Description
Finite-trace strong until at index zero: right must eventually hold and left must hold strictly before its earliest qualifying witness.
A logical calculation operates on a stated representation: truth values, token lists, counts, or an explicitly supplied relation. Checking one assignment, pair, trace, or witness is different from proving a formula or validating an entire argument. Empty domains, duplicate tokens, and scope conventions can change the result.
Finite-trace strong until at index zero: right must eventually hold and left must hold strictly before its earliest qualifying witness.
When to use this tool
Use Temporal Until One Boundary Case when you need this exact local truth, count, token, relation, or witness check within a larger logic workflow.
How to use the tool and how it works
- Enter left, right. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read holds, witnessIndex. Inspect holds before interpreting the associated values.
Require equally sized left and right Boolean arrays. Find the earliest right=true position with every earlier left entry true; return holds and its zero-based witnessIndex, or -1 when none exists.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Array of boolean; maximum items 256. |
| right | Right | Required. Array of boolean; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| holds | Holds | Required. Boolean. |
| witnessIndex | Zero-based first valid until witness, or -1 when none exists. | Required. Safe integer. |
{
"input": {
"left": [
true,
true,
false
],
"right": [
false,
false,
true
]
},
"output": {
"holds": true,
"witnessIndex": 2
}
}Limitations and assumptions
- This is strong until on a supplied finite trace starting at index zero. Left need not hold at the witness itself; an empty trace returns false, and infinite or partially observed futures are not evaluated.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use a parser, scope-aware representation, model checker, or proof procedure when the supplied token or witness representation is insufficient. A local passing check should not be promoted to global validity.
References
Similar or alternative tools
- Modal Box Vacuous Successor Case
Evaluate box and diamond on an explicit finite list of accessible successor truth values.
- Modal Successor Count Budget
Finite modal truth from supplied successor counts, with vacuous necessity at zero successors.