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Example text

Summing at rank 2, the result is the sums of each of the two pairs of threelists. 2 2 3 6 8 10 12 14 16 Armed with the rank conjunction the potential of J for expressing data manipulations is truly formidable. Here the present investigation of J must cease. As hinted in the introduction there is much, much more left for you to discover. If you have found what you have met so far has stimulated you, then you will now proceed at a very fast rate under your own direction. 42 Index Absolute value, 8 Adverb, 9, 21, 35 Agenda, 23 Alphabet, 11 Alternating sum, 9 Anti-base, 29 Append, 7, 27, 29, 41 Append items, 24, 31 Arguments, 6 Arithmetic functions, 2 ASCII characters, 11 Assignment, 3 At, 17, 41 Atop, 17, 40 Base, 29 Best fitting polynomials, 25 Bond, 19 Box, 26, 40 Cap, 21, 39, 41 Capped fork, 39 Cards, 15 Case statement, 23 Ceiling, 7, 23 Character list, 5, 12 Combinations, 15 Comments, 4 Complex numbers, 4 Concurrency, 17 Conjunctions, 17, 35 Control words, 34 Copy, 6, 9 Deal, 13 Decrement, 13 Dice, 13 Domain errors, 14, 26, 31 Dot conjunction, 31 Drawing, 36 Drop, 12, 19 Dyadic, 6 Empty list, 10 Epicycloids, 37 Explicit Programming, 20 Factorial, 15 Fibonacci numbers, 33 Fill items, 12 Floor, 7, 23 Foreign conjunction, 3, 20, 34 Fork, 16, 19 Format, 31 From, 5, 13, 23 Gerund, 23 Grade down, 21 Grade up, 21, 28 Graphs, 36 Grid, 11,18 Halve, 23 Hook, 16, 19 Hypocycloids, 37 Identity values, 10 Increment, 13 Index generator,10, 11, 29, 41 Index of, 12 Inner product, 31 Insert, 9, 40 Keyboard input, 34 Laminate, 15, 24, 27 Least squares, 24 Left, 20, 34 Link, 27 Lists, 4 Logarithms, 4 Logical verbs, 10 Matrix, 6, 24, 39 Matrix inversion, 24 Maximum, 7 Mean, 16 Median, 23, 35 Membership, 9 Minimum, 7 Monadic, 6 Multiple choice, 14 Negate, 7 Not equal, 23 Noun, 11, 33 Nub, 22 Open, 27 Or, 23 Out of, 15 Overtaking, 12 Pascal’s Triangle, 15 Permutations, 21, 28 Pi, 36 Polynomials, 25, 37 43 Power, 2, 33 Primitives, 16 Print precision, 3 Quadratics, 25 Range, 16 Rank, 39 Ravel, 15 Reciprocal, 7 Recursion, 33 Reflex, 21 Regression lines, 25 Relational verbs, 9 Remove blanks, 22 Reshape, 6 Residue, 8 Reverse, 22, 41 Right, 20, 31 Roll, 13 Rounding, 19 Scalars, 3 Scripts, 35 Sequential programming, 17 Session Manager, 35 Shape of, 6, 39 Shift, 22 Signum, 7 Sorting, 21, 41 Simultaneous equations, 24 Square Root, 4 Square, 18 System facilities, 3, 20,34 Tables, 11,15 Tacit programming, 16 Tail, 12 Take, 12 Tally, 5, 39 Tie, 23 Time, 35 Tossing coins, 13 Transpose, 30 Trigonometry, 36 Underbar, 3 Vectors, 4 Verbs, 2 Workspace, 3 Wrap around, 6 Vocabulary The table below gives the J symbols which are used in this booklet.

While J contains many sophisticated features which make it possible to express a great deal in a single phrase, it can be comforting to know that a more conventional style of conditional and looping programming is also available. We look at three ways in which a user-defined verb for Fibonacci numbers can be constructed. Fibonacci numbers are sequences which are started with two arbitrary numbers (most commonly 0 and 1), and thereafter each succeeding number is the sum of the previous two. Clearly such a series could go on indefinitely, and so for practical purposes one of the parameters of a Fibonacci verb must provide a stopping condition, for example, either a total number of numbers is given, or the series may stop after a given value has been exceeded.

Its role as a statement separator is a happy consequence of this definition. 4 :0, in which case Fib would be a strictly dyadic verb. 3 : 0 10 Fib y. y. 0 … ….. etc. The first line states that it is a dyadic verb (that is an object of class 3) which is to be defined. The 0 means that the subsequent input lines are to made from the keyboard. The colon on the second line separates the monadic and dyadic definitions, and in the present case establishes a default left argument of 10. More System Facilities You have already seen how the foreign conjunction is used to get and set print precision.

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