Ideas today:
 - create functions
 - modules
 - input/output

==================================================
SLIDES: basic syntax
==================================================

abs(-3)
sqrt(9)
from math import sqrt
sqrt(9)
from math import *
pi
pow(2, 3)

# how to implement abs, sqrt, pow?
sqrt(x) = pow(x, 0.5)
abs(x) = sqrt(x**2)

# NOTE:
 - same naming rules for function names as for variables
 - until we call them, nothing happens!

# for pow, give a default argument, and show the three styles:
 1. positional argument
 2. keyword argument
 3. default argument

==================================================
SLIDES: three ways to initialize parameters
==================================================

==================================================
WORKSHEET: do a few problems...
==================================================

==================================================
SLIDES: where to modules come from?
==================================================

dog+cat modules

from dog import *
speak_rv = speak()
fetch_rv = fetch()

print(speak_rv)
print(fetch_rv)

QUESTIONS:
 - why do we need prints in a notebook?  Show None
 - how to write a cat module?
 - how to use functions with the same name from diff modules?
 - how to find what's in a module?
 - how to document a function?
 - what's in the math module?

==================================================
SLIDES: data flow between caller, function, and screen
==================================================

# difference between returning and printing
 - syntax:    don't need parens
 - semantics: early return

def countdown_v1():
    print(3)
    print(2)
    print(1)

def countdown_v2():
    return 3
    return 2
    return 1

def countdown_v3():
    rv = "3"
    rv += "\n" + "2"
    rv += "\n" + "1"
    return rv

# more details (countdown_v1 only):
  1. what if we change the indents?
  2. add some prints to distinguish declaration from invocation
  3. do multiple invocations of countdown_v1
  4. do it in PythonTutor
     - talk about the arrow...
     - definition time vs. invocation time
     - what does it mean when the arrow points to a function?  Depends...

==================================================
WORKSHEET: do problems 19, [20], 22
==================================================

==================================================
SLIDES: approx example
==================================================

# approx.py

import math

def diff(v1, v2):
     return abs(v1 - v2)

def is_close(a, b):
     # version 1:
     return diff(a, b) / max(abs(a), abs(b)) < 0.001

     # version 2:
     return diff(a, b) < 0.000001 or diff(a, b) / max(abs(a), abs(b)) < 0.001

def is_approx_pi(x):
    return is_close(x, math.pi)

def is_approx_zero(x):
    return is_close(x, 0)

x = input("enter x: ")
print("about pi?", is_approx_pi(x))
print("about zero?", is_approx_zero(x))

# LESSONS:
 - refactoring (start by copy/paste for is_approx_pi)
 - interpreting traceback (debug divide by zero)
 - shortcircuiting (try flipping the OR)
 - purpose of main function
 - add default arguments for abs rel tolerance

==================================================

# tracing functions that call other functions (in PythonTutor)...

def h():
     print("H")

def g():
     print("G")
     h()

def f():
     print("F")
     g()

f()

# what if we swap prints and calls?

==================================================
WORKSHEET: do problem 21
==================================================

# battleship.py: refactor

add functions for:
 - ship1_hit, etc
 - is_hit
 - draw_block
 - draw_map
 - play_round (can play multiple, keep score)

==================================================

# interpolation.py
 - given points x1,y1,x2,y2, estimate new y for x
 - slope function
 - estimate function
 - error functions

==================================================

# quadratic.py
 - mult return values?