[Edu-sig] More functional programming in Python

[Kirby Urner]

 Python 2.3.3 (#51, Dec 18 2003, 20:22:39) [MSC v.1200 32 bit (Intel)] 
 on  win32
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 IDLE 1.0.2      

 >>> def compose(f,g):
        """
        Return a function f(g(x)) given two functions f,g
        """
	  def h(x):
		return f(g(x))
	  return h

 Example:

 >>> def f(x): return x+1

 >>> def g(x): return 2*x

 >>> s = compose(f,g)
 >>> s(3)
 7
 >>> f(g(3))
 7

 >>> s = compose(g,f)
 >>> s(3)
 8
 >>> g(f(3))
 8

 >>> def power(f,n):
       """
       Return a function of f composed with itself n times
       """
 	 def e(x): return x    # n=0 returns identity function
	 if n == 0: return e 
	 r = f                 # n=1 returns f itself
	 for i in range(n-1): 
		r = compose(r,f)
	 return r

 >>> f(f(f(f(f(f(f(f(f(f(1))))))))))  # f composed with itself 10 times
 11
 >>> t = power(f,10)
 >>> t(1)
 11

 >>> t = power(f,0)  # t = e(x), identity
 >>> t(1)
 1

 >>> t = power(f,1)  # t = f(x), i.e. f(x) = x+1 in this example
 >>> t(1)
 2

 >>> t = power(g,5)
 >>> 6*2**5 # 2 * 2 * 2 * 2 * 2 * 6
 192
 >>> g(g(g(g(g(6)))))
 192
 >>> t(6)   # g(g(g(g(g(x)))))
 192

 >>> def complist(funclist):
        """
        Compose a list of functions, right to left
        """
	  return reduce(compose,funclist)

 >>> r = complist([g,g,f,f,g,f,g])
 >>> r(17)
 288

 >>> g(g(f(f(g(f(g(17)))))))
 288

 >>> def m(x):
	 return 'm(%s)' % x

 >>> def n(x):
	 return 'n(%s)' % x

 >>> r = complist([m, m, n, m])
 >>> r(1)
 'm(m(n(m(1))))'

 >>> r = power(m, 5)
 >>> r(1)
 'm(m(m(m(m(1)))))'


Kirby