isEqual

TypeScript only

rel1.isEqual(rel2)

Problem

Check if two relations contain exactly the same tuples.

Example: I want to verify that my query transformation produces the same result as the expected output.

Description

The isEqual operator compares two relations for set equality. Two relations are equal if and only if they contain exactly the same tuples (regardless of order).

This is useful for:

• Testing query correctness
• Validating data transformations
• Implementing relational assertions

Requirements

Both relations should have the same heading (same attribute names) for a meaningful comparison.

Examples

Equal relations

const r1 = Bmg([
  { a: 1, b: 2 },
  { a: 3, b: 4 },
])

const r2 = Bmg([
  { a: 3, b: 4 },  // Different order
  { a: 1, b: 2 },
])

r1.isEqual(r2)
// => true (order doesn't matter)

Unequal relations

const r1 = Bmg([
  { a: 1, b: 2 },
  { a: 3, b: 4 },
])

const r2 = Bmg([
  { a: 1, b: 2 },
  { a: 5, b: 6 },  // Different tuple
])

r1.isEqual(r2)
// => false

Testing query results

const expected = Bmg([
  { sid: "S2", name: "Jones" },
  { sid: "S3", name: "Blake" },
])

const actual = suppliers
  .restrict({ city: "Paris" })
  .project(['sid', 'name'])

if (!actual.isEqual(expected)) {
  throw new Error("Query result doesn't match expected")
}

Relational semantics

Because relations are sets:

• Order of tuples doesn’t matter
• Duplicate tuples are automatically removed
• Only the presence/absence of each unique tuple matters

// These are equal (duplicates are eliminated)
const r1 = Bmg([{ a: 1 }, { a: 1 }, { a: 2 }])
const r2 = Bmg([{ a: 1 }, { a: 2 }])

r1.isEqual(r2)
// => true