CS1101S

Lecture 2: Elements of Programming

17 August 2012

Martin Henz

Elements of Programming

• Primitives
• Combination
• Abstraction

Elements of Programming

• Primitives
  • Numbers
  • Boolean values (true, false)
  • Symbols

Elements of Programming

• Combination
  • Arithmetic operators
  • Boolean operators

Elements of Programming

• Abstraction
  • Names

Elements of Programming

• Abstraction
  • Functions

A Function Is A Black Box

• Input: any number
• Output: the largest integer that is not larger than the number
• How does it work? Do we need to know in order to program the point-of-sales system?

Picture Language

• Primitives: some simple pictures such as
  • rcross_bb
  • sail_bb
  • corner_bb
  • nova_bb
  • heart_bb
  Example

Picture Language

• Combinations:
  • view combines show and clear

Picture Language

• Combinations: functions that take a picture and produce a new picture from it
  • quarter_turn_right

Picture Language

• Combination

  	      
  quarter_turn_right(quarter_turn_right(sail_bb))
  
  

Picture Language

• Abstraction: Functions and naming

  	      
  function turn_upside_down(pic) {
      return quarter_turn_right(
                  quarter_turn_right(pic));
  }
  
  

Picture Language

• Abstraction: Functions and naming

  	      
  function quarter_turn_left(pic) {
      return turn_upside_down(quarter_turn_right(pic));
  }
  
  

Picture Language

• Combination: stacking

  	      
  stack(rcross_bb, sail_bb);
  
  

Picture Language

• Combination: stacking

  	      
  stack(rcross_bb, sail_bb);
  
  

Picture Language

• Combination and abstraction:

  	      
  function beside(pic) {
      ???
  }
  
  

Picture Language

• Combination and abstraction:

  	      
  function beside(pic1, pic2) {
      return quarter_turn_right(
                 stack( quarter_turn_left(pic2),
                        quarter_turn_left(pic1) ) );
  }
  
  

Picture Language

• Naming: a more complex picture <

  	      
  var my_cross = 
     stack(beside(quarter_turn_right(rcross_bb),
                  turn_upside_down(rcross_bb)),
           beside(rcross_bb,
                  quarter_turn_left(rcrowss_bb)));
  
  

Picture Language

• Abstraction: making a cross from anything

  	      
  function make_cross(pic) {
      return stack(beside(quarter_turn_right(pic),
                          turn_upside_down(pic)),
                   beside(pic,
                          quarter_turn_left(pic)));
  }
  
  

Picture Language

• Combination: repeating the pattern

  	      
  make_cross( make_cross( nova ) )
  
  

Picture Language

• Abstraction: repeating the pattern n times

  	      
  function repeat_pattern(n, pat, pic) {
      if (n === 0) {
          return pic;
      } else {
          return pat(repeat_pattern(n-1, pat, pic));
      }
  }
  
  

Picture Language

Another nice pattern

	      
repeat_pattern(4, make_cross, rcross_bb)

Picture Language

• Combination: fractional stacking

  	      
  stack_frac( 1/3, sail_bb, rcross_bb )
  
  

Picture Language

• Abstraction: Repeating n times

  	      
  function stackn(n, pic) {
      if (n === 1) {
          return pic;
      } else {
          return stack_frac(1/n, pic, 
                            stackn(n-1, pic));
      }
  }
  
  

Picture Language

• Combination: rectangular quilting

  	      
  stackn(5, 
         quarter_turn_right(
             stackn(5,quarter_turn_left(nova_bb))))
  
  

Picture Language

• Abstraction: rectangular quilting

  	      
  function n_times_n(n, pic) {
      return stackn(n,
                quarter_turn_right(
                   stackn(n,
                          quarter_turn_left(
                             pic))));
  }
  
  

Reflection

• No idea how the primitives work (heart_bb)
• No idea how the combinations work (quarter_turn_right)
• Yet we can make complex pictures

Missions

JFDI Academy has two missions and one side-quest:

• Mission 1: Due tomorrow, Saturday, 18/8, 23:59
• Mission 2: Due Thursday, 23/8, 23:59
• Side Quest 2.1: Due Saturday, 25/8, 23:59

Still awake?

	      
function mystery(x) {
    return x * mystery(x - 1);
}

mystery(5)

What is the result?