Proof: Proof: STORE Instruction Example
The following example shows what happens when a STORE instruction is executed.
More precisely, we prove that
Let's prove the following theorem:
if the following are true:
- instruction #0 is
store src=5 addr=1 imm=1 - the PC at time 0 = 0
- value of cell 1 at time 0 = 3
- value of cell 5 at time 0 = 9
then value of cell 4 at time 1 = 9
Try out the example in the simulator:
Instructions
| Memory Cells |
|---|
| Program Counter | Time |
|---|---|
| 0 | 0 |
LW Computer Simulator
The computer copies the value in memory cell #5 (9) to cell #4. The destination is calculated by adding the value in cell #1 (3) and the immediate (1).
Proof:
Given
| 1 | instruction #0 is store src=5 addr=1 imm=1 |
|---|---|
| 2 | the PC at time 0 = 0 |
| 3 | value of cell 1 at time 0 = 3 |
| 4 | value of cell 5 at time 0 = 9 |
| # | Claim | Reason |
|---|---|---|
| 1 | value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell 5 at time 0 | if instruction #0 is store src=5 addr=1 imm=1 and the PC at time 0 = 0, then value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell 5 at time 0 |
| 2 | 0 + 1 = 1 | 0 + 1 = 1 |
| 3 | value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell ((value of cell 1 at time 0) + 1) at time 1 | if 0 + 1 = 1, then value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell ((value of cell 1 at time 0) + 1) at time 1 |
| 4 | (value of cell 1 at time 0) + 1 = 3 + 1 | if value of cell 1 at time 0 = 3, then (value of cell 1 at time 0) + 1 = 3 + 1 |
| 5 | value of cell ((value of cell 1 at time 0) + 1) at time 1 = value of cell (3 + 1) at time 1 | if (value of cell 1 at time 0) + 1 = 3 + 1, then value of cell ((value of cell 1 at time 0) + 1) at time 1 = value of cell (3 + 1) at time 1 |
| 6 | 3 + 1 = 4 | 3 + 1 = 4 |
| 7 | value of cell (3 + 1) at time 1 = value of cell 4 at time 1 | if 3 + 1 = 4, then value of cell (3 + 1) at time 1 = value of cell 4 at time 1 |
| 8 | value of cell (3 + 1) at time 1 = value of cell 5 at time 0 | if value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell ((value of cell 1 at time 0) + 1) at time 1 and value of cell ((value of cell 1 at time 0) + 1) at time 1 = value of cell (3 + 1) at time 1 and value of cell ((value of cell 1 at time 0) + 1) at time (0 + 1) = value of cell 5 at time 0, then value of cell (3 + 1) at time 1 = value of cell 5 at time 0 |
| 9 | value of cell (3 + 1) at time 1 = 9 | if value of cell (3 + 1) at time 1 = value of cell 5 at time 0 and value of cell 5 at time 0 = 9, then value of cell (3 + 1) at time 1 = 9 |
| 10 | value of cell 4 at time 1 = 9 | if value of cell (3 + 1) at time 1 = value of cell 4 at time 1 and value of cell (3 + 1) at time 1 = 9, then value of cell 4 at time 1 = 9 |
Comments
Please log in to add comments