CMU 15-112: Fundamentals of Programming and Computer Science
Class Notes: Functions Redux

1. Default args
   1. Default args example
   2. Do not use mutable default args
   3. One workaround for mutable default args
2. Variable length args (*args)
3. Keyword args (**kwargs)
4. Functions as parameters
5. Lambda functions
6. Functions inside functions
7. Closures + Non-local variables
8. Non-local variables fail on setting (use nonlocal)
9. Functions that return functions
10. Function decorators

1. Default args   video
   
   1. Default args example

      def f(x, y=10): return (x,y)
      print(f(5))   # (5, 10)
      print(f(5,6)) # (5, 6)

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   2. Do not use mutable default args

      def f(x, L=[ ]):
          L.append(x)
          return L
      
      print(f(1))
      print(f(2)) # why is this [1, 2]?

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   3. One workaround for mutable default args

      def f(x, L=None):
          if (L == None):
              L = [ ]
          L.append(x)
          return L
      
      print(f(1))
      print(f(2)) # [2] (that's better)

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2. Variable length args (*args)   video
   

   def longestWord(*args):
       if (len(args) == 0): return None
       result = args[0]
       for word in args:
           if (len(word) > len(result)):
               result = word
       return result
   
   print(longestWord("this", "is", "really", "nice")) # really
   
   mywords = ["this", "is", "really", "nice"]
   
   print(longestWord(mywords))  # ['this', 'is', 'really', 'nice']
   print(longestWord(*mywords)) # really

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3. Keyword args (**kwargs)   video
   

   def f(x=1, y=2): return (x,y)
   print(f()) # (1, 2)
   print(f(3)) # (3, 2)
   print(f(y=3)) # (1, 3) [here is where we use a keyword arg]
   
   def f(x, **kwargs): return (x, kwargs)
   print(f(1)) # (1, { })
   print(f(2, y=3, z=4)) # (2, {'z': 4, 'y': 3})

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4. Functions as parameters   video
   

   def derivative(f, x):
       h = 10**-8
       return (f(x+h) - f(x))/h
   
   def f(x): return 4*x + 3
   print(derivative(f, 2)) # about 4
   
   def g(x): return 4*x**2 + 3
   print(derivative(g, 2)) # about 16 (8*x at x==2)

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5. Lambda functions   video
   

   print(derivative(lambda x:3*x**5 + 2, 2)) # about 240, 15*x**4 at x==2
   
   myF = lambda x: 10*x + 42
   print(myF(5)) # 92
   print(derivative(myF, 5)) # about 10

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6. Functions inside functions   video
   

   def f(L):
       def squared(x): return x**2
       return [squared(x) for x in L]
   print(f(range(5)))
   try:
       print(squared(5))
   except:
       print("squared is not defined outside f")

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7. Closures + Non-local variables   video
   

   def f(L):
       myMap = dict()
       def squared(x):
           result = x**2
           myMap[x] = result
           return result
       squaredList = [squared(x) for x in L]
       return myMap
   print(f(range(5)))

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8. Non-local variables fail on setting (use nonlocal)   video
   

   def brokenF(L):
       lastX = 0
       def squared(x):
           result = x**2
           lastX = x
           return result
       squaredList = [squared(x) for x in L]
       return lastX
   print(brokenF(range(5)))
   
   def fixedF(L):
       lastX = 0
       def squared(x):
           nonlocal lastX
           result = x**2
           lastX = x
           return result
       squaredList = [squared(x) for x in L]
       return lastX
   print(fixedF(range(5)))

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9. Functions that return functions   video
   

   def derivativeFn(f):
       def g(x):
           h = 10**-5
           return (f(x+h) - f(x))/h
       return g
   
   def f(x): return 5*x**3 + 10
   fprime1 = derivativeFn(f)
   fprime2 = derivativeFn(fprime1)
   print(f(3))    # 145, 5*x**3 + 10 evaluated at x == 3
   print(fprime1(3)) # about 135, 15*x**2 evaluated at x == 3
   print(fprime2(3)) # about 90, 30*x evaluated at x == 3

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10. Function decorators   video
    

    @derivativeFn
    def h(x): return 5*x**3 + 10
    print(h(3)) # 135, matches fprime1 from above.

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