CS 61A: SICP - week2 - 2

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  1. Designing Functions 1.1 Designing Functions

     A function's domain is the set of all inputs it might possibly take as arguments.
     A function's range is the set of output values it might possibly return.
     A pure function's behavior is the relationship it creates between input and output.
     
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1.2. A Guide to Designing Function

    Give each function exactly one job, but make it apply to many related situations
    Don’t repeat yourself (DRY): Implement a process just once, but execute it many times
    Define functions generally
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2. Designing Functions

  1. Higher-Order Functions

3.1

    The common structure among functions may be a computational process, rather than a number
    
    def cube(k): return pow(k, 3)
    def summation(n, term):      
         total, k = 0, 1
         while k <= n:
         total, k = total + term(k), k + 1
         return total
         
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3.2. Functions as Return Values

    Functions defined within other function bodies are bound to names in a local frame
    
    def make_adder(n):
         def adder(k): return k + n 
         return adder
         
    那么make_adder(1)(2) 返回多少你知道吗
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3.3 The purpose of higher-order functions

    Functions are first-class: functions can be manipulated as values in our programming language
    
    hight-order function: a function that takes a function as an argument value or returns a function as a return value
    
    higher-order functions:
    . express general methods of computation
    . remove repetition from programs
    . separate concers among functions
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4. Lambda Expressions

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4.1 Lambda Expressions Versus Def Statements

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  1. Return 5.1 Return Statements

     A return statement completes the evaluation of a call expression and provides its value: f(x) for user-defined function f: switch to a new environment; execute f's body return statement within f: switch back to the previous environment; f(x) now has a value Only one return statement is ever executed while executing the body of a function
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  2. Conditional Expressions

     <consequent> if <predicate> else <alternative> 
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Evaluation rule:

1. Evaluate the <predicate> expression.
2. If it's a true value, the value of the whole expression is the value of the <consequent>.
3. Otherwise, the value of the whole expression is the value of the <alternative>.
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