Description
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.
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.
Compare flat single-binder token bodies, rejecting potential free-variable capture; nested binders are outside this model.
When to use this tool
Use Alpha Equivalence Bound Variable Pair 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 firstBinder, firstBody, secondBinder, secondBody. 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 equivalent. Inspect equivalent before interpreting the associated values.
Require nonempty binder strings and reject simple token-capture conflicts between the two bodies and opposite binders. Compare equal-length bodies, requiring a firstBinder token to match secondBinder and all other tokens to match literally; return equivalent.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstBinder | First Binder | Required. Text; maximum UTF-16 length 8192. |
| firstBody | First Body | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| secondBinder | Second Binder | Required. Text; maximum UTF-16 length 8192. |
| secondBody | Second Body | Required. Array of text; maximum UTF-16 length 8192; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| equivalent | Equivalent | Required. Boolean. |
{
"input": {
"firstBinder": "x",
"firstBody": [
"P",
"x"
],
"secondBinder": "y",
"secondBody": [
"P",
"y"
]
},
"output": {
"equivalent": true
}
}Limitations and assumptions
- This handles one flat binder pair over pretokenized bodies. It is not a parser or a complete alpha-equivalence test for nested binders, shadowing, structured terms, or general capture avoidance.
- 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
- Quantifier Bound Variable Shadow Count
Count shadowing in an explicitly ordered nested binder path, without parsing formulas or proving equivalence.
- Formula Free Variable Count
Count explicitly annotated variable occurrences; binding scope is supplied rather than parsed.