XBRL Formula

The XBRL Formula specification defines a standardised mechanism for creating validation rules within taxonomies using XPath 2.0 expressions.

Why Formulas?

The calculation linkbase only handles simple addition/subtraction. Formulas handle everything else:

• Complex mathematical relationships
• Cross-checking between different parts of a report
• Mandatory field checks
• Date comparisons
• Conditional logic

Three Types of Assertions

1. Value Assertions (Most Common)

A boolean expression evaluated against matched facts:

test="$Assets = $Equity + $Liabilities"

Passes if true, fails if false.

2. Existence Assertions

Verify that required data exists:

evaluation-count="count($Revenue) >= 1"

Ensures "Revenue" is reported at least once.

3. Consistency Assertions

Compare a calculated value against a reported value within a tolerance:

• Used for cross-checking derived data

Anatomy of a Formula Rule

Formula Rule
├── Rule Name / ID (generates error codes on failure)
├── Test Expression (XPath 2.0 logic)
├── Variables (inputs selecting specific facts)
│   └── Filters (refine which facts each variable selects)
├── Preconditions (optional: when to run the rule)
├── Severity (ERROR or WARNING)
└── Messages (what to display on pass/fail)

Variable Filters

Filter Type	Purpose
Concept Filter	Select facts by concept name
Explicit Dimension Filter	Constrain to specific dimensional members
Typed Dimension Filter	Work with typed dimension values
Period Filter	Match across time periods
Concept-Relation Filter	Leverage taxonomy hierarchies
Aspect-Cover Filter	Override implicit filtering

Implicit Filtering

A powerful built-in mechanism that automatically groups facts sharing uncovered aspects (period, unit, entity, dimensions). This means a single rule can apply across multiple scenarios without explicit enumeration.

Example: A rule $Assets = $Equity + $Liabilities will automatically apply to every combination of entity, period, and dimensions where all three concepts are reported.

Example from the LEI Taxonomy

The LEI taxonomy includes formula assertions that validate Legal Entity Identifiers:

<va:valueAssertion
  id="lei-fact-checksum"
  test="lei-fn:validate-checksum( $v )"
  implicitFiltering="true"
  aspectModel="dimensional">

This validates that every reported LEI fact has a valid checksum. If it fails:

"The value 'ABC123...' is not a valid Legal Entity Identifier (invalid checksum)"

Severity Levels

• ERROR (default) -- the report is invalid
• WARNING -- potential issue, but the report may still be valid

Common Validation Patterns

Pattern	Example
Aggregation	Totals = sum of components
Mandatory checks	Certain concepts must be reported
Date comparisons	End date must be after start date
Roll-forward	Opening balance + changes = closing balance
Cross-period	Instant values match duration endpoints
Format validation	Values match expected patterns (like LEI checksum)

Messages

Rules can include localised messages with dynamic content using XPath:

<msg:message xml:lang="en">
  The value '{ $v }' is not a valid Legal Entity Identifier
</msg:message>

The { $v } is replaced with the actual value at runtime.