The on-wiki version can be found here:
* * *
Today we will talk a little bit about how the catalog of functions will
actually work. A more formal and comprehensive description of this is
but here we want to create a more intuitive explanation.
Every page in the new wiki will contain one *Object*. Every Object is of
exactly one *Type*. Types decide what the Object means. Types also decide
what makes an Object valid or not. An Object that is of a certain Type is
called an *instance* of that Type. Every Object that is stored as a wiki
page is called a *Persistent Object*, and such an Object has a Z-ID by
which it can be referenced. The Z-ID is the name of the page.
What does it mean that the Type decides what the Object means? Let’s look
at an example. An Object of Type *Positive Integer* with the value
the number 2020. That’s the number you get when you multiply 4, 5 and 101.
And because it has the Type of Positive Integer, we know it is a number. If
the Type of "2020" was String, then that wouldn’t represent the number
2020, but rather a sequence of four characters, "2", "0",
"2", and 0. If
the Type of it was *Gregorian Calendar Year* then this would represent the
year 2020 in that calendar, a leap year starting with a Wednesday and
ending with a Thursday.
The Type decides what you can do with an Object -- or, more formally
speaking, which Functions you can apply to the given Object. If you have a
String, you can count the length of the String, *i.e.* how many characters
are in the sequence. The result for "2020" above would be four. If you have
a Gregorian Calendar Year, you might also be able to ask for the 'length',
but the result should probably be 366 days (as it is a leap year). If you
have a Positive Integer and ask for its length, you might be asking for the
logarithm in base 10, or you might be asking for the multiplicative
persistence <https://en.wikipedia.org/wiki/Persistence_of_a_number>. But
all of these would be different Functions (that may well have the same
label, “length”, in English; their descriptions would explain in more
detail what they would do). The Function states which Types it can take,
and the Type decides what an Object means.
Types can be very diverse. Some Types might have a small, explicitly
defined number of instances. These are called *Enumerations*, because all
the instances of the Type are known in advance and enumerated, and each
instance must be one of these few possible values. The classic example of
such a Type is *Boolean*, named after George Boole
<https://en.wikipedia.org/wiki/George_Boole>, which has exactly two
instances: *True* and *False*. Another Enumeration would be the *Days of
the Week*. Other Types can be simple but have an infinite number of
possible instances. Examples of such Types are *String* for sequences of
characters, and *Positive Integer* for the counting numbers. Other Types
can be composed of simpler Types. For example, one way to represent an
*Integer* would be to compose it from a Positive Integer and a Boolean,
where the Boolean decides whether the Integer is positive or negative, and
the Positive Integer represents the absolute value.
Not every Object has to be stored as a wiki page. For example, there is no
need to store the number 2020 as an Object in the wiki, as it can be easily
just created on the fly.
This is how Objects are built and represented. Objects of almost all Types
are called *Literals*. A Literal is an Object that, when evaluated, results
in itself. For example, when you evaluate the number 2020, the result is
the number 2020. But there are two very special Types whose instances are
not Literals, and these two types are *References* and *Function Calls*.
References are a special Type of Object that refers to a Persistent Object
by its Z-ID. It basically just says “here, this Reference, should really be
just this Object that is referenced to by this Z-ID”. Evaluating a
Reference results in the referenced Object. A Reference does not need to be
evaluated immediately, but can be evaluated whenever needed. In fact, it is
sometimes impossible to evaluate all References fully, as it can easily
lead to a recursion and infinite objects.
The other special Type of Object is the Function Call. A Function Call
consists of a *Function* and a *List of Arguments*. Evaluating a Function
Call is the core 'magic' of the whole system: it is basically replacing a
Function Call with the result of that Function Call, *e.g.* evaluation
would be replacing the Function Call to the Function with the label
"length" and the argument "2020" of Type String with the value
"4" of Type
Function Calls are usually created on the fly. We wouldn’t, in general,
create a new wiki page with a Persistent Object in which we store the
Function Call described above, but rather we would send that Function Call
to an evaluation engine which, in turn, evaluates the Function Call and
returns the result. There is really not much more to the system than that.
A Function Call is in many ways analogous to using a MediaWiki template
<https://www.mediawiki.org/wiki/Help:Templates> with parameters.
I hope that this explanation made some sense and helped with understanding
the planned system. We are currently developing the part of the system that
allows contributors to create Types inside the wiki itself, so that the
community can create and control which Types exist. Please feel free to ask
The voting for the final round of the naming contest
ongoing. Voting will be open until Monday, November 16. If you haven’t
already, please vote here and decide on a name for the new project where
all of these Objects we described above will be available. The proposals we
are voting on are, in reverse alphabetical order: *Wikimedia Functions*,
*Wikilambda*, *Wikifusion*, *Wikifunctions*, *Wikicodex*, and *Wikicode*.
Let us know your preferences and decide on the name of the new project by