Automatic translation still has certain issues.

The purpose of a computer is to perform computations. A computer is a calculator that can push it's own buttons.

A programming language is a notation for describing a computation.

• People need to think about problems.
• Computers need to perform computations.

Can people think like a computer? Can computers "think"?

There are many ways to think about programming a computer. Unfortunately, the beginning programming course tends to overemphasize operational semantics such as thinking like a computer, thinking in a particular language, etc., with an over-emphasis on traditional mathematical expertise. No matter how smart the person, there is a limit to what a human can do when programming is based primarily on operational semantics. Other ways of thinking about programming and the programming process will be presented that are not based on thinking like a computer and which allow one to more easily create larger and more complicated software systems. Ways to incorporate these ideas into the beginning programming course will be covered (as done by the author). The (now retired) author, with a PhD in computer science in the area of applied programming language theory, has spent many years teaching in academia, doing software research and development in industry, and, in the process, writing about a thousand pages of code each year for useful programs, small and large, in many different programming languages.

One wants to abstract to think about the problem being solved and not about the machine details of how it is being done.

• Thinking like a machine is implementation-oriented.
• Thinking like a human is solution-oriented.

To some, computer science is the same as coding.

Is computer science about computers?

Can you provide a reasonable definition of each of the following?

• Computer science
• Software engineering
• Business
• Education

Can you provide a reasonable objective function (goal) for each of the above? [perceptions]

Does the definition have a connection to the objective function.

Computer science is the search for finite representations of (potentially) infinite objects.

• More finite time: computation runs faster
• More finite space: computation takes less space

Computer science is mostly at the logic level of truth involving symbol manipulation.

Software engineering (and data science and business) is mostly at the reality level of truth.

Simplified definition:

• The goal of "computer science" is to order events and objects in space and time according to some efficiency constraints.

More simplified definition: Can you bag groceries?


This is a description as a constraint logic problem.

The goal of software engineering is to develop software on-time, on-budget and that meets the needs of the customer.

• fast (development time)
• cheap (overall cost)
• good (customer needs)

You can only get, at most, two of the three. You may get less.

The more math or computer science oriented a person is, the more difficult it is to make software engineering and business trade-offs. [CS SE vs. IS SAD]

The Amazon slogan about "pick two" between "low prices" and "fast delivery", reminds one of the software engineering definition and trade-offs. Who at Amazon came up with this idea?

What is the purpose of business?

The goal of business is to provide value to the customer - whoever those customers are. The customer is willing to contribute for that value.

Applies to business for profit and to non-profit, political, educational organizations, etc.

BPR = Business Process Reengineering defined business, for the first time, in the 1990's. "Do more with less".

Business process reengineering is the fundamental rethinking and radical redesign of business processes to achieve dramatic improvements in critical, contemporary measures of performance, such as cost, quality, service, and speed. Hammer, M., & Champy, J. (1993). Reengineering the corporation. New York: HarperBusiness., p. 32.

Interestingly, Michael Hammer had a Ph.D. in computer science and applied OOP (Object Oriented Programming) ideas to business processes. James Champy helped fill in the human-management perspective.

What is a reasonable definition of the goal of the educational system? Assume college level.

It is a business. The goal of business is to provide value to the customer.

Is there only one customer - the student? For those who get confused by the word "customer" the word "stakeholder" is used.

[customer segmentation, supply and demand, quality]

In computer science, software engineering and business, one has to often deal with trade-offs between theory and practice.

• In theory, there is no difference between theory and practice. But, in practice, there is. Jan L. A. van de Snepscheut.
• Theory and practice sometimes clash. And when that happens, theory loses. Every single time. Linus Torvalds.



More: Thinking: theory and practice

An important trade-off between theory and practice in business and software engineering is called a business-technical trade-off.

• Technical considerations dictate one solution.
• Business considerations dictate a different solution.

This must be recognized and a trade-off determined. This needs to be presented to a manager for an informed decision.

Two types of issues arise in business-technical trade-offs.

• IT (Information Technology) , software engineers, etc., making inappropriate business decisions.
• Managers making inappropriate technical decisions.

In thinking about problem solving and programming, semantics and meaning are important.

Semantics and meaning:

• functional - Church lambda calculus (LISP)
• operational - Turing machine (C)

The Church-Turing hypothesis/thesis is that these ways of thinking can compute the same functions.

Each way may not be as beneficial as the way for a human to think about computing.

Command execution of an assignment statement is a two step process.

• 1. Evaluate the expression e on the RHS (Right Hand Side) to a value.
• 2. Replace the previous value of variable v on the LHS (Left Hand Side) with the new value.

Whatever value was in variable v before is lost (forever).

• 1. Evaluate the expression e on the RHS to a value.

• 2. Replace the previous value of variable v on the LHS with the new value.

Whatever value was in variable v before is lost (forever).

Will the following code fragment correctly swap the values that are in integer variables x and y? Why or why not?

• Explain your reasoning.

Did you think like a machine to reason about your answer?

Thinking like a machine is thinking operationally.

How would you explain your reasoning to a student learning programming?

How could you test your program to make sure it is correct?

Would a flow chart help?

It is only two assignment statements. How hard could that be?

Fallacy: One can test a program to insure it is correct.
Let us adapt Dijkstra's argument from 1972 to this problem. For two 64 bit integers, there are 2¹²⁸ possible ways to do the swap code.

There are only about 2⁸⁰ microseconds in 16 billion years.

So it would take about 250,000,000,000,000(about 250 trillion) computers about 16 billion years to go through all the ways of swapping two 64 bit values.

Testing (brute-force) only helps find errors! It does not show that program code is correct.

Let us show/use program verification techniques to determine correctness.

The precondition and postcondition are as follows.

Apply the axiomatic semantics proof rule by working backwards in a top-down backward-chaining manner.

Algebra is critical to proving program fragments correct. Is knowing algebra important to learning programming?

Many students have trouble working backwards, using algebra, and realizing when the proof is done.

• 1. Substitute
• 2. Simplify

Stair analogy:

• Top-down: work backward from top step (last statement): 5 if 4 if 3 if 2 if 1
• Bottom-up: work forward from bottom step (first statement): 1 then 2 then 3 then 4 then 5

Many students tend to be very used to thinking like a machine and not algebraically using symbol manipulation.

They may spin their wheels confused. It is like climbing the Penrose steps.

Aside: When is the program (or software) done? Think laser eye surgery.

Interpretation: The statements

will correctly swap the values in x and y if and only if x and y have the same initial values.

This result follows without thinking operationally (like a machine). We only have to apply the rules and interpret the results.

From the axiomatic rules used to prove program code correct, one should see that algebra is an integral part of that process.

Thus, the ability to algebra, as in substitute and simplify, is an important and implicit part of the programming process.

Much of programming reduces to learning code invariant transformation rules and abstraction rules and applying them in a iterative refinement process - often without thinking about what they mean.

That is the purpose of algebra. That is, to transform mathematical expressions without thinking about what they mean (in an operational sense).

• 1. Substitute
• 2. Simplify

Remember Miller's Law that one can only keep about up to 7 things in memory at once.

Programmers who rigidly enforce this force you to go through many screens, each of which has only a few choices. One can quickly lose track of where things are in the interface.

More: George Armitage Miller

Viewpoints:

• Most users: How can I get the software to do this.
• Some programmers: How can I make the software do this.

Moving code around using invariant transformations is to a programmer who has memorized that code and thinks like a computer, like moving things around in a house where a cat lives. The cat's memory map of where everything is located needs to get relearned.

1. Think like a computer:

2. Thinking like a computer not required:

Think like a computer: Yes: What is the output of each code fragment? No: Which code fragment can compute a different output? Assume all variables are integers and declared (omitted).
i = 0; while (i != 8) { i += 1; print(i); }	h = 0; while (h != 8) { print(h); h += 1; }	k = 1; while (k != 8) { print(k); k += 1; }

The for loop has very subtle semantics that vary from language to language. Best to avoid except for 1 to n or 0 to n-1. Python does not have a for loop.

What do the following assignment statements do? That is, what is their effect.

Explain how you arrived at your conclusion.

The exclusive or operation can be used for the same effect.

More: The XOR operation and one-time pads

Parallel assignment: (syntax varies)

• Lua
• JavaScript (since 1.7)
• PHP
• Python
• PowerShell
• Ruby

A procedure can be used to swap values.

This handles the noncomputer-checked redundancy.

Reference parameters are needed. Some languages do not have reference parameters.

More: Procedure to swap values

Here is the C code [#1]
#include <stdio.h> void swap(int *a1, int *b2) { int c3; c3 = *a1; *a1 = *b2; *b2 = c3; } int main() { int x1; int y2; x1 = 2; y2 = 3; printf("before x1=%d y2=%d\n",x1,y2); swap(&x1,&y2); printf("after x1=%d y2=%d\n",x1,y2); return 0; }

Here is the output of the C code.
before x1=2 y2=3 after x1=3 y2=2

A procedure can be considered a textual macro that is expanded in-line with the parameters.

Macro expansion can be used such as is found in C, C++, Julia, etc.

Redundancy is generated but is handled by the computer.

Here is the C code [#2]
#include <stdio.h> #define swap(x,y) { x = x + y; y = x - y; x = x - y; } int main() { int x1; int y2; x1 = 2; y2 = 3; printf("before x1=%d y2=%d\n",x1,y2); swap(x1,y2) printf("after x1=%d y2=%d\n",x1,y2); return 0; }
Note: Due to the replacement of swap(x1,y2) with a block (delimited by curly braces), a terminating semicolon can be used or not used.

Here is the output of the C code.
before x1=2 y2=3 after x1=3 y2=2

A text formatter approach uses macros to expand text in-line. Somewhat like AOP = Aspect Oriented Computing

Another way:

Combined way:

Code and data are two views of the same phenomena.

• Code can be data.
• Data con be code.

Von Neumann first noticed this in the 1950's though it is assumed by Turing in his limits of computation work involving the Halting Problem in the 1930's.

Redundancy is repetition. This can be good or bad.

• Noncomputer-checked redundancy is bad. Human error.
• Computer-checked redundancy is good. Backup systems, type-checkers, spell-checkers, etc.

Not to be overly repetitive and redundant: Have you tired of the global worldwide pandemic that is everywhere?

Noncomputer-checked redundancy is the primary problem in software systems.

Design goal: Every important aspect of a program should be changeable in one and only one place. To make a change, find that one place.

Design goal: In general, every block of code should have one entry point and one exit point.

As with all rules: unless you have a really good reason.

Data redundancy issues: Solved with RDBMS = Relational Database Management System and SQL = Structured Query Language.

• Top-down: ER (Entity Relationship) model
• Bottom-up: Data normalization rules.

Still present in No-SQL systems.

• Data model part (no code needed)
• Business rule part (requires code)

Code redundancy issues: Solved (in part) with OOP = Object Oriented Programming.

• Top-down: object-oriented design
• Bottom-up: structured programming, modular programming, classes and objects.

Still present in non-OOP systems (Go, Julia, etc.)

Text (and code) world involves text formatting using macros, etc.

It is almost always better to move "code-driven programming" to "data-driven programming".

• Code driven: Long if-then-else for each day of the week.
• Data driven: Array indexed lookup of result.

This should be covered in the first programming course so students learn both ways and which is better.

• Code flow: control flow charts (avoid)
• Data flow: data flow charts (use)

Better to transform the data to new data without changing the data in-place (assignment statement issues), the idea of XSLT.

Functional requirement: Customer-facing output is to be "Hello. How is you today.".

Nonfunctional requirement: Use the Go (or golang) programming language.

Here is a code example in Go.
package main import "fmt" func main() { fmt.Printf("Hello. How is you today.\n") }
If you change the output text in any way, you lose points.

The customer specifies the customer-facing requirements.

The company (teacher) will specify the programmer-facing requirements.

The only way to determine if the code has an error is to compare it to a specification.

Fallacy: The programmer is allowed to change the customer-facing specifications when they think it will make a better program.
The customer gets what they requested and approved. In real situations, one goes to the manager, the manager goes to the client, and a change to the specification is worked out.

In a beginning programming course, the customer-facing parts of the program are the input and output statements.

• Customers can be very particular about the output. Every character and space must be what they want.
• The same goes for input prompts and input echo - text for this course, but the graphical user interface in general.

Statistics analogy:

• Small (Bayesian) sample to estimate population mean (opportunity to learn)
• Complete sample to determine population mean (educate)

• operational
• declarative
• axiomatic

... more to be added ...

... more to be added ...

... more to be added ...

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.

Go: Procedural abstraction introduction 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.

Go: Procedural abstraction introduction 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.

Some ways of programming without thinking like a machine have been presented. Many more were omitted.

• Operational: How it works (control)
• Functional: What it does (logic)
• Algebra: transform without thinking
• Abstraction: similarities and differences
• Code-driven to data-driven
• Code flow to data flow (avoid update in place)

Questions and comments and more information.

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• https://robinsnyder.org (mirror)
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• https://ycp.powersoftwo.org (class web site from 2019-2020)

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