788 \section*{Alternatives to CPS}

   789 

   790 While I appreciate that this handout is already pretty long, this

   791 section is for students who think the CPS-translation is too much of

   792 voodoo programming---there is a perhaps simpler alternative. This

   793 alternative is along the lines: if you cannot bridge the gap in

   794 a single step, do it in two simpler steps. Let's look at the

   795 simple expression $1 + (2 + 3)$. The CPS-translation correctly

   796 generates the expression

   797 

   798 \begin{lstlisting}[language=LLVMIR,numbers=left,escapeinside={(*@}{@*)}]

   799 let tmp0 = add 2 3 in   

   800 let tmp1 = add 1 tmp0 in 

   801   return tmp1 

   802 \end{lstlisting}

   803 

   804 \noindent

   805 where $(2 + 3)$ is pulled out and calculated first. The problem is that it

   806 requires a bit of magic. But with the ability to give a separate variable

   807 to each indivifual computation, we could do the following: The expression

   808 $1 + (2 + 3)$ is a tree like this

   809 

   810 \begin{center}

   811 \begin{tikzpicture}[line width=1mm]

   812   \node {root} [grow'=up]

   813     child {node {1}}

   814     child {node[circle,draw] {+}

   815       child {node {2}}

   816       child {node {3}}

   817     };

   818 \end{tikzpicture}

   819 \end{center}

   820 

   821 \noindent

   822 and we could perform a completely standard recursive traversal of the

   823 tree: each inner node gets a new variable and assignment.  

   824 

   825