Class 03: Basic Types: Symbols, Lists, and Numbers

Held: Wednesday, 22 January 2003

Summary: Today we consider many of the core types in Scheme, particularly symbols, lists, and numbers.

Related Pages:

• Reading on Symbolic Values in Scheme.
• Reading on Lists in Scheme.
• Reading on Numbers in Scheme.
• Lab on Types in Scheme.

Assignments:

• Read Procedures in Scheme (due Fri).
• Do Laboratory Writeup 1 (due Mon).

Handouts:

• Instructions for Laboratory Writeups.

Overview:

• Overview of Types
• Symbols
• Lists
• Numbers
• Lab on Types

Types in Scheme

• Like most programming languages, Scheme provides different types.
• What is a type? There are two key perspectives:
  • 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.
• What are the advantages and disadvantages of Scheme's solution?
• Scheme provides a number of core types:
  • Primitive types: Numbers, Symbols, Characters, Truth Values
  • Compound types: Lists, Vectors (like Arrays), Strings, Functions/Procedures

Symbols

• A key aspect of Scheme.
• The easiest way to build a symbol is with the quote operation.

  > 'a
  a
  > a
  reference to undefined identifier: a
  > (quote a)
  a
  

• Useful when you want to represent something atomically (as an idea that can't be pulled apart).

Lists

• The core of Scheme.
• Dynamic: Lists can "grow" and "shrink"
  • Or at least you can build larger or smaller lists from other lists.
• The simplest list: the empty list is null or ().
• You extend a list at the front (or, more precisely, build a new list) with

  (cons thing-for-the-front rest-of-the-list)
  

• For example,

  > (cons 'a null)
  (a)
  > (cons 'b (cons 'a null))
  (b a)
  

• You can also create lists with list.

  > (list 'a 'b 'c)
  (a b c)
  

• You extract parts of lists with three operations (we'll reflect on the naming later in the semester):
  • car: get the initial element of the list.
  • cdr: get all but the initial element of the list.
  • list-ref: get the ith element of the list.
• One disadvantage: Scheme lists look a lot like procedure applications, so it's sometimes hard for beginning programmers to tell what's going on.
  • You can always tell by context, but it takes some time to get used to contexts.

Numbers

• Scheme provides a hierarchy of numeric types. include complex, real, rational, and integer.
• You've already done some exploration of numbers, so there's not much more to say.
• Any questions?

Lab

• Do the types lab.
• We'll try to use the last five minutes of class to reflect.
• You may have to complete the remainder of the lab on your own.
• You have a laboratory writeup to complete on this lab.