The wish to consider rewriting systems with bound variables emerges natually.The various equations with bound variables that are present in both logic and mathematics give rise to rewrite rules as soon as they are oriented.The #beta#-axiom of lambda-calculus is oriented as (#lambda#x.M)N -> M[x:=N].The so-obtained rewriting system was used to provide consistency proofs Another well-known equation with bound variables is the axiom for #um#-recursion.Its usual orientation gives rise to the rewrite rule #um#x.M -> M[x:=#um#x.M].Equivalences in logic may contain bound variables like in x.P(x)<->x. P(x).
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机译：考虑使用绑定变量的重写系统的愿望自然而然地出现了。逻辑和数学中都存在的带有绑定变量的各种方程式一经定向，便产生了重写规则.lambda-演算的＃beta＃公理被定向。如（＃lambda＃xM）N-> M [x：= N]。如此获得的重写系统用于提供一致性证明。另一个著名的带有绑定变量的方程式是＃um＃-递归的公理。方向引起了重写规则＃um＃xM-> M [x：=＃um＃xM]。逻辑上的等价项可能包含绑定变量，例如xP（x）<-> x。 P（x）。
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