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

2. 2  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. 3 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. 4  2002 - FDIC contract motivates solutions oConceptual prototype based on XSL oExcel-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. 5  Information producer oValidate data types and values oConsistency and quality checks  Information consumer o (ditto) oCompleteness checks oAugment received data with calculated values oAugment received data with annotations

6. 6  Calculation linkbase oWell behaved roll-ups of compatible numerical values o(Proposed) Aggregation of dimensional values  Calculation linkbase can’t do oCross-context (ending bal = starting bal + changes) oCross-unit (dollars = price per share X nbr shares) oDimensional aggregation (all = red wine + white wine) oMissing items checks oThreshold and limits (sum amounts ± € 5)

7. 7 Input inst. DTS contexts units fact items Formula LB* Formula Processor Output inst. computed fact items *Formula LB is part of DTS

8. 8  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. 9 Input inst. DTS contexts units fact items Formula Processor Output inst. computed fact items Formula LB* Parameter ( select expr.) custom function variable filter loclabelref. formula arc precondition *Formula LB is part of DTS

10. 10 Input inst. DTS contexts units fact items 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 Output inst. computed fact items Formula Processor *Formula LB is part of DTS

11. 11  Test that “assets = liabilities + equity” oInput instance has assets, liabilities, and equity oOutput boolean test result, true or false

12. 12  Processing flow Input inst. DTS assets, liab, equity Formula LB* Formula Processor Output inst. Test result boolean *Formula LB is part of DTS

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

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19. 19  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. 20  Taxonomy has monetary concepts for assets, liabilities, equity  Here output is the assets concept (vs. boolean) Last example:

21. 21  Instance document input has values to add  Output is the monetary result of adding the sum same context units match

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23. 23  Parameter  Function declaration  Formula  Variables  Filters  Precondition  Generic label  Generic reference

24. 24  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. 25  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. 26  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. 27  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. 28  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. 29  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. 30  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. 31  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. 32  Concept filter  Dimension filter  Entity filter  General filter  Period filter  Tuple filter  Unit filter  Value filter  PWD-2 additions: Boolean, Match, Relative

33. 33  Filter by name of concept  Filter by facet of concept ◦ Balance ◦ Data type ◦ Substitution group ◦ Period type ◦ Custom attribute

34. 34  Sum test uses a concept filter on each variable eg:assets

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

36. 36  Ending balance = beginning balance + changes  Inputs have cross-context matching oStarting balance’s date matches duration’s start oEnding balance’s date comes from duration’s end

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

39. 39  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. 40 Context Entity - IdentifierAll - SegmentAll PeriodAll ScenarioAll Unit Name MeasureAll ConceptAll Default Implicit Search Criteria + Explicit Criteria from Variable Definition Context Entity - Identifier - Segment Period Scenario Unit Name Measure Concept‘Balance’ = Search Criteria for Variable Context Entity - IdentifierAll - SegmentAll PeriodAll ScenarioAll Unit Name MeasureAll Concept‘Balance’ Carried forward Implicit Search Criteria Context Entity - Identifier01 - SegmentNone PeriodI-2007 ScenarioNone Unit Name MeasureUSD ConceptAll LocationAll Location All LocationNot tuple

41. 41 Context Entity - Identifier01 - SegmentNone PeriodI-2007 ScenarioNone Unit Name MeasureUSD ConceptAll Beginning Balance Implicit Search Criteria + Explicit Criteria from Variable Definition Context Entity - Identifier - Segment PeriodInst match duration start Scenario Unit Name Measure Concept‘Changes’ = Search Criteria for Variable Context Entity - Identifier01 - SegmentNone PeriodD-2008 ScenarioNone Unit Name MeasureUSD Concept‘Changes’ Carried forward Implicit Search Criteria Context Entity - Identifier01 - SegmentNone PeriodD-2008 ScenarioNone Unit Name MeasureUSD ConceptAll LocationNot tupleLocation not tuple LocationNot tuple

42. 42  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. 43  Result concept takes concept of a bound variable instead of loc & arc

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

45. 45  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. 46 result’s period is duration end period start filtering

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

48. 48  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. 49  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. 50 balance-brought-forward 242678.26 D … standard 242678.26 D … account balances period’s changes D – debit C - credit Check if sections are in balance: sum(amts with ‘D’ siblings) = sum(amts with ‘C’ siblings)

51. 51  Just an XPath 2 expression ◦ Need to test if sibling of amount is credit code 242678.26 D ◦ test=“../gl-cor:debitCreditCode eq ‘D’”

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53. 53  Value matches an XPath 2 expression  Not Nil test  Nil test  Precision expression

54. 54 balance-brought-forward 5100 Supplies account 242678.26 D beginning_balance … standard … … aggregate by account skip ending_balances

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56. 56  Added 2 more variables ◦ For each account  Get amount for ending-balance entry with ‘C’ (credit) code  Get amount for ending-balance entry with ‘D’ (debit) code ◦ Change equation to test  Sum (credits which are not ending-balance - debits which are not ending-balance + credit which is ending-balance – debit which is not ending-balance) < 1.00

57. 57  Try it, examine it, execute it online: ◦ Directory …examples\0007 GL Examples  Instance-trial-balance-check.xml  Instance-test-ending-balance.xml  Instance-compute-ending-balance.xml

58. 58  Explicit Dimension filter ◦ Fact has QNamed dimension (in context or default) ◦ Constrained if arcs to allowed member concepts  Dimension Member filter ◦ Constrains to member’s children or its descendants  Typed Dimension filter ◦ Typed dimension is specified by QName ◦ XPath 2 expression tests dimension value

59. 59  Primary items with multiple dimensions ◦ Dimensions explicity filtered ◦ Remaining dimensions implict matched ◦ Remainder of segment/scenario implicit matched  Example has 2 dimensions (product, region) ◦ Aggregation check by product or region requires implicit matching of other dimension

60. 60  Test aggregation of each member  Products & region dimensions have member hierarchy

61. 61  Multiple periods for used dimensions  Multiple dimensions per contexts (Charlie’s aggregation example)

62. 62  Will require checking of aggregation for ◦ Product dimension ◦ Region dimension  Formula shown for product dimension (region is same except for dimension name)  Demonstrates mixed explicit/implicit dimension filtering

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64. 64  Try it, examine it, execute it online: ◦ Directory …examples\0005 Pharmaceutical

65. 65  Weighted average of its dimensional children by another primary item

66. 66  Excel formulas:  Make PD controlling fact, get PD and EV of dimensional children  General variable for PDxEV member matching

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68. 68  Try it, examine it, execute it online: ◦ Directory …\xml\examples\0006 Weighted Avg

69. 69  Boolean filter ◦ Allows grouping and/or filter expressions  Match filter ◦ Specifies specific aspects to match  Relative filter ◦ Specify matching all non-covered aspects

70. 70  Assertions are alternate to formula item production  Fact Consistency assertion ◦ Produced fact matches corresponding fact(s), in value  Existence assertion ◦ Filtering constructs find existing fact item  Value assertion ◦ Value-assertion expression is true

71. 71  Built-in functions ◦ Functions 1.0 December 7, 2006 http://www.xbrl.org/Specification/XF-PWD-2006-12- 07.htm  User-defined functions ◦ Signatures provided in linkbase resources ◦ Code provided to formula processor somehow  Maybe XQuery  Maybe Java or other coding language

72. 72  Precision ◦ xfi:precision( item ) ◦ xfi:decimals( item )  Accessors ◦ xfi:context( item ) ◦ xfi:unit( item ) ◦ xfi:period( context ) ◦ xfi:period-start, :period-end, :period-instant( period )

73. 73  Comments to re-issued PWD  Implement formula processors  Implement formula editors  Discuss additional desired features ◦ Formula chaining ◦ Tuple output production ◦ Multiple-input instances, DTSes ◦ other

74. 74 Herm Fischer herman.fischer@ubmatrix.com fischer@markv.com +1-818-995-7671 +1-818-404-4708 http://herm.ws/XBRL/files/docs/FormulaTutorial.ppt THANK YOU! Let us help you get your first formulas easily!