reduce2($f$;$k$;$i$;${\it as}$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$Case of ${\it as}$; nil $\rightarrow$ $k$ ; $a$.${\it as'}$, rec: $\rightarrow$ $f$($a$,$i$,reduce2($f$;$k$;$i$+1;${\it as'}$))
\\[0ex]\emph{(recursive)}