TI-BASIC Control Flow Puzzle

iPhoenix · friendly neighborhood site admin (Posts: 1912)

Ignoring the control-flow catastrophe in the middle, let’s take for granted that the outer For( loop runs exactly twice, once with K=0 and once with K=1. Let’s consider each of these cases individually. We’ll first consider the K=1 case, as it is more straightforward than the K=0 case.

Case: K=1

If 1
Then
Goto A
End
While 0
Lbl A
Else
End

The bolded code is the path taken. Remember, the calculator executes the program line by line, so a Lbl/Goto in the middle of an If statement like this does not affect the interpretation of the If statement.
So, stepping through this program:

If 1:Then: The calculator sets aside a little piece of memory to remember that it had taken a true If-Then statement.
Goto A: the Goto is taken (without disturbing that little piece of memory set aside earlier)
Else: The Else checks the little piece of memory to see if it had taken a true If-Then statement (ERR:SYNTAX otherwise), and searches for an End to jump to, which it finds immediately. We won’t yet consider the exact mechanics of searching for an End. This Else is the first conditional to search for and find this End statement.
End: The End frees the little piece of memory.

Now, let’s perform the same analysis on the program when K=0.

Case: K=0

If 0
Then
Goto A
End
While 0
Lbl A
Else
End

In this case, both the If statement and the While loop fail to meet their conditions and search for Ends:

If 0:Then: The condition fails, so the If statement searches for an End and finds the End after the Goto. Execution continues after this End statement.
While 0: This condition also fails, and it finds the End statement after the Else. This While is the second conditional to search for and find this End statement.

The While finding this End is somewhat unexpected, so it’s worth examining exactly what happens when a While or For( loop searches for an End. (n.b. I suppose this isn't strictly necessary to understand the solution. Still, the point of this puzzle was to get you thinking about the minutiae of control flow, so I present it anyway.) It’s straightforward: the While checks the first tokens of successive lines, adding one to a counter if it finds a For(/While/Repeat/If-Then and subtracting one if it encounters an End. The search ends if it encounters an End when the counter is back where it started, and there is no error for reaching the end of the program.

I speculate that at the time when the End-searching was implemented, someone incorrectly assumed that every Else would be preceded by an If-Then (or, more generously, deemed it unnecessary given the additional time-and-space cost of doing it “right”). My less-generous theory is perhaps corroborated by merth’s finding that an isolated Else does not throw an ERR:SYNTAX on specific early TI-82 versions (later pinpointed by Logical to be 8.0 or earlier).

Using my method, you cannot find three statements that find the same End. Specifically, you would need to find three control statements A, B, C such that

A, B, C all search for an End
A ignores B and C when looking for its End (*)
B ignores C when looking for its End

I am thoroughly convinced that the starred condition cannot be met without using DelVar or some undiscovered method.

Using DelVar forms the basis of Zeroko’s first solution. Because While only checks the first token on each line, a While placed on the same line as a DelVar will not be seen (the following elegant solution for three conditionals is due to commandz):

LogicalJoe · Member (Posts: 165)

Structure 2 with For(: 23 bytes

merthsoft · im shaun (Posts: 3885)

LogicalJoe · Member (Posts: 165)

iPhoenix · friendly neighborhood site admin (Posts: 1912)

In this code, the Disp is only reached if A is false or B is true. A proof:

Suppose A is false. Then If B is skipped and flow continues directly at the Disp 1. Now suppose A is true. Then If B is checked and Disp 1 is reached if and only if B is true.

What if I repeat this one hundred times (like the following)?