深入解析Python中的lambda表达式的用法
普通的数学运算用这个纯抽象的符号演算来定义，计算结果只能在脑子里存在。所以写了点代码，来验证文章中介绍的演算规则。
我们来验证文章里介绍的自然数及自然数运算规则。说到自然数，今天还百度了一下，据度娘说，1993年后国家规定0是属于自然数。先定义自然数及自然数的运算规则：
用lambda表达式定义自然数（邱齐数）
0 := λf.λx.x 1 := λf.λx.f x 2 := λf.λx.f (f x) 3 := λf.λx.f (f (f x)) ...
上面定义直观的意思就是数字n, 是f(x)的n阶函数。1就是f(x), 2就是f(f(x))....，严格来说，这样表述并不准确。其实每个邱奇数都是一个二阶函数，它有两个变量f和x。用二元命名函数来表达就是：
0 -> num0(f,x)=x 1 -> num1(f, x)=f(x) 2 -> num2(f,x)=f(f(x)) 3 -> num3(f,x)=f(f(f(x))) ...
其中参数f是一个函数。这一段有点绕，但是不能理解这个，对后面的lambda演算理解会比较困难。
首先用递归法，定义邱齐数（自然数）
0是自然数， 度娘说1993年后，国家规定0是属于自然数。
每个自然数，都有一个后续。
用代码表达就是：
NUM0=lambda f: lambda x:x SUCC=lambda n: lambda f: lambda x: f(n(f)(x))
后面则是定义运算符，包括加法，乘法，减法和幂。维基文章里没有介绍除法，估摸着除法定义比较复杂，一时讲不清楚。那我们也不验证了。
################################################ #define number calculus rules ################################################ #define Church numeral inductively. #0 := λf.λx.x #1 := λf.λx.f x #2 := λf.λx.f (f x) #3 := λf.λx.f (f (f x)) #... NUM0=lambda f: lambda x:x SUCC=lambda n: lambda f: lambda x: f(n(f)(x)) #define Operator PLUS=lambda m: lambda n: m(SUCC)(n) MULT= lambda m: lambda n: m(PLUS(n))(NUM0) #define predecessor to obtain the previous number. PRED= lambda n: lambda f: lambda x: n(lambda g: lambda h: h(g(f)))(lambda u:x)(lambda u:u) SUB=lambda m: lambda n: n(PRED)(m) POW=lambda b: lambda e: e(b)
定义完了什么是自然数和自然数的运算子。那么自然数的运算，就可以用lambda演算的方式计算了。
问题是上面的定义都是抽象的符号演算，我们需要有一个编码器来把上面的抽象的Church numeral符号编码成可以人来阅读的形式，还需把人输入的数字解码成抽象符号。
################################################
#create encoder to input/output Church numeral
################################################
class LambdaEncoding:
@staticmethod
def encoding(exp,encoder):
return encoder().encoding(exp)
@staticmethod
def decoding(s, decoder):
return decoder().decoding(s)
class NumEncoder:
def encoding(self,num):
f=lambda x:x+1
return str(num(f)(0))
def decoding(self,s):
n=int(s)
num=NUM0
for i in range(n):
num=SUCC(num)
return num
嗯，有了编码器，就可以方便的来验证了。
################################################
#calculus demo
################################################
print("demo number calculus.\n"
"don't input large number,"
"it will cause to exceed maximum recursion depth!\n")
n1=input('input a number: ')
n2=input('input anohter number: ')
#decode string to Church numeral
num1=LambdaEncoding.decoding(n1,NumEncoder)
num2=LambdaEncoding.decoding(n2,NumEncoder)
#add
result=PLUS(num1)(num2)
print('{0} + {1} = {2}'.format(
n1,
n2,
LambdaEncoding.encoding(result, NumEncoder)))
#mult
result=MULT(num1)(num2)
print('{0} X {1} = {2}'.format(
n1,
n2,
LambdaEncoding.encoding(result, NumEncoder)))
#sub
result=SUB(num1)(num2)
print('{0} - {1} = {2}'.format(
n1,
n2,
LambdaEncoding.encoding(result, NumEncoder)))
#POW
result=POW(num1)(num2)
print('{0} ^ {1} = {2}'.format(
n1,
n2,
LambdaEncoding.encoding(result, NumEncoder)))
测试结果如下：
>>> demo number calculus. don't input large number,it will cause to exceed maximum recursion depth! input a number: 4 input anohter number: 3 4 + 3 = 7 4 X 3 = 12 4 - 3 = 1 4 ^ 3 = 64 >>>
神奇吧。
lambda和def的区别
python lambda是在python中使用lambda来创建匿名函数，而用def创建的方法是有名称的，除了从表面上的方法名不一样外，python lambda还有哪些和def不一样呢？
1 python lambda会创建一个函数对象，但不会把这个函数对象赋给一个标识符，而def则会把函数对象赋值给一个变量。
2 python lambda它只是一个表达式，而def则是一个语句。
下面是python lambda的格式，看起来好精简阿。
lambda x: print x
如果你在python 列表解析里用到python lambda，我感觉意义不是很大，因为python lambda它会创建一个函数对象，但马上又给丢弃了，因为你没有使用它的返回值，即那个函数对象。也正是由于lambda只是一个表达式，它可以直接作为python 列表或python 字典的成员，比如：
info = [lamba a: a**3, lambda b: b**3]
在这个地方没有办法用def语句直接代替。因为def是语句，不是表达式不能嵌套在里面，lambda表达式在“：”后只能有一个表达式。也就是说，在def中，用return可以返回的也可以放在lambda后面，不能用return返回的也不能定义在python lambda后面。因此，像if或for或print这种语句就不能用于lambda中，lambda一般只用来定义简单的函数。
下面举几个python lambda的例子吧
1单个参数的：
g = lambda x:x*2 print g(3)
结果是6
多个参数的：
m = lambda x,y,z: (x-y)*z print m(3,1,2)
结果是4
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