Homework 2: Type Checking

Assigned: Thursday, 29 January 2004
Due: 10:00 a.m., Wednesday, 4 February 2004
No extensions!

Summary: In this assignment, you will develop a procedure that computes the type of a Scheme value.

Purposes: To give experience writing procedures that use conditionals and recursion. To help you think further about Scheme's type system.

Collaboration: Although you may discuss this assignment with your colleagues, and even get help debugging, each student should write his or her own program. If you receive help from anyone, you should clearly document that help.

Helpful References:

• Instructions for Laboratory Writeups

Turning it in: Email me your answers.

Assignment

You have learned a number of types in Scheme already, including lists, procedures, Boolean values, symbolic values, and a host of numeric types. Many Scheme programmers, but particularly beginning Scheme programmers, benefit from learning the type of a value.

Write and test a Scheme procedure, type, that returns the a symbol that represents the narrowest possible interpretation of the type of its argument. If the argument is a list, you should determine if all the component values are the same basic type. If so, return the symbol list-of-type. If not, return heterogeneous-list. Classify exact non-integer real and rational numbers as rational. Classify inexact non-integer real and rational numbers as real.

For example,

> (type 3)
integer
> (type 3.0)
real
> (type 3.5)
real
> (type 7/2)
rational
> (type (list 1 2 3))
list-of-integer
> (type 'one)
symbol
> (type (list 'one))
list-of-symbol
> (type (list 1 'one))
heterogeneous-list
> (type "hello")
string
> (type 'type)
symbol
> (type type)
procedure