高阶函数
- 将函数作为参数
- 例如
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1 def sum_naturals(n):2 total, k = 0, 13 while k <= n:4 total, k = total + k, k + 15 return total
def sum_cubes(n): total, k = 0, 1 while k <= n: total, k = total + k*k*k, k + 1 return total
def pi_sum(n): total, k = 0, 1 while k <= n: total, k = total + 8 / ((4*k-3) * (4*k-1)), k + 1 return total
- 以上三个例子中有许多共同的部分
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def
(n): total, k = 0, 1 while k <= n: total, k = total + (k), k + 1 return total
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- 高阶函数形式
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def summation(n, term): total, k = 0, 1 while k <= n: total, k = total + term(k), k + 1 return totaldef cube(x): return x*x*xdef sum_cubes(x): return summation(x,cube)
- 黄金比例
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def improve(update, close, guess=1): while not close(guess): guess = update(guess) return guessdef golden_update(guess): return 1/guess + 1def square_close_to_successor(guess): return approx_eq(guess * guess, guess + 1)def approx_eq(x, y, tolerance=1e-15): return abs(x - y) < toleranceimprove(golden_update, square_close_to_successor)
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- 高阶函数的不足
- 在全局环境中名称复杂
- 每一个函数的形参个数是由限制的
函数的嵌套定义
- 解决高阶函数存在的不足
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def sqrt(a): def sqrt_update(x): return average(x, a/x) def sqrt_close(x): return approx_eq(x * x, a) return improve(sqrt_update, sqrt_close)
- 嵌套定义中的函数作用域
- 每一个嵌套的函数在定义函数内环境
- #不是函数的调用处
- 函数作用域的实现方法
- 每一个函数都有他的父环境
- 当函数被调用时，在其父环境中评估
- 函数作用域的好处
- 局部环境中的绑定不会影响全局环境
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def square(x): return x * xdef successor(x): return x + 1def compose1(f,g): def h(x): return f(g(x)) return hsquare_successor = compose1(square,successor)result = square_successor(12)
牛顿法
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def newton_update(f, df): def update(x): return x - f(x) / df(x) return updatedef find_zero(f, df): def near_zero(x): return approx_eq(f(x), 0) return improve(newton_update(f, df), near_zero)def square_root_newton(a): def f(x): return x * x - a def df(x): return 2 * x return find_zero(f, df)
Currying
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>>> def curried_pow(x): def h(y): return pow(x, y) return h>>> curried_pow(2)(3)8
def curry2(f): """Return a curried version of the given two-argument function.""" def g(x): def h(y): return f(x, y) return h return g
def uncurry2(g): """Return a two-argument version of the given curried function.""" def f(x, y): return g(x)(y) return f
匿名函数
- 可以看做
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lambda x : f(g(x))"A function that takes x and returns f(g(x))"
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函数装饰器
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>>> def trace(fn): def wrapped(x): print('-> ', fn, '(', x, ')') return fn(x) return wrapped>>> @trace def triple(x): return 3 * x>>> triple(12)->( 12 )36 - @trace等同于
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>>> def triple(x): return 3 * x>>> triple = trace(triple)