# 自由变量和约束变量

## 例子

${\displaystyle \sum _{x=1}^{10}f(x,y),}$

${\displaystyle \sum _{y=1}^{10}f(x,y),}$

${\displaystyle \int _{0}^{\infty }x^{y-1}e^{-x}\,dx,}$

${\displaystyle \lim _{h\rightarrow 0}{\frac {f(x+h)-f(x)}{h}},}$

${\displaystyle \forall x\ \exists y\ \varphi (x,y,z),}$

### 变量约束算子

${\displaystyle \sum _{x=1}^{10}\qquad \qquad \int _{0}^{\infty }\cdots \,dx\qquad \qquad \lim _{x\to 0}\qquad \qquad \forall x}$

## 形式解释

${\displaystyle \forall x\,(\exists y\,A(x)\vee B(z))}$

${\displaystyle (x_{1},\ldots ,x_{n})\mapsto \operatorname {t} }$

λ演算中，如果x是项M = λ x. T中的约束变量，而且是T中的自由变量，则我们称x在M中是约束的，在T中是自由的。如果T包含一个子项 λ x . U，则x在这个项中是再约束的。这种嵌套的、内层的x的约束被称为外层约束的“阴影”。 x在U中的出现是新x的自由出现。

## 引用

A small part of this article was originally based on material from the Free On-line Dictionary of Computing and is used with permission under the GFDL. Most of what now appears here is the result of later editing.