技術標籤：SICP (or CS61a) Lecture Notespython

Lecture 02 Names & Functions

These are my notes for SICP(Structure and Interpretation of Computer Programs). Hope they’ll be of some help to you.

Names

Description

• Values can be assigned to names to make referring to them easier.

• A name can only be bound to a single value.

• One way to introduce a new name in a program is with an assignment statement.

Statement

Statements affect the program, but do not evaluate to values.

Assignment

x = 1 + 2*3 - 4//5

• Names are bound to values in an environment

To execute an assignment statement:

1. Evaluate the expression to the right of =.
2. Bind the value of the expression to the name to the left of = in the current environment.

Functions

Description

• Functions allow us to abstract away entire expressions and sequences of computation

• They take in some input (known as their arguments) and transform it into an output (the return value)

• We can create functions using def statements. Their input is given in a function call, and their output is given by a return statement.

Defining functions

from math import pi
def volum(r): #def <name>(<parameters>): -Function signature
    return (4/3) * pi * (r**3) #return <return expression> -Function body

• Function signature indicates name and number of arguments
• Function body defines the computation performed when the function is applied
• Def statements are a type of assignment that bind names to function values

Procedure for calling/applying user-defined functions (for now)

1. Create a new environment frame (we call it local frame, included in global frame)

2. Bind the function’s parameters(formal arguments) to its arguments(actual arguments) in that frame

3. Execute the body of the function in the new environment

from operator import mul #built-in function
def square(x):
    return mul(x, x) #user-defined function
y = square(-2)

Some built-in functions

from math import pi #pi = Π = 3.1415926......
from math import e #e = 2.71828......
from math import exp #exp(x) = e ^ x
from math import expm1 #expm1(x) = e ^ x - 1
from math import log #log(x,y) = lnx/lny; log(x) = lnx
from math import log10(x) #log10(x) = lgx
from math import log1p(x) #log1p(x) = ln(1+x)
from math import ceil #ceil(x) = [x] + 1
from math import floor #floor(x) = [x]
from math import pow #pow(x, y) = x ^ y
from math import sqrt #sqrt(x) = the square root of x
from math import fabs #fabs(x) return the absolute of x and the return number is a float
from math import factorial #factorial(x) = x!
from math import hypot #hypot(x, y) = sqrt(x*x + y*y)
from math import sin
from math import asin
from math import cos
from math import acos
from math import tan
from math import atan

abs(x) #abs(x) = |x| even if x is complex
complex(x, y) #create a complex with x to be real and y to be imaginative; y is not necessary
pow(x, y) #pow(x, y) = x ^ y
round(x, y) #round x to y decimal places, you don't have to input y if y = 0
input([prompt])
print(...)

Summary

• Programs consist of statements, or instructions for the computer, containing expressions, which describe computation and evaluate to values.

• Values can be assigned to names to avoid repeating computations.

• An assignment statement assigns the value of an expression to a name in the current environment.

• Functions encapsulate a series of statements that maps arguments to a return value.

• A def statement creates a function object with certain parameters and a body and binds it to a name in the current environment.

• A call expression applies the value of its operator, a function, to the value(s) of its operand(s), some arguments.