Truth, Falsehood, and Equality（真、假和等价）

Truth, Falsehood, and Equality（真、假和等价）

Two last bits of basic knowledge you need to get under your belt are Common Lisp’s notion of truth and falsehood and what it means for two Lisp objects to be “equal.” Truth and falsehood are—in this realm—straightforward: the symbol NIL is the only false value, and everything else is true. The symbol T is the canonical true value and can be used when you need to return a non-NIL value and don’t have anything else handy. The only tricky thing about NIL is that it’s the only object that’s both an atom and a list: in addition to falsehood, it’s also used to represent the empty list. This equivalence between NIL and the empty list is built into the reader: if the reader sees (), it reads it as the symbol NIL. They’re completely interchangeable. And because NIL, as I mentioned previously, is the name of a constant variable with the symbol NIL as its value, the expressions nil, (), 'nil, and '() all evaluate to the same thing—the unquoted forms are evaluated as a reference to the constant variable whose value is the symbol NIL, but in the quoted forms the QUOTE special operator evaluates to the symbol directly. For the same reason, both t and 't will evaluate to the same thing: the symbol T.

最后两个需要了解的基本知识是 Common Lisp 对于真和假的表示法以及两个 Lisp 对象“等价”的含义。真和假的含义在这里是直截了当的：符号 NIL 是唯一的假值，其他所有的都是真值。符号T是标准的真值，可被用于需要返回一个非 NIL 值却又没有其他值可用的情况。关于 NIL，唯一麻烦的一点是，它是唯一一个既是原子又是列表的对象：除了用来表示假以外，它还被用来表示空列表。这种 NIL 和空列表的等价性被内置在读取器之中：如果读取器看到了 ()，它将作为符号 NIL 读取它。它们是完全可以互换的。并且如同我前面提到的那样，因为 NIL 是一个以符号 NIL 作为其值的常值变量名，所以表达式 nil、()、 'nil 以及 '() 求值结果——未引用形式将被看出是对值为符号 NIL 的常值变量的引用未进行求值，而在引用形式中 QUOTE 特殊操作符将直接求解出符号 NIL。基于同样的理由，t 和 't 的求值结果也完全相同：符号 T。

Using phrases such as “the same thing” of course begs the question of what it means for two values to be “the same.” As you’ll see in future chapters, Common Lisp provides a number of type-specific equality predicates: = is used to compare numbers, CHAR= to compare characters, and so on. In this section I’ll discuss the four “generic” equality predicates—functions that can be passed any two Lisp objects and will return true if they’re equivalent and false otherwise. They are, in order of discrimination, EQ, EQL, EQUAL, and EQUALP.

使用诸如完全相同这样的术语，理所当然会引申出关值“等价”的这个问题上。在后面的章节里将会看到，Common Lisp 提供了许多特定于类型的等价谓词：= 用来比较数字，CHAR= 用来比较字符，依此类推。本节将讨论四个“通用”等价谓词——这些函数可以被传入任何两个 Lisp 对象，然后当它们等价时返回真，否则返回假。按照介绍的顺序，它们是 EQ、EQL、EQUAL 和 EQUALP。

EQ tests for “object identity”—two objects are EQ if they’re identical. Unfortunately, the object identity of numbers and characters depends on how those data types are implemented in a particular Lisp. Thus, EQ may consider two numbers or two characters with the same value to be equivalent, or it may not. Implementations have enough leeway that the expression (eq 3 3) can legally evaluate to either true or false. More to the point, (eq x x) can evaluate to either true or false if the value of x happens to be a number or character.

EQ 用来测试“对象标识”，只有当两个对象相同时才是 EQ 等价的。不幸的是，数字和字符的对象标识取决于这些数据类型在特定 Lisp 平台上实现的方式。带有相同值的两个数字或字符可能会被 EQ 认为是等价的也可能会是不等价的。语言实现者有足够的空间让表达式 (eq 3 3) 被合法地求值成无论真还是假。更有甚者 (eq x x) 可能有时求值为真，有时为假——如果 x 恰好是数字或字符。

Thus, you should never use EQ to compare values that may be numbers or characters. It may seem to work in a predictable way for certain values in a particular implementation, but you have no guarantee that it will work the same way if you switch implementations. And switching implementations may mean simply upgrading your implementation to a new version—if your Lisp implementer changes how they represent numbers or characters, the behavior of EQ could very well change as well.

因此，你应该永远不要将 EQ 用于比较可能是数字或字符的值上。在个别实现的特定值上，它可能会以一种可预测的方式工作，但如果切换语言实现，则它将不保证以相同的方式工作。而切换实现可能意味着只是简单地把实现升级到一个新版本——而如果 Lisp 实现者改变了表示数字或字符的方式，那么 EQ 的行为也将很有可能发生改变。

Thus, Common Lisp defines EQL to behave like EQ except that it also is guaranteed to consider two objects of the same class representing the same numeric or character value to be equivalent. Thus, (eql 1 1) is guaranteed to be true. And (eql 1 1.0) is guaranteed to be false since the integer value 1 and the floating-point value are instances of different classes.

因此，Common Lisp 定义了 EQL 来获得与 EQ 相似的行为，除此之外，它也可以保证当相同类型的两个对象表示相同的数字或字符值时，它们是等价的。因此，(eql 1 1) 能被确保是真。而 (eql 1 1.0) 则被确保是假，因为整数值 1 和浮点数 1.0 是不同类型的对象。

There are two schools of thought about when to use EQ and when to use EQL: The “use EQ when possible” camp argues you should use EQ when you know you aren’t going to be com-paring numbers or characters because (a) it’s a way to indicate that you aren’t going to be comparing numbers or characters and (b) it will be marginally more efficient since EQ doesn’t have to check whether its arguments are numbers or characters.

关于何时使用 EQ 以及何时使用 EQL，这里有两种观点：“凡有可能就用 EQ” 阵营认为，当知道不存在比较数字或字符时就应该使用 EQ，他们认为 (a) 这是一种说明你不在比较数字或字符的方式，以及 (b) 因为 EQ 不需要检查它的参数是否为数字或字符，所以它将会稍微更有效率。

The “always use EQL“ camp says you should never use EQ because (a) the potential gain in clarity is lost because every time someone reading your code—including you—sees an EQ, they have to stop and check whether it’s being used correctly (in other words, that it’s never going to be called upon to compare numbers or characters) and (b) that the efficiency difference between EQ and EQL is in the noise compared to real performance bottlenecks.

但 “总是使用 EQL” 阵营则认为永远不该使用 EQ，因为 (a) 每次有人（包括你自己在内）阅读你的代码时看到了一个 EQ，就得停下来检查它是否被正确使用了（换句话说，它永远不该被用来比较数字或字符），这样就会损失潜在的代码清晰性，以及 (b) EQ 和 EQL 之间的效率差异相比于实际的性能瓶颈来说微不足道。

The code in this book is written in the “always use EQL“ style.

本书中的代码是以 “总是使用 EQL” 风格写成的。

The other two equality predicates, EQUAL and EQUALP, are general in the sense that they can operate on all types of objects, but they’re much less fundamental than EQ or EQL. They each define a slightly less discriminating notion of equivalence than EQL, allowing different objects to be considered equivalent. There’s nothing special about the particular notions of equivalence these functions implement except that they’ve been found to be handy by Lisp programmers in the past. If these predicates don’t suit your needs, you can always define your own predicate function that compares different types of objects in the way you need.

另外两个等价谓词 EQUAL 和 EQUALP 更为通用，因为它们可以操作在所有类型的对象上，但又不像 EQ 或 EQL 那样基础。它们每个都定义了相比 EQL 稍微宽松一些的等价性，允许认为不同的对象是等价的。除了它们曾经被过去的 Lisp 程序员认为是有用的之外。如果由这些函数所实现的特殊含义的等价性没有什么特别的，这些谓词不能满足需要，也可以自己定义谓词函数，以自己所需方式来比较不同类型对象。

EQUAL loosens the discrimination of EQL to consider lists equivalent if they have the same structure and contents, recursively, according to EQUAL. EQUAL also considers strings equivalent if they contain the same characters. It also defines a looser definition of equivalence than EQL for bit vectors and pathnames, two data types I’ll discuss in future chapters. For all other types, it falls back on EQL.

EQUAL 相比 EQL 的宽松之处在于,它将在归相上具有同结构和内容的列表视为等价。EQUAL 也认为含有相同字符的字符串是等价的，它对于位向量和路径名也定义了比 EQL 更加宽松的等价性，我将在未来的章节里讨论这两个数据类型。对于所有其他类型，它回退到 EQL 的水平上。

EQUALP is similar to EQUAL except it’s even less discriminating. It considers two strings equivalent if they contain the same characters, ignoring differences in case. It also considers two characters equivalent if they differ only in case. Numbers are equivalent under EQUALP if they represent the same mathematical value. Thus, (equalp 1 1.0) is true. Lists with EQUALP elements are EQUALP; likewise, arrays with EQUALP elements are EQUALP. As with EQUAL, there are a few other data types that I haven’t covered yet for which EQUALP can consider two objects equivalent that neither EQL nor EQUAL will. For all other data types, EQUALP falls back on EQL.

EQUALP 甚至更加宽松它和 EQUAL 是相似的。它在考察两个含有相同字符的字符串的等价性时忽略了大小写的区别。它还认为如果两个字符只在大小写上有区别，那么它们就是等价的。只要数字表示相同的数学意义上的值，它们 EQUALP 下面就是等价的。因此，(equalp 1 1.0) 是真的。由 EQUALP 等价的元素所组成的列表也是 EQUALP 等价的。同样地，带有 EQUALP 元素的数组也是 EQUALP 等价的。和 EQUAL 一样，还有一些我尚未涉及的其他数据类型，EQUALP 可认为两个对象是等价的，但 EQL 或 EQUAL 则不会。对于所有的其他数据类型，EQUALP 回退到 EQL 的水平上。