Paragraph citing theory of tables (#16)

Author: ajreynol

language/references.bib

@@ -43,3 +43,10 @@ @article{oracles
   pages     = {693--726},
   year      = {2017}
 }
+@article{theoryOfTables,
+author = {Reynolds, Andrew and Wang, Chenlong},
+year = {2021},
+pages = {},
+title = {Proposal for a Theory of Tables},
+howpublished = {\url{https://github.com/SyGuS-Org/docs}},
+}

language/sygus.tex

@@ -1741,8 +1741,33 @@ \subsubsection{Other Theories}
 In this section, we mention theories that are of interest to synthesis applications
 that are not included in the SMT-LIB standard.
 
-\paragraph{Tables}
-TODO
+\paragraph{Bags and Tables}
+An SMT-LIB compliant theory of tables is proposed in~\cite{theoryOfTables}.
+We give the salient details of this theory here.
+
+The theory of tables is implemented as an extension of a theory of bags (multisets).
+The signature of this theory includes all sorts of the form
+$\texttt{(Bag\ T)}$
+for all sorts $\texttt{T}$. 
+This sort denotes bags (i.e. multisets) of elements of sort $\texttt{T}$.
+The theory of bags includes a multitude of operators for e.g.
+taking unions, intersections and differences of bags,
+as well as higher-order operators like 
+$\texttt{map}$, $\texttt{fold}$ and $\texttt{partition}$.
+A \emph{table} is a bag whose element sort $T$ is a tuple,
+where a tuple is a parametric sort taking $n$ types corresponding to the
+types of the elements that comprise the tuple.
+For example, $\texttt{(Tuple\ Int\ Int)}$ denotes tuples
+of arity two.
+The sort $\texttt{(Table\ Int\ Int)}$ is syntax sugar for
+$\texttt{(Bag\ (Tuple\ Int\ Int))}$ and is used to denote tables with two integer
+columns.
+A table value is a multiset union of tuple values.
+The number of rows in a table value is equal to its cardinality.
+Notice that ordering of rows is not semantically captured,
+and thus not modelled in this theory.
+For further details on the complete signature and semantics of this
+theory is available in~\cite{theoryOfTables}.
 
 \subsection{Features and Feature Sets}
 \label{ssec:feature-sets}

tableTheory/tableTheory.tex

@@ -55,7 +55,7 @@
 
 \begin{document}
 
-\title{Proposal for Theory of Tables}
+\title{Proposal for a Theory of Tables}
 
 \author{Andrew Reynolds \and Chenglong Wang}