Teacher answer key

The Stack and Functions

Gather four kinds of evidence: prediction of relevant state; behavior across varied cases including boundaries; explanation using trace/state evidence; and a reasoned correction of one mismatch. Mark each as emerging, with support or independent using paper or your school’s existing approved process. A challenge pass is machine-behavior evidence, not proof of authorship or complete mastery. Accept equivalent correct programs; the public key is a model, not the only possible answer.

Public teaching material. Solutions are examples; equivalent correct programs may also pass the actual checks.

19. Stack Operations: Last In, First Out

Save values on the data stack and restore them in reverse order.

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1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 11
PUSH
LOAD 22
PUSH
POP
PRINT
POP
PRINT
HALT

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 22, 11

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	11	`{"registers":[11,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
PUSH	1	2	11	11	`{"registers":[11,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":254,"stack":[11],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOAD	2	3	11	22	`{"registers":[22,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":254,"stack":[11],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read two integers, save both on the data stack, then print them in reverse order. Use PUSH and POP rather than hardcoded values.

Required instruction types: INPUT, PUSH, POP

Example challenge solution

INPUT
PUSH
INPUT
PUSH
POP
PRINT
POP
PRINT
HALT

Actual checker fixtures

Case 1

Input: 3, 8
Initial memory: All bytes initially zero
Expected output: 8, 3

Case 2

Input: -4, 0
Initial memory: All bytes initially zero
Expected output: 0, -4

Case 3

Input: 9, 9
Initial memory: All bytes initially zero
Expected output: 9, 9

3. Explain the machine

Why does the second supplied value print first?

Reasoning and teaching note

PUSH/POP are LIFO; with inputs3,8 output 8,3; call frames are not data values.

20. Calling a Subroutine

Reuse code and return to the instruction after CALL.

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1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 3
CALL square
PRINT
LOAD 4
CALL square
PRINT
HALT
square: MUL R0
RETURN

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 9, 16

Instruction	PC before	PC after	R0 before	R0 after	Relevant state	Output
LOAD	0	1	0	3	`{"registers":[3,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
CALL	1	7	3	3	`{"registers":[3,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":254,"stack":[],"callStack":[2],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
MUL	7	8	3	9	`{"registers":[9,0,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":254,"stack":[],"callStack":[2],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read two integers. Call the same square subroutine for each and print the two squares in input order.

Required instruction types: INPUT, CALL, MUL, RETURN

Example challenge solution

INPUT
CALL square
PRINT
INPUT
CALL square
PRINT
HALT
square: MUL R0
RETURN

Actual checker fixtures

Case 1

Input: 3, 4
Initial memory: All bytes initially zero
Expected output: 9, 16

Case 2

Input: -2, 5
Initial memory: All bytes initially zero
Expected output: 4, 25

Case 3

Input: 0, 8
Initial memory: All bytes initially zero
Expected output: 0, 64

3. Explain the machine

Why do two calls to the same code return to different places?

Reasoning and teaching note

Each CALL saves its own PC+1 in a distinct call frame; function body is shared but caller continuation differs.

21. Preserving a Caller’s State

Use a save/restore convention when a function needs scratch space.

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1. Predict and trace

Before running the Try program, predict its output and trace the first three executed instructions. Track the relevant registers, flags or memory as needed. Then step the program to compare.

LOAD 1 R1
LOOP 3
LOAD R1
CALL double
PRINT
LOAD R1
ADD 1
COPY R0 R1
RETURN
HALT
double: MUL 2
RETURN

Queue input: None

Initialize memory: All bytes initially zero

Try prediction key

Output: 2, 4, 6

Instruction	PC before	PC after	R0 after	Relevant state	Output
LOAD	0	1	0	`{"registers":[0,1,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[],"memoryReads":[],"memoryWrites":[]}`	None
LOOP	1	2	0	`{"registers":[0,1,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[{"start":1,"end":8,"remaining":3,"callDepth":0}],"memoryReads":[],"memoryWrites":[]}`	None
LOAD	2	3	1	`{"registers":[1,1,0,0,0,0,0,0],"flags":{"zero":false,"negative":false,"overflow":false},"sp":255,"stack":[],"callStack":[],"loopStack":[{"start":1,"end":8,"remaining":3,"callDepth":0}],"memoryReads":[],"memoryWrites":[]}`	None

2. Build and check

Read a saved value into R1, then a function argument. Call a helper that returns argument + 1 while temporarily using R1 as scratch space. Print the result and then the preserved first value. Use PUSH and POP to preserve R1.

Required instruction types: INPUT, PUSH, POP, CALL, RETURN

Example challenge solution

INPUT
COPY R0 R1
INPUT
CALL helper
PRINT
LOAD R1
PRINT
HALT
helper: COPY R0 R2
LOAD R1
PUSH
LOAD 99 R1
LOAD R2
ADD 1
COPY R0 R2
POP
COPY R0 R1
LOAD R2
RETURN

Actual checker fixtures

Case 1

Input: 12, 3
Initial memory: All bytes initially zero
Expected output: 4, 12
Expected final registers: R1: 12

Case 2

Input: -8, 0
Initial memory: All bytes initially zero
Expected output: 1, -8
Expected final registers: R1: -8

Case 3

Input: 7, -5
Initial memory: All bytes initially zero
Expected output: -4, 7
Expected final registers: R1: 7

3. Explain the machine

Which saved state belongs to the caller rather than the function result?

Reasoning and teaching note

The preservation agreement identifies R1; save/restore it while returning the result via R0 and leaving separate call frames intact.