CSC151.02 2003F, Class 8: Numeric Values in Scheme

Admin:
* Homework due.  Email me your URLs.  We may spend some time on Thursday looking at your homework (then again, we may not).
* Read "Defining Your Own Procedures in Scheme"
* EBoards linked

Topics:
* Are there questions from yesterday's lab?
* Data types
* Numbers in Scheme
* Lab
* Reflection

Reflection on Lists and Symbols Labs:

Q: Why join lists?
A: Supppose I had a list of all my students in CSC151 and a list of all my students in CSC297.  If I wanted to send mail to "all my students", I'd join the two lists together first.

Q: Can one use append to join more than two lists?
A: I dunno, let's try it.
A: Yes, you can append 0, 1, 2, 3, or more lists

Q: Did anyone try the complex list with only cons
	(a (b c) (d (e)))
A: Hmmm ... that sounds like a good exam question.

New topic: Types

* Types are ways of classifying values
  * 23 is an integer
  * 'a is a symbol
  * (1 2 3) is a list
  * cons is a function
* Why bother?
  * It's easier to catch errors in a program
  * It reminds us what we can do with our data
* Scheme has a lot of types
  * It even has lots of kinds of numbers
  * integers
  * rational numbers (expressible as the ratio of two integers)
  * real numbers (potentially a fractional component)
  * imaginary numbers (potentially include an imaginary component)
* Some languages check "type safeness" as soon as possible (when you write your code)
  * Scheme checks "type safeness" when you run the program
* Scheme can represent some numbers in two different ways: exactly or inexactly
* The inexact? and exact? predicates let you determine whether a number is exact or inexact

Try the Lab

Reflection:

* Yes, you may have to review the reading (e.g., for really large numbers, for exact numbers, for inexact numbers) #i1/3
  * Also for info on the procedures
* Intended moral: There are a variety of ways you explore the "meaning" of a procedure
  * Experimentally
  * By reading documentation intended for experts
  * By reading documentation intended for novices
  * By asking someone else
  * By some combination

* So, what do you know about the following procedures?
  * floor, ceiling, truncate, round 
    * Convert numbers with a decimal part to integers (but in different ways)
    * floor rounds down
    * ceiling rounds up
    * truncate chops of the decimal part and is therefore just like floor for positive numbers and ceiling for negative numbers
    * round is like what we learned in grade school
      * if the decimal part is above 0.5, rounds up
      * if the decimal part is below 0.5, rounds down
      * if the decimal part is 0.5, rounds toward even
  * quotient, remainder, modulo
  * max, min
  * numerator, denominator
  * gcd, lcm