Set Disjoint Union Tagged Element Key Tool

Description

Parse bounded elementJson and serialize the tuple of tag and that JSON value as key.

A finite set records membership, while a multiset also records multiplicity. An ordered set adds an ordering rule, and an interval adds endpoint-closure choices. A witness for one element, a count budget, and equality of complete sets establish different facts.

Parse bounded elementJson and serialize the tuple of tag and that JSON value as key.

When to use this tool

Use Set Disjoint Union Tagged Element Key when you need the stated finite-set, interval, multiplicity, membership, or ordering operation under the given equality convention.

How to use the tool and how it works

Enter tag, elementJson. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read key. Use the output convention below.

Parse bounded elementJson and serialize the tuple of tag and that JSON value as key.^[1]

Input field	Meaning and units	Accepted input
tag	Tag	Required. Text; maximum UTF-16 length 8192.
elementJson	Element Json	Required. Text; maximum UTF-16 length 8192.

Output field	Interpretation	Returned shape
key	Key	Required. Text; maximum UTF-16 length 8192.

json

{
  "input": {
    "tag": "A",
    "elementJson": "\"x\""
  },
  "output": {
    "key": "[\"A\",\"x\"]"
  }
}

Limitations and assumptions

This tags a supplied element for a disjoint-union representation. Object property order can affect the serialized key, so it is not universal structural canonicalization or a mathematical-set equality procedure.
The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Signed zero is exported as zero.

Alternative or Complementary methods

Use a full set operation when one element or count cannot establish the required relation. Preserve the distinction between strings, typed scalar atoms, nested sets, ordered lists, and multisets.

References

Calculation and input contract: set/set-disjoint-union-tagged-element-key — tool.io

Similar or alternative tools

Set Element Canonical Key Type Tag
Parse valueJson as a bounded JSON scalar and return a key consisting of its type tag and JSON serialization, treating null with its own tag.
Set Union One Element Cardinality Delta
Return delta zero for alreadyMember or one otherwise and add it to nonnegative integer cardinality.