9. Vocabulary

Memorizing lists of words is a tedious and ineffectual way to
learn a language, and better techniques should be employed:

A)   Conversation with a native speaker who allows you to do
most of the talking.

B)   Reading material of interest in its own right.

C)   Learning how to use dictionaries and grammars so as
to become independent of teachers.

D)   Attempting to write on any topic of interest in itself.

E)   Paying attention to the structure of words
so that known words will provide clues to the unknown.
For example, program (already analyzed) is related
to tele (far off) gram, which is in turn related
to telephone. Even tiny words may possess
informative structure: atom means not cuttable,
from a (not) and tom (as in tome and


In the case of J:

A)   The computer provides for precise and general conversation.

B)   Texts such as
Fractals, Visualization and J [7],
Exploring Math [8], and
Concrete Math Companion [14]
use the language in a variety of topics.

C)   The appended dictionary of J provides a complete
and concise dictionary and grammar.

D)   J Phrases [9] provides guidance
in writing programs, and almost any topic provides problems of
a wide range of difficulty.

E)   Words possess considerable structure, as in +:
and -: and *: and %: for double,
halve, square, and square root.
Moreover, a beginner can assign and use mnemonic names appropriate
to any native language, as in sqrt=:%: and entier=:<.
(French name) and sin=:1&o. and SIN=:1&o.@(%&180@o.)
(for sine in degrees).


We will hereafter introduce and use new primitives with
little or no discussion, assuming that the reader will
experiment with them on the computer, consult the dictionary
to determine their meanings, or perhaps infer their meanings
from their structure. For example, the appearance of the
word o. suggests a circle; it was used dyadically
above to define the sine (one of the circular functions),
and monadically for the function pi times, that is,
the circumference of a circle when applied to its diameter.

For precise oral communication it may be best to use the names
(or abbreviations) of the symbols themselves, as in:

<  Left a (ngle) /  Slash &  Amp (ersand) %  Per (cent)
[  Left b (racket)  Back (slash) @  At ;  Semi (colon)
{  Left c (urly bracket) |  Stile ^  Caret ~  Tilde
(  Left p (arenthesis) _  (Under) Bar `  Grave *  Star


9.1   Experiment with a revised version of the program MAP
of Exercise 7.1, using the remainder or residue
dyad (|) instead of the minimum (<.),
as in M=:map@(6&|) and compare its results with those
of MAP.

9.2   Experiment with the programs sin and SIN
defined in this section.

9.3   Write programs using various new primitives found in the
vocabulary at the end of the book.

9.4   Update the table of notation prepared in Exercise 2.2.