Held: Friday, 29 January 2016

Back to Outline 03 - An Introduction to Scheme. On to Outline 05 - RGB Colors.

Summary

We explore a bit more about data in Scheme, particularly the ways in which our version of Scheme supports numbers.

Related Pages

• Reading: Symbolic Values
• Reading: Numeric Values
• Lab: Numeric Values
• EBoard 4 (Source 4)

Overview

• Values and types.
• Kinds of numbers.
• The modulo operation.

Administrivia

• Continue partners from Wednesday!
• Office hours: MTWF 10-11, Tu 1-2.
  • Sign up at http://rebelsky.youcanbook.me.
  • Also feel free to stop by when my door is open.
  • Or to email me for an appointment.
• Tutor hours
  • Sunday, 3-5 p.m.
  • Sunday-Thursday, 7-10 p.m.
• Weekly review sessions:
  • Wednesday at 8pm in the CS Commons with Zacharcy
  • Thursday at 10am in this room with SamR
  • Thursday at 8pm in the CS Commons with Kumar
• Friday PSA.

Upcoming Work:

• Readings for Monday:
  • Design and Color
  • RGB Colors
• Assignment 2 due next Tuesday at 10:30 p.m.
• Lab Writeup: Problem _
  • Send email titled CSC 151 Lab Writeup 4 (Your Names)
  • Do not include the underscores.
  • Due before class on Tueday.

Extra Credit

Academic

• CS Table, Tuesday, Noon, White PDR: Facebook's Walled Internet. (Readings available Monday)
• Community Conversations on Race, 7:30 p.m., Tuesday, February 2, Lazier 3rd Floor Lounge

Peer

• Track and Field at Cornell this Saturday.
• Swimming at Macalester this Saturday.

Future

• Track and Field Grinnell Invite February 6.
• Swimming February 6 vs. UN and IAState.

Miscellaneous

• Caucus on Monday night. (Or observe a Caucus on Monday night.)

Types

• If you reflect on the first algorithms we wrote, you'll note that we worked with different kinds of things (e.g., knives, jars, bags).
• While there are some commonalities between what you do with things (e.g., you can drop a knife or jar or bag on the floor), different things often imply different operations (e.g., you can unscrew a jar, but not a knife).
• Computer scientists use the term type to refer to the things/values we work with.
• In order to design algorithms, we need to know what kinds of operations the computer already knows. Typically, these operations are associated with types. For example, you can multiply numbers and concatenate strings. (You can't do much at all with symbols, other than make them and compare them.)
• As you may have noted in your first experiments with Scheme, Scheme assigns types to values.
• For example, a value might be a number, or a string, or a procedure, or ....
• Computer scientists often think of types in two different ways:
  • Data-driven: A type is a set of values.
  • Purpose-driven: A type provides information on the valid operations that may be applied to a piece of data.
• We will alternate between the two definitions.
• Many languages (particularly the ones you've reported being familiar with) require you to assign a type to a variable when you declare that variable.
• Scheme does not require you to assign types ot variables; it checks the type of each operand when it executes a procedure.
  • Scheme also provides procedures that let you determine the type of a value.
• As the semester progresses, you will learn new types.
• As you learn each type, you'll learn a variety of things (that correspond, in some sense, to those two approaches):
  • How to express values in the type. For example, we express string values by surrounding them with double-quotation-marks and we express numbers in much the way we always have.
  • What operations are possible on values in the type. For example, we can use the addition operation (+) on numbers and we can use the string-append operation on strings.
• Each time we encounter a type, I'll either tell you or ask you (or both) how you might express values and what obvious operations there are.

Lab

• Do the lab on numeric values
• Be prepared to reflect.

Scheme's Numeric Types

• Instead of a general "numbers" type, Scheme provides a variety of kinds of numbers.
• Integers are numbers without a fractional component.
• Rational numbers can be expressed as the ratio of two integers.
• Real numbers appear somewhere on the number line.
  • In mathematics, real numbers can be rational or irrational.
  • In Scheme, real numbers are all rational.
• Complex numbers may include an imaginary component.
• You can (almost) always use an integer when a real is expected, but you cannot always use a real when an integer is expected.
• Scheme also represents some numbers exactly and some numbers inexactly. (That is, it approximates some numbers.)
  • It certainly has to approximate irrational numbers.
  • But it also approximates many other numbers.
  • It may surprise you to see which numbers are represented inexactly. (We'll return to this issue later.)
• Some important numeric predicates (procedures that return true or false): number?, real?, integer?, exact?, and inexact?.

Modulo

• The mod (modulo, modulus) operation is one of the trickier operations we use in this class (and we use it a lot).
• mod is like remainder except that it always gives positive values, even when the dividend is negative.
  • For negative dividend, (mod dividend divisor) is (+ divisor (quotient dividend divisor)).
• Essentially, mod is used to break up the number line into even chunks.
  • If you mod by 7, you break the number line up into chunks of size 7.
  • If you mod by 23, you break the number line up into chunks of size 23.
• For each chunk, we start counting at 0.
• For example

Number line:  -9 -8|-7 -6 -5 -4 -3 -2 -1| 0  1  2  3  4  5  6| 7  8  9 10 11 
Modulo 7:      5  6| 0  1  2  3  4  5  6| 0  1  2  3  4  5  6| 0  1  2  3  4 

• The (modulo *i* *n*) operation allows us to cycle through the numbers between 0 and *n*-1.