About triples

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Hi ticlers,
[N.B.: If attached a - hopefully - recent version of this as open office 
document.]

About triples

How it all started
Project requirements
When using plone we figured out a lack of features we badly needed in one of 
our projects. The project required a large number of documents to be linked 
together. The links had to have a type and required referential integrity, 
neither being feasible using standard plone features. So we decided to 
program a link manager to fullfill our needs. The link manager would care to 
prevent us from deleting objects which are still linked (that is ensuring 
referential integrity) and would provide links which could freely be typed 
and configured by a "constraint manager". The constraint manager simply 
checked the type of the objects that were to be linked and provided a simple 
interface for configuring new constraints. If a constraint is violated the 
constraint manager will not allow the creation (or deletion) of a link. So 
the constraint manager had only two basic methods: canAdd(link) and 
canDelete(link) both returning a boolean indicating wether a link can be 
added or deleted.
Here is a sample for a link constraint:
	(person_type, isAuthorOf, content_type)
This example shows how the link type "isAuthorOf" can be configured by the 
constraint manager. We define the link type "isAuthorOf" as a type that links 
to objects who have to have the type person_type for the first object and 
content_type for the second object.

As a consequence the constraint manager will not allow an "isAuthorOf" link to 
be used with an Object that of content_type as first and an other Object of 
person_type unless you provide a second specification which does:
(content_type, isAuthorOf, person_type)
This constraint shows the following important things:
1.The constraint manager can put more than one constraint on one link type.
2.The constraint manager will not prevent you from designing semantically 
malicious constrains. In other words: the constraint manager does not check 
semantics but syntax. The constraint above is fullfilled if :
The type is "isAuthorOf"
The type of the first object is "content_type"
The type of the second object is "person_type"

With this combination of link and constraint manager we were able to meet the 
project requirements. The implementation was done with the project and 
specific performance considerations in mind so that the resulting "product" 
is full of customer specific code leading to a lot of limitations of the idea 
of using triples. In this paper I like to give an idea what else might be 
achieved using triples. We renamed the project to "ticle" (though I hope we 
might find a new name since ticle pronounces like "Tcl" of "Tcl/Tk").

TICLE and triples
To give back something to the community we decided to make the link and 
constraint manager open source - but this time with all it's powerful 
features unleashed - and a new name: ticle.
Since ticle is not yet ready to be described, because it is doomed to undergo 
many changes, I like to tell something about the underlying concepts ticle 
relys on: triples. 
A triple (that is a tuple of exactly three items) is capable of modelling a 
lot of things; I will try to show what and how virtually everything can be 
expressed using triples.
(HINT: You might have wondered where the links have gone. We still talk about 
links here. A triple can (and will) be intepreted as a link. Thus a link is a 
triple.
link = (source_of_link, type_of_link, target_of_link)
And a triple is a link and a relation between objects - all the same - just in 
case you might have wondered.)

Obviously it is possible to model a typed relation between to two objects with 
a triple.
(A, relatesTo, B)
So we have A relating to B in a "relatesTo" fashion. As we already have 
learned this relation is directed. If A relates to B that will not ensue B 
relating to A. Expressing other kind of relations between A and B will result 
in using a different type:
(A, relatesInSomeOtherFashionTo, B)
So far we have not said anything about the nature of the items in the triple. 
Please consider the items in the triple as something we can refer to by a 
unique name. We do not need to go into any further detail to understand the 
concept of using triples.
If we supply every triple with a unique name (or ID if you like), then links 
migth also be objects in a triple. Thus unleashing the full potential of 
ticle:
label_1: (A, relatesTo, B)
label_2: (B, relatesTo, A)
label_3: (label_1, isReversed, label_2)
In a nested notation we would write:
((A,relatesTo,B), isReversed,(B, relatesTo, A))
The nested notation and the notation using IDs are equal in meaning.
Though "relatesTo", "isReversed" or "isAuthorOf" are human understandable link 
types or in other words: they carry natural language semantics, they are pure 
syntax to ticle. Ticle will not care about linking anything stupid unless 
constraints are defined which prevent us from doing so. We will see later how 
such constraints can be modeled. First I like to show some sample 
applications which could be done with ticle.
Case study - Linking
A very simple and yet powerful application of ticle is linking objects 
together. Consider the following setup: you have 1500 people all working on 
(potentially) many different documents. All in all let's assume we have got 
12.000 documents. The people relate in different manners to the documents. A 
person might be the author of one document and the translator of another 
document - or both of the same document.
Persons and documents must be objects to ticle in other words: they must in 
some way be referable to - like by a unique ID (=uid). Given this 
prerequisits we can start using ticle to link documents and persons.
some_id : (dave, authorOf, document1234)
other_id: (naomi, translatorOf, document1234)
In this application we usually will not be refering to triples (i.e. "some_id" 
and "other_id"), that is why I used meaningless names. "dave" is a uid, 
"authorOf" is a uid and "document1234" is a uid, too. In a real world 
application "dave" will point to a user-object (containing metadata about 
dave), "authorOf" is just a name to distinguish the different types of 
relations in which people can be to documents and "document1234" would be the 
id of a document.

When we used "what is now called ticle", we used a tab on plone document 
object showing all linked people listed by linktypes. Thus giving an overview 
about the people involved in the creation process.
Case study - Workflow
Let us consider a simple editorial workflow: There is an author actually 
producing content, a designer making the content visually attractive and an 
editor deciding if the content and design is matching the desired quality and 
keeping an eye on deadlines.
This workflow might be analysed in many other ways and I am well aware of it. 
Please regard the analysis as arbitrary but given - for the sake of 
explanation.
The workflow covers the following aspects: persons performing actions with 
documents,  pictures being inserted into documents and deadlines controlling 
the progress of production.
Ticle has no implicit or inherent semantics. Not even for types, classes, 
objects, properties or whatever. To model such things as types and properties 
we have to make them ourselves. This is fairly easy. We add an object named 
"Type" and an object name "hasProperty". We use these objects so that 
anything that refers to "Type" by "hasProperty" i.e. all triples: 
(...,hasProperty,Type) is considered a type. Please do not forget that the 
name "Type" and "hasProperty" are arbitrary. They do not carry any meaning. 
The meaning emerges solemnly from how we use these objects. To tell link 
types (or predicates) and objects from another we use camelcaps with a 
lowercase starting letter for predicates and uppercase camelcaps names for 
objects.
Since we have identified the things we want to model in the workflow (see 
above words in bold) as types of things we want to model, we can now tell 
them to be types of objects. [N.B.: We do not need to type objects. I just 
wanted to show you can, with the side effect of clarity.]
id_0 	= link(Type,	hasProperty, Type)
id_1	= link(Author,	hasProperty, Type)
id_13	= link(Designer,hasProperty, Type)
id_12	= link(Editor,	hasProperty, Type)
id_2 	= link(Document,hasProperty, Type)
id_3 	= link(Deadline,hasProperty, Type)
id_4 	= link(Picture, hasProperty, Type)
id_5 	= link(Action, 	hasProperty, Type)
But of course not everything in our workflow model will be of type Type. To 
indicate something being an instance of a type we create the predicate: 
isInstanceOf.
id_6 	= link(Report,	isInstanceOf,	Document)
id_7 	= link(2003_10_10,isInstanceOf,	Deadline)
id_20	= link(2003_10_12,isInstanceOf,	Deadline)
id_21	= link(2003_10_15,isInstanceOf,	Deadline)
id_8 	= link(Castle,	isInstanceOf,	Picture)
id_9 	= link(writes,	isInstanceOf,	Action)
id_10	= link(publishes,isInstanceOf,	Action)
id_11	= link(addsPicture,isInstanceOf,Action)
In our workflow we have some persons performing different jobs. So we tell 
them to have some "job":
id_15 = link(Icheb, isInstanceOf, Designer)
id_16 = link(Harry, isInstanceOf, Author)
id_14 = link(Naomi, isInstanceOf, Editor)
At this points it starts getting interesting again! Now we can model a the 
time constraint: "until" and the "into" relation (which we do not make a type 
here), which both use links instead of objects.
id_18 = link(until, hasProperty, TimeConstraint)
id_17 = link(Harry, writes, Report)
id_24 = link(Castle, into, Report)
id_22 = link(Naomi, addsPicture, id_24)
id_23 = link(Icheb, publishes, Report)
id_19 = link(id_17, until, 2003_10_10)
id_25 = link(id_22, until, 2003_10_12)
id_26 = link(id_23, until, 2003_10_15)
So what does this thing mean? Harry has to write (= finish) his report until 
the deadline 2003_10_10, Naomi has to add a specific picture to the report 
until 2003_10_12 and Icheb has to publish the report until 2003_10_15.

But why all these types in the beginning? An application does not necessarily 
understand words like "writes" and it would not be very configurable to 
program every possible action directly into the workflow engine. By adding 
the types the workflow engine can query for all possible actions, authors, 
deadlines and so on. If a new workflow is build up for a document then the 
engine could
1.show all possible actions
2.show all available authors, editors, ...
3.show all available deadlines
By adding constraints the available items can be reduced to a minimum.


Constraints
Why constraints?
In the case studies we have seen many different "linktypes" (= predicated,=the 
second item in a triple). Obviously it is not possible to pick predicates out 
of the blue. Predicates have a meaning evolving from their interpretation and 
usually apply only to a restricted number of subject and objects. The 
"authorOf" predicate for example will possibly want to link people to 
documents and not birds to cars.
So if we want to create a predicate, that makes only sense with a particular 
set of objects and subject, we need two constrain these sets. The currently 
persued method is to create a "constraint", which is simply a set of three 
filters - one for each triple item. The constraint may also be attached to a
Filters
The concept of filters is crucial for constraints. Constraints check if a 
triple appears in a list of triples returned by a filter. (Or - which is 
likely to be more performant: return true when the first matching triple is 
found.)
So a filter is "positive" it does not specify what to reject, but what to 
accept. A filter itself is a triple used to compare with the triple(s) in 
question. In other words: everything that is equal to the filter triple 
passes - the rest is rejected.
[N.B.: In the previous version, the LinkManager, triples were unique. Are they 
still? If yes, we get only one answer, if not, we might get more than 
one...!]
Obviously we do need something like a wildcard here, since otherwise we would 
need exactly as many filters as we have triples to match.
So the filter triples may contain the item "any" which matches any triple 
item:
all_triples: 	(any, any, any)
dave_triples:	(dave, any, any)
writing_triples:(any, write, any)
single_filter:	(id123, id432, id234)
The all_triples filter will match all triples. Whereas the "dave" filter will 
match all triples containing the uid "dave" as subject. Note that the uid 
must be the same, not the referenced value.
The "writing_triples" will match all

Besides the "any" filter, that matches anything, we will also need an atom 
functioning as placeholder. That placeholder could be used like a parameter.

some_uid:	(hans, writes, document)
person_filter:	(placeholder, isA, Person)

So the person_filter applied on "hans" will return true if there is a triple 
"(hans, isA, Person)"


Well, I know this has to be worked out a lot. I really do appreciate any help 
and any comment on this is welcome.

Sebastian

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