Add 14 examples for THF10.

code_table2.tex

+\lstset{language=[Objective]Caml,columns=fixed,basicstyle=\linespread{0.43}\ttfamily\scriptsize,aboveskip=-0.5em,belowskip=-1em,xleftmargin=-0.5em}
+\begin{table}
+  {\scriptsize
+    \begin{tabular}{|@{\,}c@{\,}|p{0.54\textwidth}@{}|@{\,}p{0.41\textwidth}@{\,}|}
+      \hline
+                             & Code                    & Inferred type            \\
+      %    \hline
+      \hline
+      1                      &
+      \begin{lstlisting}
+(* Assumes: add1 : Int -> Int *)
+let example1 = fun (x:Any) ->
+     if x is Int then add1 x else 0
+\end{lstlisting} & \vfill
+      $\Int \to \Int$
+      \\\hline
+      2                      &
+      \begin{lstlisting}
+(* Assumes strlen: String -> Int *)
+ let example2 = fun (x:String|Int) ->
+  if x is Int then add1 x else strlen x
+\end{lstlisting} & \vfill
+      $(\Int \to \Int) \land (\String \to \Int)$                                  \\\hline
+      3                      & \begin{lstlisting}
+let example3 = fun (x: Any) ->
+    if x is (Any \ False) then (x,x) else false  \end{lstlisting}  & \smallskip
+      $(\False \to \False) \land (\lnot \False \lnot (\lnot \False,\lnot\False))$
+      \\\hline
+      4                      &
+      \begin{lstlisting}
+(*Uses `is_int` from Table 1.3 and `or_` from Table 1.5,
+  assumes f : (Int|String) -> Int *)
+let is_string = fun (x : Any) ->
+  if x is String then true else false
+
+let example4 = fun (x : Any) ->
+   if or (is_int x) (is_string x) is True then x else 'A'
+
+ \end{lstlisting} & \vfill
+  $(\String\to\Keyw{True})\land(\lnot\String\to\Keyw{False})$\newline
+  ~\newline
+  $(\Int \to \Int) \land  (\String \to \String)  \land$\newline
+  $(\lnot \Int \to (\String \lor \Keyw{'A'})) \land $\newline
+  $(\lnot \String \to (\Int \lor \Keyw{'A'})) \land $\newline  
+  $(\lnot(\String \lor \Int) \to \Keyw{'A'})$
+               \\\hline
+      5                      &
+      \begin{lstlisting}
+(*Uses `and_` from Table 1.6,
+  assumes strlen : String -> Int *)
+let example5 = fun (x : Any) -> fun (y : Any) ->
+   if and_ (is_int x) (is_string y) is True then
+    add x (strlen y) else 0
+\end{lstlisting}
+                             & \smallskip\vfill
+$(\Int \to \String \to \Int) \land (\Int \to \lnot \String \to 0))~\land$\newline
+$(\lnot \Int \to \String \to 0) \land (\lnot \String \to 0)$ 
+      \\\hline
+      6                      &
+\begin{lstlisting}
+let example6 = fun (x : Int|String) -> fun (y : Any) ->
+if and_ (is_int x) (is_string y) is True then
+  add x (strlen y) else strlen x
+\end{lstlisting}
+                             & \vfill 
+Type error for \texttt{strlen x},
+\texttt{x} has type $\Int\lor\String$. \\\hline
+      7                      &
+      \begin{lstlisting}
+let example7 = fun (x : Any) -> fun (y : Any) ->
+if  
+ (if (is_int x) is True then (is_string y) else false)
+  is True then
+  add x (strlen y) else 0
+\end{lstlisting} &
+$(\Int \to \String \to \Int) \land (\Int \to \lnot \String \to 0))~\land$\newline
+$(\lnot \Int \to \String \to 0) \land (\lnot \String \to 0)$ 
+(identical to example 5)
+      \\\hline
+ 8 & \begin{lstlisting}
+let example8 = fun (x : Any) ->
+ if or_ (is_int x) (is_string x) is True then true else false
+\end{lstlisting}  &
+$(\Int \to \True)\land(\String \to \True)~\land$\newline
+$(\lnot(\String\lor\Int)\to \False)$
+      \\\hline
+ 9    &
+      \begin{lstlisting}
+let example9 = fun (x : Any) -> 
+if 
+  (if is_int x is True then is_int x else is_string x)
+  is True then  f x else 0
+\end{lstlisting} &
+$(\Int \to \Int) \land (\String \to \Int)~\land$\newline
+$(\lnot (\String\lor\Int)\to 0)$
+      \\\hline
+10   & \begin{lstlisting}
+let example10 = fun (p : (Any,Any)) ->
+  if is_int (fst p) is True then add1 (fst p) else 7
+\end{lstlisting} & \vfill
+$((\Int,\Any) \to \Int) \land ((\lnot (\Int,\Any) \to 7)$
+      \\\hline
+      11                     & \begin{lstlisting}
+let example11 = fun (p : (Any, Any)) ->
+  if and_ (is_int (fst p)) (is_int (snd p)) is True
+  then g p else no   
+\end{lstlisting} & \vfill\medskip\smallskip
+   $((\Int, \Int) \to \Int) \land
+    (((\Any, \lnot \Int)\lor(\lnot Int, \Any))\to\Keyw{no})$
+      \\\hline
+      12                     & \begin{lstlisting}
+let example12 =
+   fun (p : (Any, Any)) ->
+   if is_int (fst p) is True then true else false
+\end{lstlisting} & \vfill
+$((\Int,\Any) -> \True) \land ((\lnot \Int,\Any) -> \False) )$
+      \\\hline
+      13                     & \begin{lstlisting}
+let example13 = fun (x : Any) -> fun (y : Any) ->
+  if and_ (is_int x) (is_string y) is True then 1
+  else if is_int x is True then 2
+  else 3
+\end{lstlisting} & \vfill
+$(\Int \to \String \to 1) \land (\Int \to \lnot\String \to 2)) \land$\newline
+$(\lnot \Int \to Any \to 3)$
+              \\\hline
+14   & \begin{lstlisting}
+let example14_alt = fun (input : Int | String) ->
+ fun (extra : (Any, Any)) ->
+  if (input, is_int (fst extra)) is (Int, True) then
+     add input (fst extra)
+  else if (input, is_int (fst extra)) is (Any,True) 
+  then add (strlen input) (fst extra)
+  else 0 \end{lstlisting}
+  & \vfill
+  $(\Int \to (\Int,\Any) \to \Int) ~\land~
+  (\Int \to (\lnot \Int, \Any) \to 0) ~\land~$\newline
+  $(\String \to (\Int,\Any) \to \Int) ~\land~
+  (\String \to (\lnot \Int, \Any) \to 0)$
+  \\\hline
+    \end{tabular}
+  }
+  \caption{Comparison with the 14 examples of \cite{THF10}}
+  \ifsubmission%
+    \svvspace{-10mm}
+  \fi%
+  \label{tab:implem2}
+\end{table}

practical.tex

@@ -33,6 +33,9 @@ anonymized
 online toplevel available at
 \url{https://occtyping.github.io/}%
 \input{code_table}
+
+\input{code_table2}
+
 In Table~\ref{tab:implem}, the second column gives a code fragment and the third
 column the type deduced by our implementation. Code~1 is a
 straightforward function similar to our introductory example \code{foo} in (\ref{foo},\ref{foo2}). Here the