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: