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

2. WWSD? Remember! XBRL OTSOG W3C XBRL FL OTSOG XPath Therefore: and
(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/>
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. Inputs are buried in the formula
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
DTS and Formula
Linkbase
New
Formula
Processor

15. Formula linkbase example – Average Shares
<formulaLink xlink:type="extended" xlink:role="
<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="
<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="$this.instant=‘ ’"/>
<variable select="co:FixedAssets" name="FixedAssets" filterRef="rf2.1"/>
<filter id="rf2.1" test="$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=‘ ’"/>
<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.
Items
Context
Unit
.value .context .period .startDate .endDate
.instant
.entity .identifier
.segment
.scheme
.scenario
.period .startDate .endDate
.instant .entity .identifier
.measure

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>
<resultPeriod>
<resultStartDate select="$Shares.instant + P1D"/>
<resultEndDate select="$SharesNext.instant"/>
</resultPeriod>
<resultEntity select="$Shares.entity"/>
<resultScenario select="$Shares.scenario"/>
<resultUnit select="$Shares.unit"/>

23. Formula linkbase example – Average Shares
<formulaLink xlink:type="extended" xlink:role="
<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="
<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. Expressing formulas as metadata
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