Description
Check whether a supplied free-variable list contains only the candidate variable.
Formal annotations separate declared truth values, domain assumptions, variable lists and source interpretations. A direct self-reference differs from an indirect cycle, and one self-loop differs from a globally reflexive relation. Local token operations do not parse a complete argument, derive its assumptions or establish truth or validity.
Check whether a supplied free-variable list contains only the candidate variable.
When to use this tool
Use Logical Formula Single Free Variable Flag when you already have candidateVariable, suppliedFreeVariables and need to check whether a supplied free-variable list contains only the candidate variable.
How to use the tool and how it works
- Enter candidateVariable, suppliedFreeVariables. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read isOnlyFreeVariable. Inspect isOnlyFreeVariable before interpreting the associated values.
Require candidateVariable nonempty; return true exactly when the list is nonempty and every entry equals the candidate.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| candidateVariable | Candidate Variable | Required. Text; minimum UTF-16 length 1; maximum UTF-16 length 8192. |
| suppliedFreeVariables | Supplied Free Variables | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| isOnlyFreeVariable | Nonempty supplied list containing only the candidate, allowing repeats. | Required. Boolean. |
{
"input": {
"candidateVariable": "x",
"suppliedFreeVariables": [
"x",
"x"
]
},
"output": {
"isOnlyFreeVariable": true
}
}Limitations and assumptions
- Repeated identical entries are allowed; no formula is parsed, variables resolved or free-variable list derived.
- 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
Parse or formalize the complete expression and declared semantics when validity is the question. Inspect the full reference or accessibility relation for cycles and global properties; a supplied annotation, self-loop or variable list establishes only its local predicate.
References
Similar or alternative tools
- Modal Accessibility Edge Reflexive Label
Check whether one supplied modal-accessibility edge is a self-loop.
- Quantifier Domain Emptiness Flag
Expose empty-domain vacuity flags from a supplied domain size.