Formula Linkbase Tutorial (afternoon)

1. Formula Linkbase Tutorial(afternoon) David vun Kannon Phillip Engel KPMG LLP

2. Remember! • XBRL OTSOG W3C • Therefore: • XBRL FL OTSOG XPath • and • WWSD? • (What Would SQL do?)

3. Basic Design Decisions • How important is extensibility? • Do you need a linkbase or just appinfo? • How important is it to fit into existing tool sets and thinking? • Is FL • A resource linkbase? • Item – formula • A relationship linkbase? • Item – inputs (+ formula)

4. Linkbase • Separates definition of formula from output item • Allows prohibition and override • Uses linkbase ideas popularized by XBRL 2.1 • But • Can’t use the linkbase element!

5. Top Level Design <fl:rulebase> <fl:formulaLink/> </fl:rulebase> Except for substituting rulebase for linkbase, this is a standard XBRL linkbase, with extended link roles for DTS use. (Don’t want to break the DTS model!)

6. formulaLink Design Inputs are buried in the formula <fl:formulaLink> <fl:formula/> <xl:loc/> <fl:formulaArc/> </fl:formulaLink> This is very similar to other (label, reference) “resource style” linkbases. Result element

7. formulaArc Design • Only one arc role defined so far • Item-formula

8. Formula Design <fl:formula xlink:type=“resource” xlink:label=“formula1” id = “myFormula1” > <fl:variable/> <fl:value/> <fl:result/> </fl:formula>

9. Variable Design <fl:variable name = “var1” select = “ci:Assets” filter = “ …XPath expression… ” /> What are you allowed to select? items, contexts, non-XBRL attributes? The idea of “free” variables.

10. Value Design <fl:value test = “ …Xpath expression…” select = “ …XPath expression…” /> Can use multiple value elements OR XPath 2.0 case construct in XPath expression.

11. Result Design <fl:result> <fl:resultPrecision/> <fl:resultUnit/> <fl:resultContext> <fl:resultEntity/> <fl:resultPeriod/> <fl:resultScenario/> </fl:resultContext> </fl:result>

12. FL OTSOG XPath! • Bind variables • Filter variables • Result choices • Compute results • Express API into XBRL instance documents

13. An XPath-based API • Standard predicates (functions) of XBRL 2.1 • C-equal • P-equal • S-equal • U-equal • Duplicate-item • Specific to the needs of Formula Linkbase • Decimal to precision conversion

14. Basic processing model Formula Linkbase XBRL Instance in Process Formulas Non-deterministic order XBRL Instance out Individual formula Bind variables Input Value expression Process Create result Output XBRL Instance New XBRL Instance Formula Processor DTS andFormula Linkbase

15. Formula linkbase example – Average Shares <formulaLink xlink:type="extended" xlink:role="http://www.xbrl.org/2003/role/link"> <link:loc xlink:type="locator" xlink:label="item" xlink:href="testFLconcepts.xsd#Assets"/> <formulaArc xlink:type="arc" xlink:from="item" xlink:to="formula" xlink:arcrole="http://www.xbrl.org/2004/arcrole/item-formula"/> <formula xlink:type="resource" xlink:label="formula" id="formula_2.3_AvgShares"> <variable select="co:CurrentAssets" name="CurrentAssets"/> <variable select="co:FixedAssets" name="FixedAssets" filter="flf:context-eq($this.context, $CurrentAssets.context) and flf:unit-eq($this.unit, $CurrentAssets.unit)"/> <value select="CurrentAssets.value + $FixedAssets.value"/> <result> <resultContext select="$CurrentAssets.context"/> <resultUnit select="$CurrentAssets.unit"/> </result> </formula> </formulaLink> Variables Value expression Formula Result creation

16. Binding variables • Set up the inputs to the formula • Bind to information at the XBRL abstraction level • Facts (items and tuples) • Contexts and Units • Bind to other XML data? • Filtering • Absolute and relative filters • Relate to other variable bindings • XBRL equalities • Free variables

17. Binding Variables <variable select="selction XPath expression" filter="filtering XPath expression" OR filterRef="filter id"/> • Binding in two steps 1. Select – XPath expression, context node is <XBRL> 2. Filter – Boolean XPath expression tested on each occurrence of the “select”. <variable select="co:CurrentAssets" name="CurrentAssets"/> <variable select="co:FixedAssets" name="FixedAssets" filterRef="rf2.1"/> <filter id="rf2.1" test="$this.context is $CurrentAssets.context and flf:unit-eq($this.unit, $CurrentAssets.unit) and flf:parent-eq($fact, $CurrentAssets)"/>

18. Binding Variables <variable select="selction XPath expression" filter="filtering XPath expression" OR filterRef="filter id"/> • Binding in two steps 1. Select – XPath expression, context node is <XBRL> 2. Filter – Boolean XPath expression tested on each occurrence of the “select”. <variable select="co:CurrentAssets" name="CurrentAssets" filter="$this.instant=‘2003-12-31’"/> <variable select="co:FixedAssets" name="FixedAssets" filterRef="rf2.1"/> <filter id="rf2.1" test="$this.context is $CurrentAssets.context and flf:unit-eq($this.unit, $CurrentAssets.unit) and flf:parent-eq($fact, $CurrentAssets)"/>

19. Binding variables - Filtering • Absolute filters – do not rely any other XBRL variable bindings • Relative filters – use other variables bindings to express a relationship between the variable being filtered and other variable bindings • $this variable – The current “select” being tested in the filter. • XBRL functions for filters • context-eq(), unit-eq(), parent-eq(), isFact(), isItem(), isTuple() <variable select="co:CurrentAssets" name="CurrentAssets" filter="$this.instant=‘2003-12-31’"/> <variable select="co:FixedAssets" name="FixedAssets" filterRef="rf2.1"/> <filter id="rf2.1" test="$this.context is $CurrentAssets.context and flf:unit-eq($this.unit, $CurrentAssets.unit) and flf:parent-eq($fact, $CurrentAssets)"/>

20. Free variables • Each XBRL variables creates a set of XPath variables based on what type of XBRL object is bound.

21. Value expressions • Cartesian product of bindings • Pre-testing – boolean XPath expression • Formula expression – XPath expression <value select="$CurrentAssets.value + $FixedAssets.value"/> <value test="true()" select="$Earnings.value / $Shares.value"/> <value test="$Shares" select="$Earnings.value / $Shares.value"/> <value test="$AvgShares" select="$Earnings.value / $AvgShares.value"/> <value select="fn:months-from-durations($Assets.instant - $PrevAssets.instant)"/>

22. Create the result • Value production • Context and unit production • Described from inputs or constants • Tuples – the problem child <result> <resultContext select="$CurrentAssets.context"/> <resultUnit select="$CurrentAssets.unit"/> </result> <result> <resultPeriod> <resultStartDate select="$Shares.instant + P1D"/> <resultEndDate select="$SharesNext.instant"/> </resultPeriod> <resultEntity select="$Shares.entity"/> <resultScenario select="$Shares.scenario"/> <resultUnit select="$Shares.unit"/> </result>

23. Formula linkbase example – Average Shares <formulaLink xlink:type="extended" xlink:role="http://www.xbrl.org/2003/role/link"> <link:loc xlink:type="locator" xlink:label="item" xlink:href="testFLconcepts.xsd#AvgShares"/> <formulaArc xlink:type="arc" xlink:from="item" xlink:to="formula" xlink:arcrole="http://www.xbrl.org/2004/arcrole/item-formula"/> <formula xlink:type="resource" xlink:label="formula" id="formula_2.3_AvgShares"> <variable select="co:Shares" name="SharesNext"/> <variable select="co:Shares" name="SharesPrev" filter="$this.period = $SharesNext.period - P1Y and flf:unit-eq($this.unit, $SharesNext.unit)"/> <value select="($SharesNext.value + $SharesPrev.value) / 2"/> <result> <resultPeriod> <resultStartDate select="$Shares.instant + P1D"/> <resultEndDate select="$SharesNext.instant"/> </resultPeriod> <resultEntity select="$SharesPrev.entity"/> <resultScenario select="$SharesPrev.scenario"/> <resultUnit select="$SharesPrev.unit"/> </result> </formula> </formulaLink> Result Item Result Item

24. Requirements balance The formula linkbase has to find a balance between: Expressing formulas as metadata vs. Processing formulas

25. Demo formula processor implementation • Written in XSLT – easy to create (OTSOG!!!) • Transforms a formula linkbase into an XSLT stylesheet • Each formula becomes a named template • An instance document is the input to the generated stylesheet • Output is a new valid instance document