Function
Functions are abstract mathematical representation of relations between the domain and codomain. It can be represented as a key-value pairs, or in the lambda calculus[1] form.
Tag Line
Data with continuation together makes function.
Function can be used as a generic building block to represent information in general. It can be thought of as a primitive kind of data structure. This argument can be substantiated by thinking of Lambda calculus as a generalized way of encoding functions in an explicit structured data format.
A Critical Observation
In most cases, people think of MediaWiki as a generic note taking or a dictionary of relevant pieces of static information. However, knowing the capabilities of modern browsers, HTML 5, JavaScript, and the server side PHP + Lua (Scribuntu) extension of MediaWiki, not to mention Semantic MediaWiki and its MySQL/MariaDB data storage/retrieval capabilities, the overall functions of MediaWiki must not be just seen as a passive data browsing tool, but a full blown programming and data creating environment. In programmer's term, MediaWiki can be configured to be a full blown Integrated Development Environment, for any subject matter. This is what PKC strives to become, it tries to raise users' awareness of data elements as functions, so that all data are also functions in a hyperlinked context. In other words, hyplerink is a kind of data-oriented function, that allows users to incrementally construct small and large functions at many locations and across many time scales. On the Internet, everyone is constructing some piece of a bigger function that they may never be directly conscientiously aware, but never-the-less, all users, all computers are incrementally constructing functions of many kinds through accumulating data elements, all in the hyperlinked fashion as articulated by Ted Nelson.
Scale-Free, Time-like Structures, and Ordered Namespace of Functions
Function as a data structure is not only universal, but it can also be designed to be Scale-free, meanningly that the formal properties of a specific Function, don't have to be bounded to a specific spacetime physical scale. However, in the space of all functions, the containment relationship in terms of what functions are classified into what sub-class(es) of functions can be studied in terms of Category Theory, and more specifically, in the field of Lattice Theory or just think of them in terms of Partially ordered sets. Thinking of named functions in terms of lattice or Partially ordered set, a.k.a. Posets, is an important mental model for both software engineering, and in everyday life. Thinking of functions as elements in Posets will give them a consistent abstraction in an ordered or time-like structure, so that it will build a generically applicable mental model for causal relations and in terms of an ordered namespace.
Function as Causal Relation
Function can be represented as a key-value pair of inputs and outputs, which defines a way to represent causal relations.
Design Principle
PKC models data assets in terms of functions, which is a kind of scale-free data representation. These functional data representation are in turn categorized into Page, File, and Service. Each category of function is treated as the primitive form of data, and can be recursively referenced to perform both computation and carry computational results. All pages in PKC are conceptualized as hyperlinked data points in a functional style. All data points or pages have their unique names. These names can be thought of as function names, and each function may have many key-value-pairs as its arguments.
Data Architecture
In PKC, data is consistently represented using one universal construct, directed relation. This also means that we can always use the same data type, directed relation to interpret and manipulate data.
Architecture = Invariant Properties
It is important to note that the word Architecture implies elements of a system that doesn't change. Therefore, this section will talk about the data elements of PKC that don't change over space and time.
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References
- ↑ Abelson, Harold; Sussman, Gerald; Sussman, Julie (1985). Structure and Interpretation of Computer Programs (2nd ed.). local page: MIT Press. ISBN 0-262-51087-1.
Related Pages
Represent Knowledge in Functions
Thinking about functions at all times in this primitive, yet generic construct, allows users to think of all functions as hyperlinks that relate objects from one to the other, revealing the topological structures, or the systematic structures of anything. Most importantly, users of PKC can think of writing down notes in various pages are effectively construction functions or conducting computational work in parallel and in an explicit functionally designed data storage. The storage packages are managed in terms of files. The availability and reliability of providing these pages and files are called services. This completes the three categories of scale-free data representation. The design principle that differentiate PKC from other hyperlink/hypermedia systems is that PKC considers data content within the system as an integral part of the system. Since every instance of PKC is tightly bound with its own content, all PKC must allow maximum freedom to all instances of PKCs. To accomplish this design principle, it needs to give full ownership and power to conduct changes to the owners of individual instances. In the most egalitarian scenario, we must reduce the barrier to entry, so PKCs should be convenient and cheap to be replicated or allowing for the creation of new instances that are independent from other instances of PKC, so that the functionality of PKCs can be easily shared across many application domains.
Implementation
Computationally, functions can almost always be thought of as a dictionary, or a lookup table/hashtable that relates a value of an input, to a value as the output of a function. This simplification is useful in the sense that all functions can be conceptualized as dictionaries/lookup tables, so that all functions can be treated as one type, which is a way to ensure structural purity, mathematically called a Monad. According the Beckman's talk on Don't fear the Monad[1], this monadic approach will help construct complexity out of simplicity.
PKC is based on MediaWiki, which in term installs Scribunto to enable Lua programming. Lua defines functions as below:
f = function (op, a, b)
if op == 'add' then
return a + b
else if op == 'sub' then
return a - b
end
error("invalid operation")
end
Function represented in a Logic Model
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References
- ↑ Beckman, Brian (Nov 21, 2012). Brian Beckman: Don't fear the Monad. local page: jasonofthel33t.