Let us look at procedure abstraction using a children's nursery rhyme as an example.

Note: Using a simple song has the advantage that the output is known and easily recognizable while one is programming the abstractions.

Here are the lyrics to the song, "Mary had a little lamb" as music.


The image was created with a LilyPond script. (omitted)

Here are the lyrics to the song, "Mary had a little lamb" as text.

• Functional requirements: customer facing (do not change)
• Nonfunctional requirements: code style according to company policy

Obviously, we could output this text using print statements as follows.

The student is shown how to use editor shortcuts to not type code. Just copy and paste such as printf(" ... "):.

Here is a program to do just that.
#include <stdio.h> int main() { printf("Mary had a little lamb,\n"); printf("little lamb, little lamb\n"); printf("Mary had a little lamb,\n"); printf("it's fleece was white as snow.\n"); printf("\n"); printf("And everywhere that Mary went,\n"); printf("Mary went, Mary went.\n"); printf("Everywhere that Mary went,\n"); printf("the lamb was sure to go.\n"); return 0; }
The output is as expected.
Mary had a little lamb, little lamb, little lamb Mary had a little lamb, it's fleece was white as snow. And everywhere that Mary went, Mary went, Mary went. Everywhere that Mary went, the lamb was sure to go.
Regression testing can be used to check the output with the specification.

Mary had a little lamb, little lamb, little lamb Mary had a little lamb, it's fleece was white as snow. And everywhere that Mary went, Mary went, Mary went. Everywhere that Mary went, the lamb was sure to go.	Johnny had a tiny pig, tiny pig, tiny pig Johnny had a tiny pig, it's hide was black as coal. And everywhere that Johnny went, Johnny went, Johnny went. Everywhere that Johnny went, the pig was sure to go.
Original and new requirements. There may be new similar requirements in the future.	Susan had a hopping rabbit, hopping rabbit, hopping rabbit Susan had a hopping rabbit, it's fur was brown as earth. And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

Mary had a little lamb , little lamb , little lamb Mary had a little lamb , it's fleece was white as snow . And everywhere that Mary went, Mary went, Mary went. Everywhere that Mary went, the lamb was sure to go.	Johnny had a tiny pig , tiny pig , tiny pig Johnny had a tiny pig , it's hide was black as coal . And everywhere that Johnny went, Johnny went, Johnny went. Everywhere that Johnny went, the pig was sure to go.
Colors help one see similarities and differences. Similarities: procedure body Differences: actual/formal parameters.	Susan had a hopping rabbit , hopping rabbit , hopping rabbit Susan had a hopping rabbit , it's fur was brown as earth . And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

A program such as WinMerge can help see the similarities and differences. Here is a comparison of Mary (#1) and Susan (#3). One still has to see differences between "little lamb" and "hopping rabbit" in the overall context.

Do you see that there are similarities and differences? If not, you may have a difficult time in computer science.

Some appropriate abstractions are needed.

A common example of such requirements are a web page system that must generate certain output or reports based on data in a database. The method is similar to the mail merge process in the document world.

A mail-merge process using, say, a template in Microsoft Word and a database of differences in an Excel worksheet is another example.

• Abstract: separate into differences and similarities
• Reduce: fill in the differences with the similarities

In the mail merge process, the differences (fields from each database record) are merged into the similarities (document with fill-in fields) to create the collection of documents merged documents

Here is a color-coded table of differences.

Name v. 1 v. 2 v. 3 NAME Mary Johnny Susan SIZE little tiny hopping ANIMAL lamb pig rabbit FUR fleece hide fur COLOR white black brown OBJECT snow coal earth

Susan had a hopping rabbit , hopping rabbit , hopping rabbit Susan had a hopping rabbit , it's fur was brown as earth . And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

• Similarities become the body of a procedure/function.
• Differences become actual/formal parameters.

Here is a table of differences without color.

Name v. 1 v. 2 v. 3 NAME Mary Johnny Susan SIZE little tiny hopping ANIMAL lamb pig rabbit FUR fleece hide fur COLOR white black brown OBJECT snow coal earth

Susan had a hopping rabbit, hopping rabbit, hopping rabbit Susan had a hopping rabbit, it's fur was brown as earth. And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

• Similarities become the body of a procedure/function.
• Differences become actual/formal parameters.

Here are color-coded input data sets.

Input set #1	Input set #2	Input set #3	Output #3
Mary little lamb fleece white snow	Johnny tiny pig hide black coal	Susan hopping rabbit fur brown earth	Susan had a hopping rabbit , hopping rabbit , hopping rabbit Susan had a hopping rabbit , it's fur was brown as earth . And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

Here are input data sets without color.

Input set #1	Input set #2	Input set #3	Output #3
Mary little lamb fleece white snow	Johnny tiny pig hide black coal	Susan hopping rabbit fur brown earth	Susan had a hopping rabbit, hopping rabbit, hopping rabbit Susan had a hopping rabbit, it's fur was brown as earth. And everywhere that Susan went, Susan went, Susan went. Everywhere that Susan went, the rabbit was sure to go.

For physical input, some decisions need to be made. How is the above data recognized?

• Is it separate variables?
• Is it a counter loop?
• Is it a header loop?
• Is it a trailer loop? What is the trailer value?
• Is it an endfile loop?
• Is it some other way?

Are there other data in the input, such as a debug output setting?

Some ways of creating a program to take the input data and output the text to each of the songs are the following.

• Individual variable solution: C: Procedural abstraction using variables
• Array solution: C: Procedural abstraction using arrays
• Record structure solution: C: Procedural abstraction using records
• Debugging output using defined macros

Nonfunctional requirements: code style according to company policy such as using variables, arrays, records, etc.

Each improvement is a "refactoring" of the code. It does the same thing, just differently.

Fallacy: If you are good at math, you will be good at computer science.
In the above development, and in the solutions, what is often thought of as mathematics - using addition, subtraction, multiplication, division, formulas, etc., is not needed.

The math needed is abstraction and symbol manipulation and algebra as in lambda calculus.

The core of computer science and programming involves abstraction. Many students who are good at "math" have trouble with these programs. How many students who are not good at "math" can do this type of abstraction?

Most students have problems with abstraction in that they want to think like a machine rather than doing textual pattern matching and algebraic code transformations.