  Let $\pi\colon T\times X\rightarrow X$ with phase map $(t,x)\mapsto tx$,
denoted $(\pi,T,X)$, be a \textit{semiflow} on a compact Hausdorff space $X$
with phase semigroup $T$. If each $t\in T$ is onto, $(\pi,T,X)$ is called
surjective; and if each $t\in T$ is 1-1 onto $(\pi,T,X)$ is called invertible
and in latter case it induces $\pi^{-1}\colon X\times T\rightarrow X$ by
$(x,t)\mapsto xt:=t^{-1}x$, denoted $(\pi^{-1},X,T)$. In this paper, we show
that $(\pi,T,X)$ is equicontinuous surjective iff it is uniformly distal iff
$(\pi^{-1},X,T)$ is equicontinuous surjective. As applications of this theorem,
we also consider the minimality, distality, and sensitivity of $(\pi^{-1},X,T)$
if $(\pi,T,X)$ is invertible with these dynamics. We also study the pointwise
recurrence and Gottschalk's weak almost periodicity of $\mathbb{Z}$-flow with
compact zero-dimensional phase space.
