Complete development of a lambda term ($M^{\bullet }$)

Define $x^{\bullet }=x$, $(\lambda x.M{)}^{\bullet }=\lambda x.M^{\bullet }$, and develop an application by contracting its root when that root is syntactically a beta-redex: $((\lambda x.M)N{)}^{\bullet }=M^{\bullet }[x:=N^{\bullet }]$. Otherwise $(MN{)}^{\bullet }=M^{\bullet }{N}^{\bullet }$. Newly created root redexes need not be contracted. Induction with the substitution lemma proves that if $M\Rightarrow N$, then $N\Rightarrow M^{\bullet }$. Thus any two parallel reducts share this reduct.