========================================
|
||||
\begin{itemize}
|
||||
\item Indexing in Prolog systems.
|
||||
\item Trees and tries. Unification factoring.
|
||||
\item Comparison with static analysis techniques and Mercury.
|
||||
\item Alternative: interface with a DB system?
|
||||
\item Just-In-Time and dynamic compilation techniques (VITOR, IS THERE
|
||||
ANYTHING FOR PROLOG?)
|
||||
\end{itemize}
|
||||
|
||||
|
||||
\section{Concluding Remarks}
|
||||
%===========================
|
||||
|
||||
|
||||
%==============================================================================
|
||||
\bibliographystyle{splncs}
|
||||
\bibliography{lp}
|
||||
%==============================================================================
|
||||
|
||||
\end{document}
|
||||
Reference in New Issue
Block a user