Conditional Proof Assumption Discharge Depth Tracker
Track nested begin(+1), neutral(0), discharge(-1) assumption events; not a validation of formulas or implication-introduction proof.
Description
Conditional Proof Assumption Discharge Depth Tracker: return depth after events, maximum depth, undischarged depth.
Nested assumptions create levels in a proof. Opening an assumption increases the depth; discharging one reduces it.
This tool returns depth after events, maximum depth, undischarged depth. Use the stated units and model convention when interpreting these fields.
When to use this tool
Use this tool when the supplied inputs match the specific operation described above and you need a repeatable result under its stated convention.
- Check the supported input and output contract against an existing calculation or observation.
- Use the complete example to confirm units, selector spelling and result interpretation.
How to use the tool and how it works
- Enter every field in the input table using the stated units and the exact supported selector spelling where applicable.
- Run the tool. Correct input errors before interpreting an output.
- Read the result fields below; use accompanying flags and the stated sign, boundary or model convention when interpreting a number.
Read events as +1, 0 or -1 and accumulate the depth in order. Reject a discharge that would make depth negative; report every resulting depth, the maximum and the final undischarged depth.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| assumptionEvents | Assumption events. | List of finite numbers |
| Output field | Interpretation |
|---|---|
| result | Object containing the following named result fields. |
| result.depthAfterEvents | Depth after events list, in the ordering described in the calculation. |
| result.maximumDepth | Maximum depth; use the stated units and sign convention. |
| result.undischargedDepth | Undischarged depth; use the stated units and sign convention. |
{
"input": {
"assumptionEvents": [
1,
1,
0,
-1,
-1
]
},
"output": {
"result": {
"depthAfterEvents": [
1,
2,
2,
1,
0
],
"maximumDepth": 2,
"undischargedDepth": 0
}
}
}Limitations and assumptions
- A zero final depth indicates balanced events, not a logically valid proof or correct discharge dependencies.
- Every declared field is required and unexpected fields are rejected. Numeric inputs must be finite; input errors are distinct from a valid false result or an explicitly qualified output.
- Extremely large inputs and nonfinite or excessively large outputs are rejected. List positions reported by the tool use zero-based indices unless stated otherwise.
Alternative or Complementary methods
Check the underlying observations, units and conventions independently before using the result in a larger workflow. The tools listed below address nearby tasks; compare their inputs and scope before substituting one for this operation.
References
Similar or alternative tools
- Indirect Proof Negated Goal Assumption Validator
Check an atomic classical indirect-proof initial assumption against negated goal; does not establish contradiction or validate proof completion.
- a proposition classifier
Categorical propositions use A for universal affirmative, E for universal negative, I for particular affirmative and O for particular negative.