Array notation

Array notation is a way to write most arrays literally, with no or minimal use of primitive functions, possibly over multiple code lines. It differs from the strand notation existing since APL\360 in that it can be used to write arrays of rank greater than one. Array notation is supported in dzaima/APL and BQN, and by some tools for Dyalog APL, where it is planned as an eventual language feature.

Array notation generally consists of a vector notation written with parentheses (), roughly equivalent to stranding, and a high-rank notation using square brackets [], indicating the Mix of a vector. It may also support namespaces, with dzaima/APL and Dyalog using name:value syntax in parentheses for this. In each case, elements are separated by statement separators such as ⋄ or line breaks.

Examples

Medium-sized array constants are often needed in code. Due to the lack of a native multi-line notation, programmers have resorted to various ad-hoc methods of approximating such, usually at the cost of reduced readability. A very common technique is repeated concatenation:

poss←1 2⍴'fns'  ((0 1)(0.7 0)(0.7 0)×size)
poss⍪←   'fnd'  ((0 1)(0   0)(0   0)×size)
poss⍪←   'lines'((0 0)(0.7 0)(0.7 0)×size)
poss⍪←   'lnd'  ((0 0)(0   0)(0   0)×size)

Array notation allows this multi-line construction to be made with a single assignment, and also provides an alternate syntax for the inner vectors of vectors:

poss←['fns'  ((0 1 ⋄ 0.7 0 ⋄ 0.7 0)×size)
      'fnd'  ((0 1 ⋄ 0   0 ⋄ 0   0)×size)
      'lines'((0 0 ⋄ 0.7 0 ⋄ 0.7 0)×size)
      'lnd'  ((0 0 ⋄ 0   0 ⋄ 0   0)×size)]

Description

The notation is added to the language by giving meaning to previously invalid statements. The added syntax consists of three constructs that are currently SYNTAX ERRORs:

• broken round parentheses
• broken square brackets
• empty round parentheses: ()

where broken means interrupted by one or more diamonds (⋄) or line breaks (outside of dfns).

• A broken round parenthesis creates a namespace if every diamond/line break-separated statement is a name-value pair.
• A broken round parenthesis creates a vector if every diamond/line break-separated statement is a value expression. In that case, every such statement forms an element in the resulting vector.
• A broken square bracket creates a an array where every diamond/line break-separated statement forms a major cell in the resulting array.
• () is equivalent to (⎕NS 0⍴⊂'')
• A name-value pair consist of a valid APL identifier, followed by a : and a value expression.

History

See also Array notation in Dyalog APL

One-dimensional list syntax with surrounding brackets and delimiters, matching sequence notation in mathematics, is common in programming. It appears as early as ALGOL 68 with parentheses, and square-bracket lists or arrays feature in languages from the 1970s such as ML and Icon. MATLAB uses matrix syntax with square brackets, semicolons to separate rows, and commas to separate columns.

List notation appears in Nial, with brackets and commas like [a,b,c], and in A+ and K, with parentheses and semicolons like (a;b;c). In A+ this is related to bracket indexing and an "expression group" notation written with curly braces and semicolons. It allows line breaks, but in addition to rather than in place of semicolons. The later K version corresponds more closely to APL: the semicolon is a statement separator and is interchangeable with a line break, and because K represents arrays with nested lists, it corresponds to both vector and high-rank array notation. In all three languages this syntax can be used with functions, as functions are first-class in A+ and K, and arrays of functions called "atlases" can be used for specific purposes in Nial.