Aspects of J to be aware of
Context
- A J session operates in a "workspace" of definitions and values
- A session may use one or more windows for entry and output display
- A session window record may be saved for future reference
- Data values may be saved between sessions only by explicit action
- Program-operation definitions are copied to and from script files
- Script files may be prepared with the J editor or any other
- Except in definition mode, each line is interpreted after entry
- Formatted results may be captured from screen or written externally
Syntax
- Each statement must be contained on a single line
- On any line, text following symbol NB. is commentary
- Empty lines are acceptable
- Brackets, braces, commas, and semicolons do not delimit groups
- Period and semicolon also appear in names of many J symbols
- Numbers must show a digit before any decimal point
- Negative numbers are preceded by a "low minus" (underscore)
- Names, symbols, and values may be separated by 0 or more blanks
- Numbers must be separated from any following unrelated letter
- Numbers may be decimal, rational, exponential, extended precision
- Complex numbers may be specified, either Cartesian or polar
- Stored character values may contain any character in set (a.)
- Character literal in expression may not contain newline or return
- Lists of numbers are separated/joined by blanks, not commas
- A number list following a (rank) number needs a separator
- Operations apply to number lists without need for parentheses
- Mere succession of computed values does not specify a list
- All operations expect one data value argument on the right
- Many operations also accept or require a data argument on the left
- A named program is activated via the same syntax as for symbols
- Arguments may be atomic or arbitrarily structured as needed
- A verb must be supplied some argument value to be executed
- A symbol with only a right argument will be interpreted monadically
- Presence also of a left argument will cause dyadic interpretation
- There are no execution precedences among fundamental operations
- Parentheses enclose expressions to be evaluated before others
- In a multi-operation expression, the right-most evaluates first
- Evaluation results are substituted in the remaining phrase
- Modifying adverbs and conjunctions do have "precedence" over verbs
- Conjunctions and/or parentheses can form new compound operations
- Conjunctions are required for most non-standard noun-verb sequences
- Multiple-verb sequences are evaluated by hook and/or fork rules
- A user-defined value or operation name must start with a letter
- A name may contain mixed-case letters, digits, embedded underscore
- A name ending with a tag between underscores belongs to that locale
- An ending tag following a double underscore is a variable locale
- No legal user-definable names are reserved for system use
- Defining a name used in another loaded script may cause confusion
Data structure
- Every data value in J is an array
- Every array has a rank of 0 (atom), 1 (list), 2 (table), or more
- A positive-rank array is stored as a list of lower-rank "items"
- Every array has a rectangular shape--the sizes of successive axes
- Each array is of one type--numeric, character, boxed, or symbol
- Every array has a level (or box depth) of 0 or more
- Arrays of rank 2 or higher cannot be entered literally
- Lists may be constructed with Append, Link, etc.
- Tables may be constructed with Stitch, Laminate, Table, etc.
- Sub-arrays may be rotated at any rank level
- Array axes may transposed into any order
- Arrays of level 1 or higher cannot be entered literally
- The Box of an array creates an atom of level one greater
- The Open of an array may be of one level less, but never negative
- The Open of an array will be of the greatest rank found
- The Open of a box array will fail when it finds mixed data types
- A box value is always distinct from and unequal to its Opened form
- "Symbol" values are character strings beginning with `
- Symbol values may be created, structured, stored, selected, matched
- Specified elements or sub-arrays may be copied from an array
- Consecutive head or tail elements may be selected along any axis
- Consecutive head or tail elements may be omitted from a copy
- Elements may be selected along an axis by index, possibly multiple
- Indices for an n-element axis always run 0 through n-1 (0 origin)
- Indices _1 through -n run backward from the end of the axis
- Elements may be selected from box at any level by specifying path
- An array may be copied with specified substitutions (Amend)
- An expression evaluating to data value may be stored as a named noun
- A named array may be modified only by total replacement (Is)
- Any axes of an array may have length 0--an empty array
- Reducing axis length by Drop, even to 1 or 0, does not reduce rank
- Selecting with n atoms of index yields subarray of rank n lower
- Array with a single item (singleton) is not an atom if positive-rank
- A singleton may be accepted as an atom or may give unwanted result
- Leading axes of length 1 are not apparent on printing
- The shape of a character array with many blanks may not be apparent
- Distinguishing between character and numeric is difficult in boxes
- The rank and shape of an empty value may not be apparent
- A leading axis of length 0 displays no printed lines
Operation application
- Operations use programmed, stored, and/or computed result values
Only the Is (Gets)--local or global--copies a value to storage
- No basic operation specifies output
- A final computed value, not ending as stored, will be printed
- "Foreign" verb connects to system devices and values, other programs
- Each verb has default ranks of application: monadic, left, right
- A Rank adverb may be applied to any value to direct its use
- A Rank adverb may be applied to any verb to change from its defaults
- A rank-n array is a frame of rank n-2 holding rank-2 arrays
- An operation on rank-2 subarrays composes results in the same frame
- With two arguments, one frame must match a prefix of the other
- Values in the smaller frame will repeat to fill the larger
- Smaller partial results will be filled to shape of largest
- Performing operation within box values obviates fill at that level
- Arithmetic operations use rank 0, applying to individual atoms
- Specifying another rank applies elements of one over subarrays
- Count and Shape Of use infinite rank (_), measuring a whole array
- Rotate uses ranks 0 1; multiple left values give multiple rotations
- A rank 1 (or _1) operation on a table treats whole rows together
- A whole-row operation may, in turn, process individual atoms
- +/table yields sums of rows: row+row+...+row (sums "down columns")
- +/"1 table yields sums "along" rows: (atom+...+atom),...,(atom+...)
- Some verbs apply rank-1 structural arguments to successive axes
Program structure
- The Right verb (]) can isolate an expression yet deliver its value
- The Left verb ([) can hide the result of a trailing expression
- Either Identity (] or [) can follow storage to prompt printing
- A verb-valued expression may contain monadic and dyadic definitions
- Longer programs may be introduced by the Explicit verb (:)
- The right argument may be a quoted expression, or 0 for keyed input
- Successive lines become statements in the stored program
- Control phrases (if., for., while., etc.) may punctuate the program
- An if-test value is True unless it has a leading atom of unboxed 0
- A separate single closing parenthesis terminates the definition
- Arguments to a defined verb initialize local variables x, y
- Values assigned locally (=.) are not visible anywhere else
- A break. can terminate iteration before the stated end condition
- A return. can terminate verb execution before its physical end
- The last non-control expression evaluated becomes the verb's result
Tacit definition--not using local variables
- Non-data expressions may define verbs, adverbs, conjunctions
- A defined verb may combine its arguments via other verbs, modifiers
- The first-acting verb applies to the argument(s)
- Later verbs may apply to the result, if indicated by Atop or At
- The full right argument of Atop/At usually needs parenthesization
- Aside from a nest of Atops, the most common form is a chain of forks
- Last and third-last verbs act on argument(s), middle on their results
- A verb may be Right or Left to select either argument
- A verb may introduce an additional value, via Bond
- A value Bonded to Left yields itself--when left argument is absent
- A value Bonded to Left Atop Right always yields itself
- Fork arguments are not delivered to phrases Atop fork main verbs
- x f@g y is equivalent to f (x g y) or x f@([ g ]) y
- Some nests of Atops can be strung out as successive forks
- A verb in a fork may itself be a fork, usually parenthesized
- The left verb of a fork may be Cap to force the middle one monadic
- Omitting Cap leaves a hook, which delivers arguments differently
Contributed by ArtAnger