compose{-}fpf($a$;$b$;$f$) $\,\equiv$$_{\mbox{\scriptsize def}}$$\;\;$$\langle$mapfilter($\lambda$$x$.outl($a$($x$));$\lambda$$x$.isl($a$($x$));fpf{-}domain($f$))$,\,$2of($f$)$\,\circ\,$$b$$\rangle$