In this post, I describe the different technologies that I’ve tried for writing a new book, from markdown to LaTeX.

One of the questions that I have been asked about Tawny-OWL was whether there was a manual or not. Actually, the answer is, yes, there is and has been since well before the 1.0 release.

However, it’s not rich enough. It makes requires both a reasonably good background in Clojure and in Ontology development. Given that the overlaps between these two areas of knowledge is probably limited to myself and Jennifer Warrendar this is rather less than ideal. So, I’ve started a new manual in the form of a book called Take-Wing. Getting a nice environment has been an interesting journey.

## Markdown

The orginal version of the documentation was written in Markdown. There was not really a good reason for this, other than I wanted to try it and it is well supported. It’s not a bad format and is easy to type, although it lacks in extensibility (which is, of course, why it has been extended in so many different ways!).

However, one significant problem was that I have no good way of checking that the code samples in it work. I had been hit by this when I changed function names, for example, from owlclass to owl-class, or more perniciously when I moved one entity from a variable to a function. My general solution to this linked-buffer which translates documentation into code and vice-versa. The lack of an explicit delimiter for the start and end of code blocks makes this harder to implement for markdown.

## Asciidoc

My next thought was to move to asciidoc. I like asciidoc and have used it for years. I helped to add slidy support to it, so that I can use it for slides. Most of my teaching material uses asciidoc now, because I can get slides and lecture notes from the same source, with easy to integrate code snippets that I can run, albeit maintained in independent source files which can make things a little painful.

The first version of Take-Wing used asciidoc. Because I wanted to use linked-buffer to generate Clojure source that I could test, I needed to use multiple files with a master file — the Clojure cookbook uses much the same system, albeit for a slightly different reason.

However, writing a talk or even a lecture series is a very different thing from writing a book. The main problem was not asciidoc itself, but the support from Emacs. There is an asciidoc mode but, aside from needing patching, it is heavily focused on syntax highlighting rather than document structure. So, inserting cross-references and the link were painful.

## Org-Mode

My next idea was to try org-mode. So, I used pandoc to do the translation; this wasn’t a glowing success, but it achieved the basics anyway.

And Emacs specific solution doesn’t seem ideal, but then for Take-Wing I am likely to be the main author. And I have been using org for a while, particularly for building plans both for Tawny-OWL and also, ironically, for the outline for Take-Wing.

It has clear code demarcation blocks, so adding support for linked-buffers was straight-forward enough. One significant problem is that the org-mode export framework has recently been replaced, so I have to install my own version; actually, installing a new version is not problematic as this can be done with package.el, but because org-mode is in core emacs, deleting the old version is doesn’t happen automatically. I found several version conflicts resulting from loading old files. Still, I managed to get org working, producing both a PDF and nice web page.

Org-mode was pleasant enough to use. The folding features were nice and the syntax is reasonable for typing. However, I found the same problems as with asciidoc. While, org has advanced features for linking to the rest of the world, linking within documents is not so good, especially when using a master document. Basically, I couldn’t get over the envy of my PhD students both of who have written their thesis with AucTex

## LaTeX

LaTeX itself is an old piece of software, but it does the job of document preparation like nothing else. And, the support in Emacs is fantastic. However, it’s achilles heel has been that is produces PDFs. I don’t like PDFs for a variety of reasons, but the main one is that, essentially, it’s a screenshot of a piece of paper. I’ve long gone natively digital: I write my papers, blog posts, emails and everything else on computer, and I am used to reading in this way as well. And I want the web for reading documentation.

In my time, I’ve tried lots of different technology for webifying LaTeX. The best I had found was Plastex; my post on LaTeXtowordpress is still one of my best read, and my colleague even used it to post her PhD thesis . It’s a good tool, but it’s not using TeX underneath and so it doesn’t always do the right thing as a result.

For some reason, I managed to have missed tex4ht, though, even though it has been around for quite a while. My initial impressions are, though, that it is probably the best tool that I have seen even if it has been blessed with some of the worst documentation and a very strange command line. I’m hopefully that make4ht may help this. It’s author has been fantastic on StackExchange in answering my questions. So, I decided to give it a go, so I exported by org to latex, threw away my org and started again.

The first problem that I didn’t like it’s handling of the listings package. I have fixed this by dropping code straight through to HTML. Initially, I tried highlight to do syntax highlighting, but then dropped this for prism, as the former cannot do inline highlighting also. The default footnote handling is also very strange, but this is also easy to fix with a standard package. So, now, after a lot of fiddling, it all seems to be working.

## Conclusions

It’s been quite a lot of effort and rather more fiddling than I would have hoped, but I now have an editing environment that I like, and this is important. Writing a document is hard, and the environment needs to support this and not get in the way.

I am hopeful that tex4ht will fulfil it’s initial promise. I have been using LaTeX less and less over the years, simply because of its lack of HTML support, despite the fact that it’s the best environment for writing in: so when I have been most happy as an author, I have been least happy as a reader.

All I have to do now is write the rest of the book; so far, I think it’s going well, and this is something that I shall cover in later blog posts.

## Tawny-OWL 1.2

About six months after the release of Tawny-OWL 1.1.0 , I am pleased to announce the 1.2 release. There have been a number of changes in this release, some planned, some not.

The planned changes have been an extension of the rendering capabilities of Tawny-OWL; it is now possible to render an OWLEntity entirely into Clojure data structures. The main reason for this was to allow use of core.logic for building an effective syntactic query language over OWL. This is now complete, although more work needs to be done on tawny.query if this is to be exploited to it’s fullest.

The main unplanned release was caused by a change in the OWL API which had dramatic (and negative) consequences for Tawny-OWL performance. The details of this change have been documented elsewhere . Fixing this actually resulted in small increases in rendering performance. This also lead me to some aggresive micro-optimisations of the Tawny-OWL code base, mostly meaning I can avoid using variadic function calls where necessary (these box arguments into a list, which can be quite slow). On small ontologies, Tawny-OWL will load several times faster now.

The pace of development on Tawny-OWL has slowed somewhat in recent times; partly, this is because it is now reaching a point of maturity. However, I have also been diverted by two other projects. I have put a reasonable amount of effort into Linked buffer which provides a rich literate environment, originally intended for Tawny-OWL, although it is not specific to it. And, secondly, I have started a manual for Tawny-OWL called Take Wing. This is developed using Linked Buffer. Not the first example of a literate program as a manual, I know, but probably the first example a literate ontology as a manual.

Despite the slowed pace, I have a roadmap for Tawny 1.3. I wish to support what I am calling transactional restrictions; these are a set of axioms which are either added all together or not at all. The use case for this comes from the Gene Ontology who use annotations on their annotations to describe evidence for particular statements. The meta annotations should not be added to the ontology, until the annotations are.

And secondly, I am reworking tawny.pattern — the existing value partition support has already been changed, and there are some new functions which make it easy to turn a functional pattern into a macro one; the latter produce the more attractive syntax.

No doubt there will be a few unplanned additions also!

## When is a recursive function not a recursive function?

Yesterday, I came across a very strange bug in my Tawny-OWL library . The bug was my fault, but fixing it was exacerbated by what has to go into my list of Clojure gotchas .

Consider this very simple piece of Clojure code. Is this a recursive function, i.e. one that calls itself? Intuitively the answer is yes, but I would argue that actually, you cannot tell from the information given. It could be, but is not necessarily so.

 (defn countdown [n] (if (pos? n) (cons n (countdown (- n 1))) '(LiftOff)))

Let’s run this code:

 test-project.core> (countdown 10) (10 9 8 7 6 5 4 3 2 1 LiftOff)

All is working as it should and the function is recursing, so there appears to be no problem. However, countdown is a big long to type, so lets create an alias called cdown and test that this works as expected.

 test-project.core> (def cdown countdown) #'test-project.core/cdown test-project.core> (cdown 10) (10 9 8 7 6 5 4 3 2 1 LiftOff)

All is good, cdown is doing just what we expect also, and it’s the same as countdown. However, as we as being lazy, I am easily bored, so now we make the countdown go faster by redefining the countdown function.

 (defn countdown [n] (if (pos? n) (cons n (countdown (- n 2))) '(LiftOff))) test-project.core> (countdown 10) (10 8 6 4 2 LiftOff)

Again, everything is working. But what happens when we call cdown

 (cdown 10)

If you are new to clojure, you might assume that as we have changed the definition of countdown the definition of cdown would change as well, so we should get

 test-project.core> (cdown 10) (10 8 6 4 2 LiftOff)

If you are more experienced with Clojure (as I would claim myself to now be, although others may disagree), then you would not that the alias was to the function and not the var, so cdown now contains a pointer to the old definition, so it will behave as it did before.

 test-project.core> (cdown 10) (10 9 8 7 6 5 4 3 2 1 LiftOff)

As it happens, this is not true either. What we actually get it this:

 test-project.core> (cdown 10) (10 9 7 5 3 1 LiftOff)

A wierd combination of the two functions. What is happening is this: the initial function call to cdown calls our first function definition; 10 is postive, so we subtract 1 to get 9. And, now, here is the strange bit. The function is no longer recursive, because it calls countdown through the indirection of the clojure var; we could be more explicit and replace the “recursive” call with this instead which is what is actually happening in the compiled Java class.

 ((var-get (var countdown)) 10)

So, in short, in Clojure a recursive function is not necessarily recursive, even if it is when defined. If the var changes, then the function no longer calls itself.

There are solutions to this. I should have defined my cdown alias like so:

 (def cdown #'countdown)

Now, when we defined countdown the original function gets lost and GCd rather than hanging around, a pale shadow of its former recursive self. This works but is rather counterintuitive; with a Lisp-1 you get used to refering to functions directly rather than with a quoted symbol, but here we have to use both a quote and a #.

A second solution is to use recur, which does not use var indirection. So consider this example. The first countdown2 function is recursive and will always be since it directly refers to itself, and this remains after redefinition.

 (defn countdown2 [i] (when (pos? i) (println i) (recur (dec i)))) (def cdown2 countdown2) (defn countdown2 [i] (when (pos? i) (println i) (recur (- i 2)))) ;; prints 10, 9, 8... (cdown2 10)

Of course, we cannot use this in the first example, because it is not tail recursive. And, if we want to be really picky, we could argue that countdown2 is not recursive either because it is tail-call optimised, so it doesn’t call itself. And this is not an implementation detail either because it’s the whole point of recur.

Another solution would be for Clojure to provide a recur* form (or something equivalent) which would work away from the tail position and which directly recursed, rather than using var indirection. It’s unlikely that Clojure will do this, however, because this form of recursion consumes stack and so is not a good thing to do.

It would also be possible to change the semantics of Clojure symbols so they automatically refered to vars rather than values as appropriate. So in all these cases, we would have vars. As far as I can tell at the moment, the same syntax y is refering to two different things — the value of the var y in the first two forms and the var itself in the third.

 (def x y) (def z {:x y}) (defn y[] (y))

To replicate the current behaviour, we would just use var-get.

 (def x (var-get y))

Without thinking about this too deeply, I cannot actually see a downside to this, except that it would involve more var indirection, so would probably be slower.

Finally, clojure could just remove var indirection. Actually, this is likely to happen in the form of build profiles, because it also has the advantage of making Clojure faster. As my example shows, however, it also introduces some subtle changes to the semantics of the language.

I still like Clojure. The more you use a language, I guess, the more oddities you find.

## Open-Access Communism

Godwin’s law says that sooner or later every argument on the internet ends up with someone being called a Nazi. Interestingly in the Open Access debate, this has turned out not to be true; in this case, it’s been communists instead.

Perhaps the best known example of this was the Jeffrey Beale rant, which uses the term “anti-corporatist” and “collectivizing”. A more direct communist angle comes from Moshe Vardi at ACM. He defends the idea that publishing is expensive because of all the fixed costs, something seen from the ACM before, and which I have commented on . He also makes the tired confusion that “free software” is the same thing as “anti-copyright”.

Now, personally, I do not particularly mind being called a communist — I do have left-leaning political views, but in the US “communist” is essentially used as a short-hand for being personally responsible for Stalinist purges.

For me OA is just a small part of the issue. I do want OA because I get irritated that I have to read papers at work because at home I can’t login, as well as the slightly more philanthropic ideal that scientific knowledge should be free.

But I also want the entire publication process to be easier . I want a single submission format, free from the stupidity of multiple formats. I want peer review to be open and acknowledged. I want the process to take less time, less effort and less money. I want colour figures, I want animation . OA does not necessarily provide this: both OUP and PLOS were painful. However, arXiv for example, provides cheap, rapid and simple publication at \$7 a paper. WordPress manages billions of articles as a loss leader.

Open-Access is only part of the issue. Scientific authoring is a hard, arduous and difficult process. Scientific publishing should not be. This is the issue.

## The Visitor Pattern in Clojure

I first discovered the Visitors pattern from reading the original design patterns book, sometime in the last century when, having jumped into computer science, I was busy hoovering up everything I could about programming. After reading the chapter on visitors, it made no sense to me then and I had no real cause to go near them again until I started working on Tawny-OWL . This library includes a renderer which takes a set of OWL API OWLObjects and turns them into Clojure data structures. Originally, I added this simply to generate documentation, but since then it’s grown to have rather a life of its own. In Java, this would be be implemented with a visitor. In Clojure, I implemented this with multimethods which is often used as a replacement for the visitor pattern but I am now far from convinced that this was a good decision, after the performance of my code collapsed massively. In this article, I describe the problems with multimethods, and some alternatives. For each of these, I use a small example, and bench mark them; you can follow my code on https://github.com/phillord/visitor-benchmark. The results are, perhaps, a little surprising. This should be of relevance to anyone addressing the same problem in Clojure.

## Visitors and the OWL API

The purpose of a Visitor is to crawl over a set of objects, identified by their type, typically representing an abstract syntax tree, although it can be used for other purposes. It enables the implementation of many different types of behaviour over the tree without having to extend each of the types. This works by having a Visitor which implements one method for each object type. It works well, unless you add a new type, in which case there are a lot of Visitors to re-write. This is one reason that they are found mainly around abstract syntax trees. They tend not to change very much which is a prerequesite for visitors.

The OWL API is a library which represents the OWL language  — a mechanism for representing an area of knowledge using logical statements, or an ontology . It’s a fairly complex API and implements several visitor patterns; it’s main visitor — the OWLObjectVisitor has so many methods I ended up using Clojure and reflection to count them all — 98 is the answer!

## Tawny-OWL

Now, Tawny-OWL wraps the OWL API to provide an evaluative, R-like environment for building ontologies, built using Clojure, which provides the ability to abstract away from the actual axioms; you can build functions which build axioms, examples of which can be seen in the karyotype ontology (https://github.com/jaydchan/tawny-karyotype) .

While abstractions are generally nice, it also hides the underlying axioms; so I built tawny.render which takes OWL API objects and turns them into Clojure forms, originally as a mechanism for documentation, although since I wrote it, it has taken on a life of its own.

In Java, the renderer would just have used the Visitor pattern. In Tawny-OWL, I initially implemented this using multimethods. These have quite commonly been put forward as a replacement for the visitor pattern , so it seemed a reasonable suggestion and it worked well for me, until a new version of the OWL API was released. Suddenly the performance of my test suite crashed catastrophically. Consider, these results: from 40 seconds to 4 minutes.

 git clone git@github.com:phillord/tawny-owl.git git checkout 5870a9 time lein with-profile 3.4.10 test real 0m45.186s time lein with-profile 3.5.0 test real 4m26.070s

The OWL API test suites speed up slightly between the two versions, so it seemed unlikely to be an implementation mistake. I also noticed that most of the time was in the rendering tests — which include one substantial rendering task.

Thanks to git bisect, I tracked the problem down to a single commit 2bb6a0. If you look through the entire log (it’s long, and I did!) the surprising thing is this; there are precisely no implementation changes. All that this commit does is add a (large number) of interfaces to the existing model. Why on earth would this cause a massive drop in performance?

## Visitors Revisited

There is one subtlety about the visitor pattern that is not obvious at first sight. If we have a visitor interface like so:

 class Visitor{ public void visit(A a); public void visit(B b); public void visit(C c); public void visit(D d); }

At some point, we have to decide which method to actually call. With the visitor pattern it is the entity that accepts the visitor that makes this decision, because it is this entity that calls visit. Consider this code:

 class Dimpl implements D{ public accept( Visitor v ){ v.visit(this); } }

In Java, which method to dispatch to is made on the basis of the compile time, static type of the object. Now, the Dimpl class knows it’s own type at compile time, hence we dispatch to the correct Visitor method, even though the class which makes calls the accept method does not know the underlying type of the Dimpl object. Effectively, we pass off part of the computation to the compile time type system.

Clojure cannot do this. Multimethod calls have to check the runtime type of the object to be visited at runtime against the range of possibilities. By introducing a large number of interfaces, it appears the OWL API had increased the search space over which the multimethod isa? call had to crawl. I’ll try and show here that between the two versions of the OWL API, benchmarking isa? call has got significantly slower. This is not enough to explain in performance drop of my tests, although refactoring the multimethod to reduce the number of isa? does actually address the issue, so it really does seem to be the problem.

In the rest of this article, I will consider several different alternatives, benchmarking them and comparing them for performance. Microbenchmarking of this form is hard to do. In this article, I use a combination of the excellent criterium, clojure.core/time supplemented with some macro-benchmarking — running the Tawny-OWL tests. I consider that none of these tests are definitive, and will discuss their advantages and disadvantages as I go. All results are reported to 2 significant figures. Ultimately, my aim with this article is to improve the Tawny-OWL performance, but I hope that the results are clean enough that they are relevant to other environments also.

## Set up

The rest of the code for this post is available at https://github.com/phillord/visitor-benchmark. The code in this article is a point in time, and will not be updated if I change the visitor benchmark. This project can be cloned and tested using lein with-profile production run. I will not describe all of the plumbing that makes this work here.

First, however, we define a benchmark command. Using Criterium directly is a little painful, so I define a small macro which allows me to switch between bench, quick-bench and time. My version of bench also prints out the form so I can see what is happening.

 (def bench-form ;;'clojure.core/time ;;'criterium.core/quick-bench 'criterium.core/bench ) (defmacro bench [form] (do (println "Benching:" (quote ~form)) (~bench-form ~form)))

## Establishing a base line

First we establish a base line; how long does it take to invoke a function that does nothing at all. While it varies from machine to machine, on my desktop it takes around 10ns.

 (defn f []) (visitor.benchmark.bench/bench (f)

## Some objects to work with

I have choosen to use the OWL API and Tawny-OWL to generate my objects, although my belief is that this analysis should be good for any API. I already had a lot of the code for this analysis, the OWL API uses visitors and it is big. Finally, the change between 3.4.10 and 3.5.0 that I describe earlier is a useful test. We generate three objects to use.

 (defontology ont) (defclass AClass) (defoproperty AProperty) (def ASome (first (owl-some AProperty AClass)))

## Multimethods

To test multimethods first, I used the following code, which creates a two method multimethod operating on class. After this, I also tried adding many more methods to the multimethod and calling it again.

 (defmulti multi class) (defmethod multi org.semanticweb.owlapi.model.OWLClass [e]) (defmethod multi org.semanticweb.owlapi.model.OWLObjectProperty [e]) (defn multi-on-class [] (bench (multi AClass))) (defn multi-on-property [] (bench (multi AProperty)))

Now using criterium.core/bench gives the following results, both before and after adding extra methods. The basic conclusion here is that, it makes no difference at all: the multimethod is unaffected by the change in number of method and, critically, there is no difference at all between OWL-API 3.4.10 and 3.5.0. Poor evidence for the theory that the multimethod is responsible for the performance drop.

 OWL API Class Property Big Class Big Property 3.4.10 61ns 61ns 66ns 65ns 3.5.0 62ns 57ns 60ns 63ns

Poking through the Clojure java code finds this possible issue — the method lookup appears to be cached. dispatchVal here is the value returned by the dispatch function.

 private IFn findAndCacheBestMethod(Object dispatchVal)

Testing with clojure.core/time rather confirms this. Consider the results in this table. The first thing to notice is that change in unit — we have moved from nanoseconds to milliseconds. Just for comparision our base test of an empty function reports “Elapsed time: 0.026253 msecs” or around 26μs for a simple invocation — three orders slower than criterium suggests and 5 orders faster than our multimethod invocation. Now, none of these differences are entirely believable, but what is interesting is difference of between 5 and 20 fold between the two versions of the OWL API. Of course, clojure.core/time is potentially risky because of start up time and so forth but, because this should affect the test against 3.4.10 and 3.5.0 equally; it also will also remove the effect of caching in findAndCacheBestMethod single it only runs once.

 OWL API Class Property Big Class Big Property 3.4.10 220ms 140ms 80ms 88ms 3.5.0 860ms 1400ms 450ms 1400ms

Trying to pull apart this appart a little further, let’s test the isa? method more directly, which we test with following benchmarks one of which succeeds and one of which fails.

 (bench (isa? (class AClass) org.semanticweb.owlapi.model.OWLClass)) (bench (isa? (class AClass) org.semanticweb.owlapi.model.OWLObjectProperty)))

First, comparison with criterium.core/bench which shows a massive difference between success and failure (note the change in unit); the reason for this should be obvious — if isa? succeeds it short-circuits; if it fails, it must test all superclasses and the various hierarchies that Clojure adds.

 OWL API Succeeds Fails 3.4.10 76ns 40μs 3.5.0 76ns 33μs

Using the simpler, clojure.core/time shows the same thing as well as a difference between 3.4.10 and 3.5.0.

 OWL API Succeeds Fails 3.4.10 30μs 1.4ms 3.5.0 40μs 3.8ms

This distinction is important here. If it fails, then the isa? method is really very, very slow. 3.5.0 is slower, although not that much slower, at least according to clojure.core/time.

I am still not entirely satisified with these results. They do appear to show that multimethods can be pretty slow, and they do show a difference between 3.4.10 and 3.5.0. However, the various caching that multimethods perform should help — even though the OWL API has add many new interfaces, we are still only talking about tens of interfaces.

## Implementing a Visitor with a Visitor

The most obvious way to implement a visitor pattern is to, er, implement the visitor. To achieve this in a vaguely friendly way in Clojure, we need to use reify — we cannot use proxy as it cannot overload on type which is the whole point of the visitor pattern.

We can achieve this simply with the following code:

 (defn ontology-visitor [] (reify org.semanticweb.owlapi.model.OWLObjectVisitor (^void visit [this ^org.semanticweb.owlapi.model.OWLOntology o] (println "v ontology" o)))) (defontology ont) (.visit (ontology-visitor) ont)

This works fine, but there is a problem. By default, the visitor pattern returns nothing — it works by side effect. In general, and specifically in the OWL API the visit method returns void. This is not at all useful as a replacement for multimethods in a recursive descent renderer. To work around this problem, I add some extra glue in terms of an atom which we change by side effect during visiting and then dereference to provide a return value.

 (defn visit-entity [entity] (let [r (atom nil)] (.visit (reify org.semanticweb.owlapi.model.OWLObjectVisitor (^void visit [this ^org.semanticweb.owlapi.model.OWLOntology o] (reset! r (str "visit o" o))) (^void visit [this ^org.semanticweb.owlapi.model.OWLClass c] (reset! r (str "visit class" c)))) entity) @r)) (visit-entity ont) (defclass A) (visit-entity A)

And how does it perform. Well, badly, is the answer: around 25μs for each method invocation (using bench) which is 1000x slower than our base line.

Of course, one obvious complaint with this implementation is that it involves creation of an atom, resetting that atom and so forth; actually, I have tested that as well, but for the purpose of this article, I test this simpler version.

 (defn new-object-visitor [] (reify org.semanticweb.owlapi.model.OWLObjectVisitor (^void visit [this ^org.semanticweb.owlapi.model.OWLObjectProperty o]) (^void visit [this ^org.semanticweb.owlapi.model.OWLClass c])))

This gives a base line score of about 7ns. In short, the creation of a new object is not the problem. In the examples above, I use type hinting, but actually this makes no difference to performance. The fundamental problem here is that our reified object is dispatching on type using runtime checks and reflection.

## A big Cond

Another possible option would be to replace the multimethod with a big cond form. I will not show the full code for this as it’s rather long, but an example of part of it looks like this:

 (defn- as-form-int "Render one of the main OWLEntities as one of the main functions in tawny." [c options] (condp (fn [entity-type ^OWLEntity entity] (= entity-type (.getEntityType entity))) c EntityType/CLASS (as-form-int-OWLClass c options) EntityType/OBJECT_PROPERTY (as-form-int-OWLObjectProperty c options) EntityType/DATA_PROPERTY (as-form-int-OWLDataProperty c options) EntityType/ANNOTATION_PROPERTY (as-form-int-OWLAnnotationProperty c options) EntityType/NAMED_INDIVIDUAL (as-form-int-OWLNamedIndividual c options) EntityType/DATATYPE (as-form-int-OWLDatatype c options)))

Here, we have use a cond to dispatch on the EntityType. The individual methods for the multimethod have been renamed using a rather clunky naming scheme. I do not have individual benchmarks for form of test, but looked at overall it does solve the problem. lein test runs in around 10s and there is no difference between the OWL API 3.4.10 and 3.5.0. In short, it solves the problem.

Unfortunately, the solution comes at a significant cost. Firstly and perhaps most trivially the code looks terrible. The solution also is very specific to the OWL API — without the getEntityType method this fails. In fact, getEntityType does not make all the distinctions we need; I also needed another couple of methods (getClassExpressionType and getDataRangeType) and still needed to fallback to instance? at points.

A different solution would be to just use instance? calls.

 (defn small [e] (cond (instance? org.semanticweb.owlapi.model.OWLClass e) true (instance? org.semanticweb.owlapi.model.OWLObjectProperty e) true))

This behaves as expected under benchmarking. The code shown above with only two instance of calls bench marks at 5ns; however, when expanded to perform all the instance of calls I need, performance drops to 230ns.

I have also tried a few other tricks for optimising type based look up, including replacing the cond with a map lookup. Details are available in my test code. Suffice to say, I did not achieve a solution which was performant.

## Protocols

A final solution would be to use protocols. The idea here is that OWL Objects would know how to render themselves. I have not yet tested this within the context of the OWL API, and have only benchmarks. Consider this code:

 (extend-type org.semanticweb.owlapi.model.OWLClass Render (render[this]))

A bench check of this shows highly performant invocation at around 10ns. The use of time is less happy, however, with a 0.2ms invocation (compared to 0.005ms baseline). I suspect that there is some caching happening at the protocol layer also. I would like to find the time to check protocols further, with a full implementation in the context of tawny.render. Unfortunately, this is quite a bit of (very boring!) code to rewrite.

The actual solution that I used was different to all of these, simply because it was the first acceptable solution that I found which solved the problem of very long test run. My approach to solving this problem was to address the isa? calls through memoization, using the fact that I know which classes the multimethod dispatches on.

The code for this just affects the dispatch method; we call isa? once and only once for each concrete class of object that we have. The full diff is available here.

 (defn lookup "Returns the class of the OWLEntity of which this is a subclass." [c] (first (filter (fn fn-lookup [parent] (isa? c parent)) (list org.semanticweb.owlapi.model.OWLClass org.semanticweb.owlapi.model.OWLObjectProperty org.semanticweb.owlapi.model.OWLNamedIndividual org.semanticweb.owlapi.model.OWLDataProperty org.semanticweb.owlapi.model.OWLAnnotationProperty org.semanticweb.owlapi.model.OWLDatatype)))) (def m-lookup (memoize lookup)) (defmulti multi (fn [c] (m-lookup (class c))))

My results here are a little surprising. The speed of the dispatch seems to slow down using my benchmarking (data not shown). Fortunately, I tried running my test cases BEFORE I did this bench marking, because the results overall are excellent.

 git checkout 2fab56 time lein with-profile 3.4.10 test real 0m7.875s user 0m9.547s sys 0m0.661s time lein with-profile 3.5.0 test real 0m7.950s user 0m9.641s sys 0m0.696s

As you can see, this memoized version achieves two things. Firstly, it is faster than the original by five fold. But critically, the difference between 3.4.10 and 3.5.0 has gone. For the 3.5.0 version of the OWL API this memoization is 30 fold faster.

Of course, this solution is not ideal. The multimethod is not really doing anything now. We have closed it rather than left it open. It is doing a completely pointless isa? check when all we need is an = check, and it is still doing linear time dispatch when it should be constant. Moreover, I wonder what why this form of memoization is working when the multimethod implementation itself is cached. None the less it works well enough that I am happy with it for the moment.

## Conclusions

In this article, I have investigated the visitor pattern and its implementation in Clojure. Multimethods do work, and do produce a nice code base, but they do not perform that well. As my example shows, they are potentially also sensitive to changes in the class structure of dependencies. In short, the runtime decisions of multimethods are not really a good replacement for the compile decisions of the Visitor.

Benchmarking is very difficult under the best of circumstances. Criteriums use of multiple runs brings some statistics to bear on the task, but also produces very poor results for memoized or cached functions if the real-world task defeats this caching. In this article, I have chosen a combination of simple test cases, bench and time but also my test cases from tawny.owl`, against two different versions of the OWL API. Clearly the latter is not simple and there are many other variables which could be producing these results. However, what these tests lack in cleanliness, they gain in that they are a real world problem. Although I have tested them in this environment as well as I am able, this lack of cleanliness leaves the possibility that I have just misunderstood the cause.

I would like to test protocols in this environment also. They may be a good solution and appear to run quickly, but I have only tested against benchmark; as we have seen benchmarks are not necessarily clean.

Ultimately, I feel that we need proper “dispatch on type” support in Clojure. Multimethods are much more generic even if they are generally used in this way. I would like to be able to dispatch on more than one argument, have type hints taken care of for me, and most importantly, I would like them to be highly performant. I have managed to achieve some of this by modifying the dispatch method, but I think that this is a more generic problem and should be solved properly. As it stands, I would argue that multimethods are not a good replacement for the visitor pattern.

## Acknowledgements

Thanks to Keith Flanagan for a proof read. Mistakes are my own!

## On Function, Recursion and Evolution

I was entertained to see the recent publication of a new paper on the definition of function . I met one of the authors at a meeting a few years back in Durham, and had a very nice discussion about my own contribution to this definition which I published previously .

I do not want to discuss the paper in full, which is a nice paper and worth a read. I do however want to comment more specifically about the parts that explicitly and implicitly address my own paper.

At the start of the paper, the authors discuss the criteria for their definition which includes this:

Avoidance of epiphenomenalism: Functions should be determined by current performance of its bearer, not mainly by causally inert historical facts like its (evolutionary or cultural) history or a mere ascription by its producers, users, or observers

I found this a fairly strange criteria; it’s not clear to me why historical facts are inert; especially in biology the evolutionary history of an organism is surely one of the most important features. Originally, this criteria comes from another paper by Artiga who says:

We want to find out what is the lung’s function, we would probably look at what lungs actually do in our body. We would see that they enable respiration, so we would conclude that this is their function. Why they came to be here seems completely irrelevant for function attribution.

Obviously, this means “most peoples” bodies rather than just one, given that lungs do (somewhat) different things in different people. But, I do not think that why they came to be here is irrelevant, at least not if we wish to distinguish with a role. My fingers are currently engaged in typing, but few people would describe this as a function (although most would say that precise and controlled manipulation of the world is). Or to make a more extreme position, after Robert Hoehndorf, the heart actually does produce loud thumping noises. Surely not a function?

I am also slightly disappointed that what I think is one of the key points of my own function paper has been missed from their list of criteria. In it, I say:

I consider whether these definitions are applicable; for a given set of entities how do we decide whether we have a function (of either subclass) or a role.

Given a definition, I should be able to produce at least one practical test that I can use to determine whether that definition holds; I think that this notion of applicability needs to be more widely considered.

Now, my actual definition of biological function was:

A biological function is a realizable entity that inheres in a continuant which is realized in an activity, and where the homologous structure(s) of individuals of closely related and the same species bear this same biological function.

The language has been chosen to mirror BFO since it was in this context that the paper was addressed; I think it could be simplified and made more readable, but I was constrained by the language of BFO. Now, the first criticism on my definition is on technical grounds namely:

Lord claims that his definition is recursive rather than circular, despite the occurrence of the word “function” in the definiens.

My use of this form of definition was, of course, deliberate and partly provocative; perhaps, it is something that I should not have done, since it has muddied the water somewhat as this comment shows. In fact, it is very easy to work around this criticism by simply removing the recursion:

A biological function is a …. same species bear this same realizable entity.

The technical criticism has now gone. But I do not like the definition as much because “the same realizable entity” would in fact be a biological function. I think we avoid recursive definitions because they can be circular, but this is like avoiding recursive function calls because they may not terminate. And that is a shame, because, as with recursive function calls, I think this form of definition can be quite succinct. Consider:

A spouse is a person who is married to their spouse.

or:

A brother is a man with the same parents as their brother.

If we unwind the recursion, then we get

A brother is a man with the same parents as another man.

Again, we are hiding that reality that both men in this definition are brothers.

Of course, some recursive definitions might actually be circular, and that is less good. But if the applicability of a function is also considered then this issue goes away. I can determine if some one is a spouse or a brother given these definitions, so I see no problem.

A second criticism comes from my statment that:

Hence he concludes that among the instances of realizables that are realizables for the same type of process can be both roles and functions depending on the species the realizable’s bearer belongs to. This presents a problem for the distinction between functions and roles.

I do not think that this is a problem at all, because I say quite clearly that we can distinguish between roles and functions, but that we do this for the individual role or function not at a class level:

My definition distinguishes between the two based on the nature of the relationship to the independent continuant in which they inhere. I suggest that it is very hard to make the distinction at the class level[…]. For an individual continuant bearing a realizable entity, this distinction appears to be much more straightforward.

In otherwords, “for walking on” is either a role or a function. But in human hands it is a role, while for chimps it is a function. I see no reason why the distinction at the level of the individual should be considered to be less relavant than at the class, nor why this should be problematic. Actually, it reduces the need for duplication between the role and function hierarchies; while tools like Tawny-OWL may ease the maintainence of duplication, avoiding altogether still seems sensible.

The final criticism is, I think, the least worrisome. The authors say:

Had evolution stopped after the first species, according to Lord’s definition, there would not have been any biological function at all.

The slightly flippant but none the less entirely valid argument to this is, “but it didn’t”. We could equally argue against a definition of human as having two hands on the basis that they might have evolved a third.

More importantly, though, in most definitions of life the ability to adapt or evolve is part of the definition. Without this, we have a chemical process. So, without evolution, we have no life. Given this, we can rewrite the last statement as:

Had life stopped after the first species, there would not have been any biological function at all.

Which is an entirely true statement; that it drops so nicely out of my definition for biological function is a strength of my definition and not a weakness.

I feel that my definition is still a good one. Rereading my function paper now the argument still seems coherent, and the examples clear. Although I put an entire section on applicability into the function, I do rather regret that I did not introduce it as a general criteria for all ontology definitions explicitly; that this criteria has been missed is surely my fault and not the readers. Perhaps I should have spent more time on that, than on my recursive definition which was not critical to the paper.

At the same time, the fact that discussions on definitions are still going on, for a term that biologists have been using for many years again leads me back to the conclusion that the definitions of such generic terms are not nearly as important as some make out. So long as they are useful, biologists will carry on describing things as functions if it fits their ad-hoc, informal definitions that have been developed over time within a community. I cannot help but think that this is a good thing.