I'd like to introduce a blog post by Stephen Wolfram, on the design

process of Mathematica. In particular, he touches on the importance of

naming of functions.

• Ten Thousand Hours of Design Reviews (2008 Jan 10) by Stephen

Wolfram

http://blog.wolfram.com/2008/01/10/t...esign-reviews/
The issue is fitting here today, in our discussion of “closure”

terminology recently, as well the jargons “lisp 1 vs lisp2” (multi-

meaning space vs single-meaning space), “tail recursion”, “currying”,

“lambda”, that perennially crop up here and elsewhere in computer

language forums in wild misunderstanding and brouhaha.

The functions in Mathematica, are usually very well-name, in contrast

to most other computing languages. In particular, the naming in

Mathematica, as Stephen Wolfram implied in his blog above, takes the

perspective of naming by capturing the essense, or mathematical

essence, of the keyword in question. (as opposed to, naming it

according to convention, which often came from historical happenings)

When a thing is well-named from the perspective of what it actually

“mathematically” is, as opposed to historical developments, it avoids

vast amount of potential confusion.

Let me give a few example.

• “lambda”, widely used as a keyword in functional languages, is named

just “Function” in Mathematica. The “lambda”happend to be called so

in the field of symbolic logic, is due to use of the greek letter

lambda “λ” by happenstance. The word does not convey what it means.

While, the name “Function”, stands for the mathematical concept of

“function” as is.

• Module, Block, in Mathematica is in lisp's various “let*”. The

lisp's keywords “let”, is based on the English word “let”. That word

is one of the English word with multitudes of meanings. If you look up

its definition in a dictionary, you'll see that it means many

disparate things. One of them, as in “let's go”, has the meaning of

“permit; to cause to; allow”. This meaning is rather vague from a

mathematical sense. Mathematica's choice of Module, Block, is based on

the idea that it builds a self-contained segment of code. (however,

the choice of Block as keyword here isn't perfect, since the word also

has meanings like “obstruct; jam”)

• Functions that takes elements out of list are variously named First,

Rest, Last, Extract, Part, Take, Select, Cases, DeleteCases... as

opposed to “car”, “cdr”, “filter”, “filter”, “pop”, “shift”,

“unshift”, in lisps and perl and other langs.

The above are some examples. The thing to note is that, Mathematica's

choices are often such that the word stands for the meaning themselves

in some logical and independent way as much as possible, without

having dependent on a particular computer science field's context or

history. One easy way to confirm this, is taking a keyword and ask a

wide audience, who doesn't know about the language or even unfamiliar

of computer programing, to guess what it means. The wide audience can

be made up of mathematicians, scientists, engineers, programers,

laymen. This general audience, are more likely to guess correctly what

Mathematica's keyword is meant in the language, than the the name used

in other computer languages who's naming choices goes by convention or

context.

(for example, Perl's naming heavily relies on unix culture (grep,

pipe, hash...), while functional lang's namings are typically heavily

based on the field of mathematical logic (e.g. lambda, currying,

closure, monad, ...). Lisp's cons, car, cdr, are based on computer

hardware (this particular naming, caused a major damage to the lisp

language to this day). (Other examples: pop, shift are based on

computer science jargon of “stack”. Grep is from Global Regular

Expression Print, while Regular Expression is from theoretical

computer science of Automata... The name regex has done major hidden

damage to the computing industry, in the sense that if it have just

called it “string patterns”, then a lot explanations, literatures,

confusions, would have been avoided.))

(Note: Keywords or functions in Mathematica are not necessarily always

best named. Nor are there always one absolute choice as best, as there

are many other considerations, such as the force of wide existing

convention, the context where the function are used, brevity,

limitations of English language, different scientific context (e.g.

math, physics, engineering), or even human preferences.)

----------------------------

Many of the issues regarding the importance and effects of

terminology's quality, i've wrote about since about 2000. Here are the

relevant essays:

• Jargons of Info Tech Industry

http://xahlee.org/UnixResource_dir/writ/jargons.html
• The Jargon “Lisp1” vs “Lisp2”

http://xahlee.org/emacs/lisp1_vs_lisp2.html
• The Term Curring In Computer Science

http://xahlee.org/UnixResource_dir/writ/currying.html
• What Is Closure In A Programing Language

http://xahlee.org/UnixResource_dir/writ/closure.html
• What are OOP's Jargons and Complexities

http://xahlee.org/Periodic_dosage_dir/t2/oop.html
• Sun Microsystem's abuse of term “API” and “Interface”

http://xahlee.org/java-a-day/interface.html
• Math Terminology and Naming of Things

http://xahlee.org/cmaci/notation/math_namings.html
Xah

http://www.velocityreviews.com/forums/(E-Mail Removed)
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http://xahlee.org/
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