Finite Relation Equivalence Property Report
Report equivalence property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
Description
Report equivalence property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
An equivalence relation must be reflexive, symmetric and transitive on the complete supplied universe.
When to use this tool
Report equivalence property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
- Prepare the supplied pairsJson, universe fields for this operation.
- Compare the complete example with the representation used by your own input before carrying the result into another step.
How to use the tool and how it works
- Enter pairsJson, universe. Use the exact text syntax, units and index conventions explained below.
- Run the tool. If input validation fails, correct the supplied fields before interpreting any result.
- Read result.properties, result.holds. Interpret false, null and empty lists using the distinctions below; they can be valid outputs.
Validate and deduplicate in-universe pairs, compute four relation-property flags and set holds from reflexive, symmetric and transitive.1
| Input field | Meaning and representation | Accepted input |
|---|---|---|
| pairsJson | JSON text, entered as one text field. The decoded structure is illustrated below; it is not a separate file. | Text |
| universe | universe. | List of strings; at most 128 entries |
For the JSON text fields, the following decoded structures show the example records before they are serialized into input strings. Keep field names, list nesting and value types as shown.
[
{
"field": "pairsJson",
"decoded": [
[
"a",
"b"
],
[
"b",
"a"
]
]
}
]| Output field | Interpretation |
|---|---|
| result | Object containing the named outputs below. |
| result.properties | The properties value under the stated formula or text convention. |
| result.holds | True exactly when the stated property passes; it does not establish other properties. |
{
"input": {
"pairsJson": "[[\"a\",\"b\"],[\"b\",\"a\"]]",
"universe": [
"a",
"b"
]
},
"output": {
"result": {
"properties": {
"reflexive": false,
"symmetric": true,
"antisymmetric": false,
"transitive": false
},
"holds": false
}
}
}Limitations and assumptions
- No equivalence classes or missing closure pairs are generated. Antisymmetry is reported but is not an equivalence requirement.
- All declared input fields are required and unexpected top-level fields are rejected. Numbers must be finite; lists are limited to 128 entries and ordinary text fields to 8,192 UTF-16 code units, with tighter limits where stated.
- JSON text inputs must parse within bounded nesting and size limits. Numeric outputs outside the safe finite range are rejected; large exact integer results use decimal strings. Indexes and half-open spans are zero-based unless a rank is explicitly described as one-based.
Alternative or Complementary methods
Declare the full universe and distinguish testing a property from adding its closure. Use separate functionality and totality checks before interpreting a relation as a function.
References
Similar or alternative tools
- Finite Relation Partial Order Property Report
Report partial-order property evidence for an explicit finite relation; does not assume a claimed order or repair missing pairs.
- Finite Relation Composition Pairs
Compose finite relations by following first then second, coalescing duplicate witnesses into unique endpoint pairs; order convention is explicit.