Question

Programming language: DrRacket/scheme

Hey guys,

I am preparing for my first comp sci midterm, and have two quick questions that I’d love to get some input on:

(1) What exactly is the difference between a data definition and a
structure definition?

I know that for a data definition, I can have something like:

;; a student is a 
;; - (make-student ln id height gradyear), where 
;; - ln is last name, and
;; - id is ID number, and
;; - height is height in inches, and
;; -gradyear is graduation year

but what is a structure definition?

(2) What exactly are the alphas and betas in contracts that come before functions, i.e.

take : num α-list -> α-list

Thank you in advance!

Answer 1

Quote from How to Design Programs (HtDP):

A DATA DEFINITION states, in a mixture of English and Scheme, how we
intend to use a class of structures and how we construct elements of
this class of data.

Given a problem to solve you as a programmer must decide how your input data is represented as values. In order for others to understand your program it is important to document how this is done in detail.

Some input data are simple and can be represented by a single number (e.g. temperature, pressure, etc).

Other types of data can be represented as fixed number of numbers/strings. (e.g. a cd can be represented as an author name (string), a title (string) and a price (number)). To pack a fixed number of values as one value one can represent this a structure.

If one needs to represent an unknown number of something, say cds, then one must use a list.

The data definition is simply your description of how the data are represented in your program.

To explain what a structure definition is, I’ll quote from HtDP:

A STRUCTURE DEFINITION is, as the term says, a new form of definition.
Here >is DrScheme’s definition of posn:

(define-struct posn (x y))

Let us look at the cd example again. Since there are no builtin “cd values” in Racket, one must define what a cd value is. This is done with a structure definition:

(define-struct cd (author title price))

After the definition is made one can use make-cd to construct cd values.
In order to explain that autor and title are expected to be strings, and price is expected to be a number, you must write down a data definition that explains how make-cd is supposed to be used.

I forgot to answer your second question:

(2) What exactly are the alphas and betas in contracts that come
before functions, i.e.

take : num α-list -> α-list

The alpha is supposed to be replaced with a type.

If take get a integer-list (list of integers as input) then the output is an integer-list.

If take get a string-list (list of strings as input) then the output is an string-list.

In short if take gets a list of values with some type (alpha) as input, then the output is a list of values with the same type (alsp alpha).