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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 microtome).
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.

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