Where Are All The Bugs?

Introspection in XQuery

Mary Holstege

Principal Engineer

MarkLogic Corporation

Copyright © 2013 Mary Holstege

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Where Are All The Bugs?

Introspection in XQuery

Balisage: The Markup Conference 2013
August 6 - 9, 2013

Introduction

Ensuring that software works properly can be a difficult undertaking. When a code base is small and worked on by a handful of people, you can manually generate tests with good confidence that they cover the ground. As the code base grows it develops more complex interactions, includes more features, and is modified by more and more developers. The code develops unused byways and tangles of dependencies. It becomes unfeasible to manually develop tests for every feature and combination of features. Complete automated testing of all possibilities also becomes increasing less feasible: developing cases, executing them, and analyzing the results becomes more and more time consuming. The sad truth about QA is that the difficulty of ensuring that software works correctly does not scale linearly with the size of the code base.

Analysis of code usage patterns can help focus attention where testing can do the most good. Code analysis can also provide a different perspective on the code that can lead to uncovering potential issues as well. For example, a function that is not called much probably doesn't need a lot of testing. Testing is designed to limit risk, and the risk of a bug in a rarely used function is commensurately low. On the other hand, a function that is widely called may also not need a lot of additional testing on the grounds that it is already tested in the process of testing its callers. So again, from a risk perspective, the risk of not adding additional tests for that function is also low. Beyond simple testing, analysis of usage patterns can perhaps highlight areas where APIs can be simplified by removing unnecessary options and alternatives.

The schema types and elements used in function argument and return types form an important part of the API. Analysis of the usage patterns of declared types and elements against the available pool exposed by the in scope schemas can also provide insights into possible API simplification, or testing focus.

The idea explored here is that (a) functions and types form vocabularies of sorts and the distribution of usage of those vocabularies follows the well-established laws for natural language vocabularies (i.e. Zipf's law) and as such (b) TF-IDF score calculations over those vocabularies make mathematical sense and (c) high scoring items make interesting and useful targets for testing.

This paper describes a case study in analyzing a large XQuery code base using XQuery and XML Schema introspection in an attempt to determine where to focus testing efforts, based on this idea. For functions at least, there seems to be some reason to conclude that the idea holds promise. Types, less so.

Several extensions to XQuery are required to perform this introspection: a schema component API, functions to provide lists of available functions and return types and argument types of functions. It is also convenient, in order to implement the entire processing reasonably efficiently in XQuery, to have map data types, a structured dump of the parse tree of XQuery modules, filesystem access functions, and the ability to evaluated constructed XQuery functions.

Background

About ten years ago, a handful of developers worked on a couple thousand lines of XQuery code, and one person manually constructed the tests to add to automatic regression suites. All was well. As time went by, the code grew and became more complex, the number of people manually constructing tests increased, with additional people to manually analyze regression failures. Some tests are automatically generated, but such tests tend to raise analysis costs when something does fail. The time has come to think about new approaches and find ways to focus effort.

The Code Base

The code base consists of about 630 thousand lines of XQuery code, divided roughly evenly between an old and much modified schema-driven GUI application for database configuration and management, more recent REST endpoint implementations and web applications, and a collection of library modules (including some main modules used in triggers). In total there are a little over 1500 XQuery module files, defining over 68 thousand functions. In addition, the particular XQuery implementation associated with this collection of XQuery modules also provides a little over 1800 built-in functions. XML schemas are actively used to strongly type parameters: there are over 150 schema files exposing over 12 thousand global element declarations, 26 thousand named simple type definitions, and 7 thousand named complex type definitions. The bulk of these schemas relate to XHTML, however. Setting that aside there are over 50 schema files exposing over 7 thousand global element declarations, almost 18 thousand named simple type definitions, and 3 thousand complex type definitions.

This is a live and active body of code, ranging in age from code first written ten years ago to functions still just being implemented today. A peculiar problem with this particular code base is the range of syntax in play: The code ranges from XQuery 1.0 compliant code to code using some XQuery 3.0 features or anticipatory XQuery extensions (similar to although not necessarily identical to proposed XQuery features) and some very old code still using some 2003 draft syntax. Relying on the XQuery engine itself to analyze such diverse code is helpful, because the engine already has to reconcile the syntactic differences internally. This peculiarity does mean that third party code analysis tools cannot be used.

Figure 1: Detailed statistics

XQuery code
Total1559363497
GroupFilesLines of code
Admin GUI740116714
Libraries333137983
REST endpoints and applications387101322
Misc. other997478
Schema Types
CountTotalNon-XHTML Total
Files15856
Global element declarations123247338
Named simple type definitions2653617866
Named complex type definitions70383009
Functions
GroupNumber of Functions
Built-in functions (C++)1849
XQuery module functions68191

Zipf's Law and TF-IDF Scoring

Zipf's law is an empirical observation Zipf49 that in a natural language corpus, the distribution of word frequencies (number of occurrences, that is) varies in inverse proportion to the rank of the word in frequency order. Mathematically, Frequency(R) = Frequency(1)/Rk where Frequency(R) is the frequency of the word of rank R and k is some constant. If you graph the distribution on log-log axes, you get a straight line. Such distributions are very common across various fields and applications. This paper will consider sequence types used in function parameters and return types as forming one vocabulary, and the names of functions themselves forming another, and look at the frequency distribution of these terms in the corpus of XQuery modules.

TF-IDF scoring has become a standard technique for computing relevance of documents to full-text queries since it was introduced in 1972 Jones72. TF stands for "term frequency" and is a count of how often a particular term occurs in a particular document. In the context of full-text search a term is typically a single word, but other terms for phrases or wildcards are possible. IDF stands for "inverse document frequency" and is the number of documents a term occurs in, as a fraction of the total number of documents in the corpus. The "inverse" part of IDF means that this number is divided, so that higher document frequencies lead to smaller scores.

When TF-IDF scores are used to compute relevance to a query, the term and document frequencies of each query term are combined together. The technique is based on a particular probabilistic model of documents, but the intuition behind it is simple enough: more occurrences of a query term makes a document more relevant, and occurrences of query terms that only occur in a few documents makes a document more relevant.

Various modifications and extensions of the technique are currently ubiquitous in modern search engines. It has also been put to related purposes, such as computing document similarities and clustering. In these applications there may not be a query per se, but the set of terms is taken from the documents themselves.

Here, I will attempt to use TF-IDF scores of function calls and types as a way of selecting "interesting" functions and types on which to focus QA attention. In this model, the XQuery modules play the role of documents, function calls or types play the role of terms, and the terms are taken from the documents themselves, as one would see in a clustering or similarity application.

First, we will look at the actual distributions of types and functions, to see if computing scores makes sense at all. Where it makes sense to do so, we will look at computed scores qualitatively and quantitatively to try to see whether the high scoring items are indeed interesting targets for testing focus.

Distribution of Sequence Types

XQuery XQuery30 functions may have declared sequence types for their parameters and their return values. XQuery sequence types may be either simple type names XSD11.2 or node tests of some kind. It is possible to define sequence types that name a complex type without naming a specific element. XQuery 3.0 F&O30 also allows for functions tests. XQuery sequence types also have cardinality indicators, with '?' meaning a sequence of 0 or 1 instances of the base type, '*' meaning any number, '+' meaning 1 or more, and no indicator meaning exactly 1. When no explicit sequence type declaration is given, the sequence type is the most generic, matching anything: item()*.

Figure 2

declare function my:example($x, $y as xs:string?) as element(my:result)

The declaration of an example function. The parameter $x has the (default) sequence type item()*, $y has the sequence type xs:string?, and the returned value has the sequence type element(my:result).

In this code base and the underlying XQuery engine associated with it, the built-in functions return 196 distinct declared sequence types while the XQuery modules use 629 distinct declared sequence types. In this particular XQuery implementation, it is not possible to declare different named element sequence types for parameters or return types of built-in functions. That is, a built-in function may be declared as returning element() but not element(my:result). If we consolidate all the element sequence types for module functions, there are only 103 distinct declared sequence types.

Obviously, the sequence types used in the API form but a small part of the total set exposed through the schemas. Only 3 named complex types are explicitly used, from the complete set of 3 thousand (non-XHTML) named complex types. Only 474 named elements are explicitly used, from the complete set of 7 thousand. Only 49 named simple types are explicitly used by module functions. The overabundance of named schema components is partly because named types and are used implicitly in the schema-driven configuration and administration UI, and partly a matter of stylistic preference for global element declarations and for declaring functions using generic element tests (e.g. element()) rather than specific complex types (element(*,my:example)). Regardless, it doesn't look like it would be helpful to pay special attention to types or elements that are not specifically referenced in function signatures.

Figure 3: Sequence type distribution (return values)

png image ../../../vol10/graphics/Holstege01/Holstege01-001.png
png image ../../../vol10/graphics/Holstege01/Holstege01-002.png

The frequency distribution of return value sequence types shown on a double log scale. The horizontal axis is the rank and the vertical axis is frequency. The top graph shows the distribution for built-in functions; the bottom graph shows the distribution for module functions.

The return type frequency distribution curves in Figure 3 do show that these return types mostly follow a power law distribution, although for built-in functions there is very substantial drop-off at ends, possibly as a consequence of the relatively small vocabulary size.

The distribution of function parameter sequence types looks very similar to that of function return value sequence types, including the drop-offs at the extremes for built-in functions, as shown in Figure 4

Figure 4: Sequence type distribution (parameters)

png image ../../../vol10/graphics/Holstege01/Holstege01-003.png
png image ../../../vol10/graphics/Holstege01/Holstege01-004.png

The frequency distribution of parameter sequence types shown on a double log scale. The horizontal axis is the rank and the vertical axis is frequency. The top graph shows the distribution for built-in functions; the bottom graph shows the distribution for module functions.

The top five return value and parameter sequence types share some overlap between built-ins and module functions, although there are some interesting differences. The atomic types map:map and cts:query are special built-in types, the former anticipating XQuery maps, and the latter in support of full-text queries. Given the importance of full-text queries to this implementation, the strong showing of cts:query is unsurprising. The strong showing of map:map demonstrates the utility of this feature. In both cases the distribution does suggest that these are important types and should be the focus of some QA effort.

In this code base it appears that developers use strong types on parameters more often than on function return values (as indicated by the higher prevalence of item()* for function return values but not for parameters). Simple types dominate the distribution for parameter types but less so for return types. The high frequency of empty-sequence() in return types is a consequence of the fact that the implementation supports functions that update the data store, so many functions are called for effect rather than for the return value.

Table I

Top 5 sequence types in various categories.

Return types (modules)
Overallitem()*, empty-sequence(), xs:string, node(), element(configuration)
Simple typesxs:string, xs:boolean, xs:string*, xs:string?, xs:unsignedLong
Otheritem()*, empty-sequence(), node(), element(configuration), node()*
Simple types (ignoring cardinality)xs:string, xs:unsignedLong, xs:boolean, cts:query, map:map
Return types (built-ins)
Overallitem()*, empty-sequence(), xs:string, xs:string*, cts:query
Simple typesxs:string, xs:string*, cts:query, xs:boolean, xs:unsignedLong
Otheritem()*, empty-sequence(), element()*, element(), node()*
Simple types (ignoring cardinality)xs:string, xs:unsignedLong, xs:integer, cts:query, xs:boolean
Parameters (modules)
Overallxs:string, xs:unsignedLong, map:map, item()*, xs:string?
Simple typesxs:string, xs:unsignedLong, map:map, xs:string?, xs:boolean
Otheritem()*, node(), element(configuration), node()?, element()
Parameters (built-ins)
Overallxs:string, xs:string*, xs:QName*, xs:string?, xs:anyAtomicType?
Simple typesxs:string, xs:string*, xs:QName*, xs:string?, xs:anyAtomicType
Otheritem()*, node(), node()?, node()*, item()

Type Scores

Given that the distribution of types follows a classic Zipf distribution, it is not unreasonable to apply the probabilistic document model on which TF-IDF scoring is based.

The score of a particular term t that occurs at least once in the corpus of N documents is given by the following equation, where log is the natural logarithm, TF(t) is the number of occurrences of t, and DF(t) is the number of documents in which t occurs.

Equation (a)

score(t) = log(1+TF(t)) / log(DF(t)/N)

The sequence types with the highest scores are almost all distinctly named elements, typically those used as important API elements. On the other hand, it must be said that there doesn't seem to be any qualitative difference between distinctly named elements with high scores and those with much lower scores. Various kinds of options elements are scattered throughout the range of scores, for example. element(xproc:xslt) has a much higher score than element(xproc:xquery) but again, it is hard to see a difference in the QA needs of these two sequence types. What are we to make of the fact that xs:long has a much lower score than xs:integer? Not much, I think. Perhaps the vocabulary of sequence types is too small to be useful.

Figure 5: Sequence Type Scores

39.10 element(configuration)
33.70 element(opt:options)
31.55 element(forest:forest-status)*
30.14 element(flexrep:configuration)
28.85 element(plugin:plugin-model)?
28.66 element(opt:constraint)
28.18 element(rsrc:resources)
27.74 element(alert:config)
27.26 lnk:uri
27.09 element(sec:external-security)
...
14.10 xs:integer
14.04 xs:float
...
12.45 element(xproc:xslt)
12.30 xs:integer*
12.12 xs:double
...
8.33 xs:date
7.86 xs:long
...
7.35 element(xproc:string-replace)
7.35 element(xproc:xquery)
...
4.79 cts:element-attribute-value-query
4.79 element(project)*
4.64 xs:long*
4.41 cts:word-query
4.36 function(*)+
4.35 text()
4.23 element(test)*
4.07 map:map*
4.03 function()
4.00 cts:element-value-query

The scores for the top 10, bottom 10, and some selected sequence types in between are shown, rounded to 2 decimal places.

Techniques

Type frequencies for built-in functions were computed using some introspection APIs: a function to enumerate all the defined functions, and accessor functions for the return type, the arity of the function, and the parameter types. Function accessors defined by Holstege Holstege and function introspection functions defined in XQuery 3.0 F&O30 do not quite do the job. The accessors defined by Holstege only give the atomic type names, not the full sequence types, while the XQuery 3.0 functions only give access to the function name and its arity. I used three additional built-in extension functions, one to enumerate the set of functions, and two to give the sequence types as string values. Maps kept running totals of the usage of each sequence type.

Computing type frequencies for module functions requires a little more. There are two approaches: (1) use an evaluation function that imports a given module and uses the same approach as for built-ins, but only considering functions in the proper namespace, (2) dump out the module parse tree in a structured form and analyze it for the necessary information. In this case, I used the second approach, using a built-in extension function that dumped out the parse tree. The format of this dump was not, alas, XML, so fishing information out of the text relied heavily on the XQuery 3.0 function analyze-string.

Doing everything in XQuery was convenient. Doing so meant using non-standard features such as maps and access to filesystem information. The filesystem access gave me the equivalent of a recursive find. It was handy, but not strictly necessary: one could instead use shell scripts to gather up the set of module names to process them, and then pass that to the analysis module. Strictly speaking, maps are not necessary either, but they made it much easier to write the analysis modules.

Distribution of Functions

Function call distributions show the same characteristic Zipf distribution as types (see Figure 6, although with a bit of a drop-off at the upper end of the curve. The majority of the top 10 functions are XQuery standard built-in functions, although map-related functions occur at rank 8 and 9. The top 10 most frequently called functions are: string, concat, empty, exists, xs:QName, error, data, map:put, map:get, and not.

Figure 6: Function call distribution

png image ../../../vol10/graphics/Holstege01/Holstege01-005.png

The frequency distribution of function calls shown on a double log scale. The horizontal axis is the rank and the vertical axis is frequency.

Quite a few functions are not used within the code base at all. A total of 497 built-in functions are unused, although only 16 module functions are unused. Given that there is a much larger number of declared module functions, the disproportionate nature of this result demands comment. It turns out that the unused built-in functions include a number of accessor functions for special types (defined for API completeness), some specialized functions that just happen not to be used in the applications in this code base (geospatial functions, for example), and the constructor functions for some built-in types including some relatively uncommon types such as xs:NOTATION. Figure Figure 7 gives a rough break down.

Figure 7

Table II

Characterization of the built-in functions unused in any module in the code base.

GroupPercent
Accessors and constructors for special built-in types30.6
System management and operations16.3
Advanced specialized functions14.7
Assorted standard functions13.8
Mathematical functions9.5
Assorted standard XQuery functions6.4
Debugging/profiling5.4
In active development2.4

The fact that certain specialized functions are not called anywhere in the code base is not a problem, per se, but the fact that out of an assortment of special built-in types of a particular class (geospatial, for example) only a couple are not represented at all may warrant further investigation. It may be a sign of missing functionality in higher level APIs.

The situation with the unused module functions is better: all but one of the unused functions have to do with features under active development or testing/debugging code. The remaining unused function, however, looks like it does represent a genuine oversight.

Function Scores

Again, since the function call distribution follows a classic Zipf distribution, it is not unreasonable to apply the probabilistic document model on which TF-IDF scoring is based.

Figure 8: Function Scores

43.02 agui:navItem
42.49 admin:database-set-value
41.43 agui:navItemClosed
41.35 admin:gr-config
40.60 admin:database-get-value
39.75 agui:reindex-done
39.48 admin:db-config
38.99 admin:appserver-set-value
38.48 admin:appserver-get-value
38.04 aws:add-param
...
7.35 agui:buildHTTPServer2
7.35 converters:set-response-content-type
7.35 utils:distinct-values
7.35 conf-server:create-server
7.35 pipeline:xquery
7.35 agui:get-action
7.35 entity:call-calais
7.35 search-ast:do-parse
7.35 compile:build-zip
7.35 forest:get-default-rep
      

The scores for top 10 and bottom 10 functions are shown, rounded to 2 decimal places. Function namespaces have been abbreviated to prefixes.

A look at the functions with the highest scores was encouraging: the number one function, called navItem, is in a notorious part of the code that has been subject to much revision and bug fixes. The function with the third highest score was its companion function navItemClosed. Other functions in the top ten were service functions used within administrative API. These service functions are called from many places, but only from within that one module. However, that one module is very large. Document size normalization is a common modification to TF-IDF scoring. Perhaps a similar normalization here would be useful. Most of the top 50 functions are other service functions for other modules that have similar calling patterns. Are these good functions to focus extra testing effort on? Perhaps. Directed testing of such functions is likely to expose important bugs, but probably normal API testing would have accomplished the same thing. The fact that only one or two modules uses these functions does increase the risk that fewer developers are calling them and therefore they are more likely to be making (possibly unwarranted) assumptions about how they will be used.

At the other end of the scale, with very low scores, are widely used functions with names like buildHTTPServer2 (widely used throughout the Admin UI) and do-parse (a key function for the search APIs) and rarely used functions such as call-calais and create-server. Are these good functions to avoid expending extra testing effort on? Perhaps. Certainly the very widely used functions would have been exercised many times in many different contexts through normal API testing. The rare functions have demonstrably few interactions with the rest of the code, so presumably the risk of not expending a lot of effort on testing them is low.

Quantifying the usefulness of this approach is difficult. Getting a concrete measure for the bugginess of a particular function is hard as bug reports are linked only weakly to particular files, much less individual functions within those files. Here we will take the number of source control revisions within the scope of a particular function as a measure of how likely it is to need fixing. This is obviously an imperfect measure, as source changes may reflect new functionality, or trivial formatting changes. It is also a manually intensive measure to obtain. The following graph shows statistics for functions that were used more than once in the corpus that were defined in the same module as the top scoring function. It is an admittedly very small data set.

Figure 9: Revisions as a function of score

png image ../../../vol10/graphics/Holstege01/Holstege01-006.png

The number of revisions made to functions as a function of score.

The correlation of score to the numbers of revisions is positive, although not strong (R2=0.3048). There are other associations we might expect to have stronger or more meaningful correlations. For example, one might think that the number of revisions would correlate with the age of a function, so that older functions would tend to have more revisions associated with them. This seems to be the case. For this little data set, the number of revisions does have a stronger relationship to age, using a power function (R2=0.6777), as shown in Figure 10.

Figure 10: Revisions as a function of age

png image ../../../vol10/graphics/Holstege01/Holstege01-007.png

The number of revisions made to functions as a function of the age (minimum revision number) of the function. A power curve gives the best fit.

Similar relationships held for functions in the hand-generated data for a couple of other modules as well, with scores showing a weak direct relationship with R2 values around 0.3 and age showing an inverse relationship with R2 values about double that.

However, neither of these correlations holds up well on a larger data set across modules, as you can see in Figure 11 and Figure 12. The best fit line in both cases has R2 of essentially zero, virtually indistinguishable from the mean value line. The data behind these numbers is much messier than the hand-generated set, as the automated detection of function boundaries is much more error-prone and tends to pull in large comment blocks and non-function declarations. Nevertheless, it is implausible to suggest that such factors overwhelm what would otherwise be an interesting correlation. A manual check of the statistics for a particular module from the automated data set showed only small deviations from the statistics from the manual procedure.

Figure 11: Revisions as a function of score

png image ../../../vol10/graphics/Holstege01/Holstege01-008.png

The number of revisions made to functions as a function of the score, using a larger but messier data set.

Figure 12: Revisions as a function of age

png image ../../../vol10/graphics/Holstege01/Holstege01-009.png

The number of revisions made to functions as a function of the age (minimum revision number), using a larger but messier data set.

Techniques

Some of the same introspective functions for computing the distribution of sequence types in modules were used to compute the distribution of function calls in modules. The key technique involved analyzing the structured dump of the module parse tree for function calls, using maps to store running totals, and using filesystem access functions to recursively find and process all modules in the code base.

Computing the revisions within a particular function involved using the source control system's ability to produce the source code annotated with revision numbers. The resulting output was chopped up into individual functions manually, with a little help from Emacs keyboard macros. A shell script counted up the number of distinct revision numbers as well as the minimum revision number for the function using standard Unix tools such as awk, sort, uniq, head, and wc.

The larger data set began with a file containing the annotated source files concatenated together. The XQuery function tokenize was used to chop up the file first into subfiles (by looking for the xquery version declaration) and then into functions (by looking for declare function, and finally into individual lines of code, from which the revision number was obtained. Maps were used to collect minimum, maximum, and counts of revision number.

Summary and Conclusions

XQuery introspection can be used to provide a fresh slant on a code base, even a fairly large one. An analysis of unused schema components (elements and types) proved largely uninteresting because stylistic considerations for schema writing dominated actual usage requirements in the APIs. The fact that certain extension types (in particular maps) were so common suggests that there is a real need for providing such types as part of standard XQuery. TF-IDF scores of sequence types did not produce any interesting information.

The analysis of function usage points in a different direction. A look at unused functions can highlight some interesting problems, but the most frequently used functions are mainly basic standard XQuery functions. Looking at a combination of frequency of use and rarity across modules using TF-IDF scoring can pinpoint some interesting functions that warrant more QA attention. This is a qualitative judgement. Attempts to quantify the correlation of score to quality failed, using the number of revisions applied to the function as a proxy for quality. Relationships within one module at a time hold up better, but are still weak.

One common modification to TF-IDF scoring is to normalize the TF values by the size of the document. Since the high scoring functions included many that were only found in a very large module, perhaps applying a similar normalization here would lead to better results.

To perform introspection of XQuery from within XQuery, a number of extension functions are useful:

Function accessors

  • list available functions as function items

  • return name of function item (XQuery 3.0 function-name)

  • return arity of function item (XQuery 3.0 function-arity)

  • return sequence type of return value of a function item

  • return sequence type of specific parameter of a function item

  • get type name from sequence type

Type accessors

  • list global element declarations for a particular schema

  • list named simple type definitions for a particular schema

  • list named complex type definitions for a particular schema

Parse tree accessors

  • return the parse tree for a particular module in structured form, preferably XQuery

OR:

  • list the functions declared in a particular module as function items

  • list the functions called in a particular module

File system accessors

  • list contents of a particular directory

  • determine whether a particular file is a directory

Maps

Provide a convenient means of keeping running totals keyed to function names, for example

References

[Holstege] Holstege, Mary. Type Introspection in XQuery. Presented at Balisage: The Markup Conference 2012, Montréal, Canada, August 7 - 10, 2012. In Proceedings of Balisage: The Markup Conference 2012. Balisage Series on Markup Technologies, vol. 8 (2012). http://www.balisage.net/Proceedings/vol8/html/Holstege01/BalisageVol8-Holstege01.html. doi:10.4242/BalisageVol8.Holstege01.

[Jones72] Jones, Karen. A statistical interpretation of term specificity and its application in retrieval. Journal of Documentation 28 (1): 11–21. http://www.soi.city.ac.uk/~ser/idfpapers/ksj_orig.pdf. doi:10.1108/eb026526. 1972.

[F&O30] W3C: Michael Kay, editor. XPath and XQuery Functions and Operators 3.0 Candidate Recommendation. W3C, January 2013. http://www.w3.org/TR/xpath-functions-30/

[XSD11.2] W3C: David Peterson, Shudi (Sandy) Gao 高殊镝, Ashok Malhotra, C.M. Sperberg-McQueen, and Henry S. Thompson, editors. W3C XML Schema Definition Language (XSD) 1.1 Part 2: Datatypes. W3C. April 2012. http://www.w3.org/TR/xmlschema11-2/

[XQuery30] W3C: Jonathan Robie, Don Chamberlin, Michael Dyck, John Snelson, editors. XQuery 3.0: An XML Query Language Candidate Recommendation. W3C, January 2013. http://www.w3.org/TR/xquery-30/

[Zipf49] Zipf, George Kingsley. Human Behaviour and the Principles of Least Effort. Addison-Wesley, 1949.