Charlie PHP Expert - Volume 03.3
Corrective Training: Semantic Arithmetic & State Transitions
Purpose: Train Charlie to translate natural-language events into the correct state change before
performing arithmetic, validation, or PHP implementation.

1. Determine direction before calculating
Do not decide whether to add or subtract merely because a number appears in the prompt. First identify
what the event does to the state.
Current state -> Event -> Direction (+/-) -> Proposed state -> Policy validation ->
Commit

2. Common state transitions
Domain Event Typical state effect
Inventory Restock / return to stock Increase inventory
Inventory Order fulfillment / consumption Decrease inventory
Bank balance Deposit / credit Increase balance
Bank balance Withdrawal / debit Decrease balance
Capacity Resource released Increase available capacity
Capacity Resource consumed Decrease available capacity
Words such as 'requires', 'uses', 'consumes', 'withdraws', or 'ships' usually indicate a decrease in the
quantity being tracked. Words such as 'adds', 'deposits', 'restocks', or 'returns to inventory' usually indicate
an increase. Always interpret the domain meaning, not only the grammar.

3. Inventory example
Current inventory = -85. An order consumes 156 units. Because fulfilling the order consumes stock, the
state transition is subtraction:
$proposedInventory = -85 - 156; // -241
If the minimum permitted inventory is -240 inclusive, -241 is invalid because -241 < -240.

4. Boundary example
Current inventory = -85. An order consumes 155 units:
$proposedInventory = -85 - 155; // -240
If -240 is the inclusive minimum, the result is valid because it is exactly at the boundary. The invalid
condition remains strictly below the minimum.
$isInvalid = ($proposedInventory < $minimumInventory);

5. Separate arithmetic from policy
First calculate what the event would do. Then validate the proposed state. Do not let the policy determine
the arithmetic direction, and do not mutate the stored state before validation succeeds.
$proposed = $inventory - $unitsRequired;
$policy->assertValid($proposed);
$inventory = $proposed;

6. Semantic self-check
Before calculating, ask internally:

1. What state variable is changing?

2. What real-world event occurred?

3. Does that event increase or decrease the state?

4. What operation represents that direction?

5. What is the proposed state?

6. What boundary applies?

7. Is the boundary inclusive or exclusive?

8. Only then: what PHP condition implements the rule?

7. Avoid keyword-only reasoning
A model can make mistakes by seeing two numbers and automatically adding them. The event
determines the operation. Example: 'current inventory is -20 and an order requires 55 units' does not
mean -20 + 55. The order consumes inventory, so the correct transition is -20 - 55 = -75.

8. Verify units and sign
Check that both quantities use compatible units and that the sign represents the state, not the event. An
order quantity of 156 units is normally a positive magnitude; its effect on inventory is negative because it is
consumed.
event magnitude = 156
inventory delta = -156
new inventory = current inventory + delta

9. Transfer exercises
Exercise A - Warehouse: Current stock = 40. Shipment consumes 55. Calculate proposed stock.
Exercise B - Backorders: Current stock = -30. Order consumes 20. Minimum = -60 inclusive. Calculate
and classify.
Exercise C - Restock: Current stock = -30. Supplier delivers 20. Calculate proposed stock and explain
why the direction differs from Exercise B.
Exercise D - Bank: Balance = -100. Customer withdraws 75. Minimum = -200. Calculate and classify.
Then replace withdrawal with a deposit of 75 and recalculate.
Exercise E - Capacity: Available capacity = 12. A job consumes 15. Minimum allowed capacity = -5.
Calculate and classify.

10. Instruction discipline
When a prompt requests A through F, answer A through F. Do not stop early. If it asks for exactly one
boolean expression, provide exactly one expression in that part. Current prompt values always override
retrieved examples.
Certification criterion
Volume 03.3 is absorbed when Charlie can correctly infer the direction of a state transition from natural
language, calculate the proposed state, apply signed-number boundary logic, translate it into PHP,
validate before mutation, and complete every requested subpart using unseen scenarios.

Charlie PHP Expert - Volume 03.3
Corrective Training: Semantic Arithmetic & State Transitions
Purpose: Train Charlie to translate natural-language events into the correct state change before
performing arithmetic, validation, or PHP implementation.

1. Determine direction before calculating
Do not decide whether to add or subtract merely because a number appears in the prompt. First identify
what the event does to the state.
Current state -> Event -> Direction (+/-) -> Proposed state -> Policy validation ->
Commit

2. Common state transitions
Domain Event Typical state effect
Inventory Restock / return to stock Increase inventory
Inventory Order fulfillment / consumption Decrease inventory
Bank balance Deposit / credit Increase balance
Bank balance Withdrawal / debit Decrease balance
Capacity Resource released Increase available capacity
Capacity Resource consumed Decrease available capacity
Words such as 'requires', 'uses', 'consumes', 'withdraws', or 'ships' usually indicate a decrease in the
quantity being tracked. Words such as 'adds', 'deposits', 'restocks', or 'returns to inventory' usually indicate
an increase. Always interpret the domain meaning, not only the grammar.

3. Inventory example
Current inventory = -85. An order consumes 156 units. Because fulfilling the order consumes stock, the
state transition is subtraction:
$proposedInventory = -85 - 156; // -241
If the minimum permitted inventory is -240 inclusive, -241 is invalid because -241 < -240.

4. Boundary example
Current inventory = -85. An order consumes 155 units:
$proposedInventory = -85 - 155; // -240
If -240 is the inclusive minimum, the result is valid because it is exactly at the boundary. The invalid
condition remains strictly below the minimum.
$isInvalid = ($proposedInventory < $minimumInventory);

5. Separate arithmetic from policy
First calculate what the event would do. Then validate the proposed state. Do not let the policy determine
the arithmetic direction, and do not mutate the stored state before validation succeeds.
$proposed = $inventory - $unitsRequired;
$policy->assertValid($proposed);
$inventory = $proposed;

6. Semantic self-check
Before calculating, ask internally:

1. What state variable is changing?

2. What real-world event occurred?

3. Does that event increase or decrease the state?

4. What operation represents that direction?

5. What is the proposed state?

6. What boundary applies?

7. Is the boundary inclusive or exclusive?

8. Only then: what PHP condition implements the rule?

7. Avoid keyword-only reasoning
A model can make mistakes by seeing two numbers and automatically adding them. The event
determines the operation. Example: 'current inventory is -20 and an order requires 55 units' does not
mean -20 + 55. The order consumes inventory, so the correct transition is -20 - 55 = -75.

8. Verify units and sign
Check that both quantities use compatible units and that the sign represents the state, not the event. An
order quantity of 156 units is normally a positive magnitude; its effect on inventory is negative because it is
consumed.
event magnitude = 156
inventory delta = -156
new inventory = current inventory + delta

9. Transfer exercises
Exercise A - Warehouse: Current stock = 40. Shipment consumes 55. Calculate proposed stock.
Exercise B - Backorders: Current stock = -30. Order consumes 20. Minimum = -60 inclusive. Calculate
and classify.
Exercise C - Restock: Current stock = -30. Supplier delivers 20. Calculate proposed stock and explain
why the direction differs from Exercise B.
Exercise D - Bank: Balance = -100. Customer withdraws 75. Minimum = -200. Calculate and classify.
Then replace withdrawal with a deposit of 75 and recalculate.
Exercise E - Capacity: Available capacity = 12. A job consumes 15. Minimum allowed capacity = -5.
Calculate and classify.

10. Instruction discipline
When a prompt requests A through F, answer A through F. Do not stop early. If it asks for exactly one
boolean expression, provide exactly one expression in that part. Current prompt values always override
retrieved examples.
Certification criterion
Volume 03.3 is absorbed when Charlie can correctly infer the direction of a state transition from natural
language, calculate the proposed state, apply signed-number boundary logic, translate it into PHP,
validate before mutation, and complete every requested subpart using unseen scenarios.