derive.tex

\section{Derived expression types}
\label{derivedsection}

This section gives rewrite rules for the derived expression types.  By
the application of these rules, any expression can be reduced to a
semantically equivalent expression in which only the primitive
expression types (literal, variable, call, \ide{lambda}, \ide{if}) occur.

\newcommand{\iet}{\hbox to 2em{\hfil $\equiv$}}  % is equivalent to

\begin{schemenoindent}
(cond (\hyper{test} \hyper{expression})
      \hyperii{clause} \dotsfoo)
\iet  (if \hyper{test}
          (\hyper{expression})
          (cond \hyperii{clause} \dotsfoo))

(cond (else \hyper{expression}))
\iet  (\hyper{expression})

(cond)
\iet  \hyper{some expression returning an unspecified value}
\end{schemenoindent}

\begin{schemenoindent}
(and)         \=\iet  \schtrue
(and \hyper{test})\>\iet  \hyper{test}
(and \hyperi{test} \hyperii{test} \dotsfoo)
\iet  (if \hyperi{test} (and \hyperii{test} \dotsfoo) \schfalse{})

(or)          \>\iet  \schfalse
(or \hyper{test})\>\iet  \hyper{test}
(or \hyperi{test} \hyperii{test} \dotsfoo)
\iet  (if \hyperi{test} \hyperi{test} (or \hyperii{test} \dotsfoo))

(let ((\hyperi{variable} \hyperi{init}) \dotsfoo)
  \hyper{body})
\iet  ((lambda (\hyperi{variable} \dotsfoo) \hyper{body}) \hyperi{init} \dotsfoo)
\end{schemenoindent}

%Since expressions have no side effects, the value of test1 in the expansion
%for "or" only needs to be calculated once.