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Vector Notation

Vector notation complements array notation with a clean syntax for vectors.

A series of two or more adjacent expressions results in a vector whose elements are the enclosed arrays resulting from each expression. This is known as vector (or strand) notation. Each expression in the series may consist of one of the following:

  1. a single numeric value
  2. the empty numeric vector symbol ⍬
  3. zero or more characters, within a pair of quotes
  4. array notation
  5. the name of a variable or system variable
  6. a special namespace or dfn name like ##, ⍵, and so on
  7. the evaluated input symbol ⎕
  8. the character input symbol ⍞
  9. the name of a niladic, defined function or system function yielding a result
  10. any other APL expression which yields a result, within parentheses

Examples

      ⍴A←2 4 10
3
      ⍴TEXT←'ONE' 'TWO'
2

Numbers and characters may be mixed: 

      ⍴X←'THE ANSWER IS ' 10
2
      X[1]
 THE ANSWER IS
      X[2] + 32
42

Blanks, quotes or parentheses must separate adjacent items in vector notation. Redundant blanks and parentheses are permitted. In this manual, the symbol pair '←→' indicates the phrase 'is equivalent to'. 

      1  2  ←→ (1)(2) ←→ 1  (2)  ←→ (1)  2
      2'X'3 ←→ 2 'X' 3 ←→ (2) ('X') (3)
      1  (2+2) ←→ (1) ((2+2)) ←→ ((1))  (2+2)

Vector notation may be used to define an item in vector notation: 

       ⍴X ← 1 (2 3 4) ('THIS' 'AND' 'THAT')
3
      X[2]
 2 3 4
      X[3]
  THIS  AND  THAT

Expressions within parentheses are evaluated to produce an item in the vector: 

      Y ← (2+2) 'IS' 4
      Y
4  IS  4

The following identity holds: 

      A  B  C  ←→ (⊂A), (⊂B), ⊂C