16 th XBRL International Conference Demystifying XBRL Formulas December 5, 2007 Herm Fischer

1. 16th XBRL International Conference Demystifying XBRL Formulas December 5, 2007 Herm Fischer

2. Overview • Why, who needs formulas for what? • Historical perspectives • Process flow of formulas • Formula Linkbase • Contents • Formula processing • Features by use case example • DTS discovery • Functions • Built-in • End-user • Roadmap

3. Why formulas Calculation Linkbase is Enough • Roll-ups validates item sums • Addition within equal context • Period, entity, dimension are equal Calculation Linkbase Can’t Do • Cross context • Movement (start + changes = end) • Dimensions • Business rules

4. Historical Perspectives • 2002 - FDIC contract motivates solutions • Conceptual prototype based on XSL • Excel-like, implicit matching (now in use) • “ - Rule base Requirements IWD • 2003 - XPath syntax chosen • “ - Functions spec drafted. • 2004 - Formula drafts, some implementations • 2006 - Alternative approach with XQuery • 2007 Jan- Issued Formula PWD • Feb, Mar - Survey of users, feedback • June – PWD update based on survey feedback • Dec (late) – PWD-2

5. Original motivationEffective exchange of data • Information producer • Validate data types and values • Consistency and quality checks • Information consumer • (ditto) • Completeness checks • Augment received data with calculated values • Augment received data with annotations

6. XBRL without formulas • Calculation linkbase • Well behaved roll-ups of compatible numerical values • (Proposed) Aggregation of dimensional values • Calculation linkbase can’t do • Cross-context (ending bal = starting bal + changes) • Cross-unit (dollars = price per share X nbr shares) • Dimensional aggregation (all = red wine + white wine) • Missing items checks • Threshold and limits (sum amounts ± €5)

7. Process flow of formulas Formula LB* Output inst.computedfact items Input inst.DTS contextsunitsfact items FormulaProcessor *Formula LB is part of DTS

8. Input instance processing • Instance provides producer’s taxonomy, facts, and producer’s formulas • Consumer may have their own formulas, their own resulting items taxonomy • Formula processor ‘fires’ formulas that match to input fact items • Formula processor produces output instance with result fact items

9. Formula linkbase contents Formula LB* formula arc precondition Parameter(select expr.) variable filter customfunction loc label ref. Input inst.DTS contextsunitsfact items Output inst.computedfact items FormulaProcessor *Formula LB is part of DTS

10. Formula processing Formula LB* • For each/any formula (unordered) • Evaluate parameters (if any) • Filter/bind variables in their order • Nested variable iteration • Test precondition (if any) • Evaluate value • Produce output fact FormulaProcessor Input inst.DTS contextsunitsfact items Output inst.computedfact items *Formula LB is part of DTS

11. Assets sum test, pseudo code • Test that “assets = liabilities + equity” • Input instance has assets, liabilities, and equity • Output boolean test result, true or false

12. Assets sum test, flow • Processing flow Formula LB* FormulaProcessor Output inst.Test resultboolean Input inst.DTS assets, liab, equity *Formula LB is part of DTS

13. Assets sum test, instances • Instance document input has values to test • Output is the boolean result of testing the sum units match same context

14. Assets sum test, formula linkbase

15. Assets sum test, formula resources

16. Assets sum test, formula - compiled

17. Assets sum test, formula execution

18. Assets sum test, formula input

19. Variation: Compute the assets • Prior example tested assets = equity + liabilities • 3 inputs (assets, equity, liabilities) • 1 output (boolean test) • Now no input sum - compute sum as the result • 2 inputs (equity, liabilities) • 1 output (monetary assets)

20. Compute assets, taxonomy • Taxonomy has monetary concepts for assets, liabilities, equity • Here output is the assets concept (vs. boolean) Last example:

21. Compute assets, instances • Instance document input has values to add • Output is the monetary result of adding the sum units match same context

22. Compute assets, formula linkbase

23. Formula linkbase resources • Parameter • Function declaration • Formula • Variables • Filters • Precondition • Generic label • Generic reference

24. Parameter resources • Provide input parameters to formula processor • From external source (invocation of processor) • Or from XPath expression in Parameter • May be required (or optional) • Evaluated before any formula variable (Parameter resources can have arcs to labels & references)

25. Function declaration resources • Declare functions usable in XPath expressions • May be user-supplied • May be built-in to formula processor • May relate to formula registry • Function input parameters • Order, data type • Function name • Function output data type (Function declarations can have arcs to labels & references)

26. Formula resource • Value expression • Concept (either fact variable name or arc to loc) • Context & Unit (where needed) • Fact variable reference (copy from fact variable) • Override facets by xml (e.g., period, measure) • Arcs to variables, precondition (Formula resources can have arcs to labels & references)

27. Variable resources • Fact variables • Bind to input instance fact items/tuples • Arcs to filters constrain which input facts to bind to • Iterates through filtered input facts or returns sequence • General variables • An XPath expression (not to input fact nodes) • Produce sequence or individual atomic results • No arcs to filters • Order in formula by dependency of variables & filters (Variables may have arcs to labels & references)

28. Filter resources • Specify a facet to use as fact predicate • Have arc(s) from fact variable(s) • Available filter facets • Concept, Dimension, Entity, Period, Tuple, Unit, Value, and General (XPath expression) • Implicit filtering • Automates matching non-explicitly filtered facets • Variable-set • PWD 2 feature facilitating filter grouping (Filters can have arcs to labels & references)

29. Precondition resource • Provides an XPath expression to test • Runs after parameters and variables are bound • Arc-connected from formula resource(s) • PWD 2 adds variable-set precondition feature (Preconditions can have arcs to labels & references)

30. Generic label resources • Annotates descriptive text on any • Resource (e.g., any in formula LB) • Element in xsd (e.g., concept, arc type, etc.) • Arc connected (from resource or element) • Unconstrained contents

31. Generic reference resources • Provides link:part’s to any • Resource (e.g., any in formula LB) • Element in xsd (e.g., concept, arc type, etc.) • Arc connected (from resource or element)

32. Fact variable filters • Concept filter • Dimension filter • Entity filter • General filter • Period filter • Tuple filter • Unit filter • Value filter • PWD-2 additions: Boolean, Match, Relative

33. Concept filter • Filter by name of concept • Filter by facet of concept • Balance • Data type • Substitution group • Period type • Custom attribute

34. Concept name filter • Sum test uses a concept filter on each variable <cf:conceptName xlink:type="resource" xlink:label="filter_assets“> <cf:name strict=“true”> <cf:qname>eg:assets</cf:qname> </cf:name> </cf:conceptName>

35. Period filter • Match completely another variable’s period • Match date date/time of: • periodStart • periodEnd • periodInstant • periodInstantDuration • Matching by an XPath 2 expression

36. PeriodStart filterMovement example • Ending balance = beginning balance + changes • Inputs have cross-context matching • Starting balance’s date matches duration’s start • Ending balance’s date comes from duration’s end

37. Use case, movement example

38. Period filter • PeriodStart filter matches change’s duration start dateto beginningBalance’s instant date <pf:periodStart date=“xfi:period-instant( xfi:period($beginningBalance))” />

39. Aspects • Location (tuple nesting) (both tuple & item) • Concept (namespace & name) ( “ ) • Entity identifier (item only) • Period ( “ ) • Segment (complete, nonXDT, or dimension) ( “ ) • Scenario ( “ ) ( “ ) • Unit (numeric items only)

40. Implicit filter, beginning balance Carried forward Implicit Search Criteria Default Implicit Search Criteria Explicit Criteria from Variable Definition Search Criteria for Variable = +

41. Implicit filter, changes Beginning Balance Implicit Search Criteria Explicit Criteria from Variable Definition Carried forward Implicit Search Criteria Search Criteria for Variable = +

42. Implicit scenario & segment issues • Dimensional implicit filters • Dimension contents are matched with d-equals • Remaining contents matched with s-equals • Non-dimensional implicit filters • Contents matched with s-equals

43. Result concept taken from input fact • Result concepttakes conceptof a boundvariable insteadof loc & arc

44. Movement example • Try it, examine it, execute it online: • Directory …\xml\examples\0004 Movement

45. Use case, stock flow • Ending stock = starting stock + inflow – outflow • Starting context (instant at start date) • Flow/change context (duration from start to end) • Ending context (instant at end date) • Inputs have cross-context period matching • Starting stock’s instant date matches inflow & outflow duration starts • Both inflow & outflow need periodStart matching • Output result (ending stock) gets inflow/outflow duration ending date • Formula specifies period for ending stock

46. Use case, stock flow result’s period is duration end period start filtering

47. Stock Flow example • Try it, examine it, execute it online: • Directory …\xml\examples\0003 Stock Flow

48. Tuple filter • ParentTuple • Concept name of the fact’s tuple parent • AncestorTuple • Concept name of a fact’s ancestor • TupleSibling • Another variable’s fact is a sibling of this fact • TupleLocation • Another variable’s fact is a given relation to this fact • E.g., $a is “../eg:tupleB/*” related to this fact

49. GL-based tuple examples (tuples in, non-tuples out) • Trial balance in-balance checks • For each entry details section check if in-balance • Output string result item (for this example) • Trial balance ending balances report • For each account add changes to balance brought fwd • Aggregate account across entry detail sections • Output string result item (acct name & ending balance) • (Research into tuple generation is discussed later)

50. GL trial balance check <xbrli:xbrl> <gl-cor:accountingEntries> <gl-cor:entryHeader> <gl-cor:qualifierEntry …>balance-brought-forward</ …> <gl-cor:entryDetail> <gl-cor:amount …>242678.26</ …> <gl-cor:debitCreditCode …">D</ …> </gl-cor:entryDetail> … </ gl-cor:entryHeader> <gl-cor:entryHeader> <gl-cor:qualifierEntry …>standard</ …> <gl-cor:entryDetail> <gl-cor:amount …>242678.26</ …> <gl-cor:debitCreditCode …">D</ …> </gl-cor:entryDetail> … </ gl-cor:entryHeader> </ gl-cor:accountingEntries> </ xbrli:xbrl> accountbalances D – debit C - credit period’schanges Check if sections are in balance: sum(amts with ‘D’ siblings) = sum(amts with ‘C’ siblings)