Prototype

∊ ⊤

Prototype (∊, ⊤) is a monadic function which in the nested array model gives information about the type and structure of its argument array's elements. The result is derived from the first element of the array in ravel order, or, if the array is empty, from information stored alongside the array (usually this information is just the prototype itself). An array's prototype is used as a fill element for operations involving that array, and to determine some identity elements.

Support

Few dialects have Prototype as a primitive function. Dyalog APL uses ∊ (as in prototypical element), but only when migration level is 0, while NARS2000 uses monadic ⊤ (resembling the Latin letter T for Type).

However, an arrays prototype can always be determined by enclosing the array in an empty array, and then coercing our a fill value. Since prototypes are used as fill elements, the resulting array will be the prototype of the original array:

      ⊃ 0 ⍴ ⊂ 1 2 'ab'
┌─┬─┬──┐
│0│0│  │
└─┴─┴──┘

APLs with a flat array model do not typically store prototype information, instead using only the array's type (character, numeric, or boxed) to determine its fills.

Examples

The prototype is used when an array is expanded or when empty elements are inserted in some other way. Take and Expand on a character array produce an array with spaces, because ' ' is the prototype of a character array:

      ¯12 ↑ 'whitespace'
  whitespace
      (5 1 5/1 ¯2 1) \ 'whitespace'
white  space

The Rank operator combines its left operand's result cells by extending them to a common shape like Mix does. Numeric vectors of different lengths will be expanded with 0, the prototype for a simple numeric array.

      (⍳⍤0) 2 3 4
1 2 0 0
1 2 3 0
1 2 3 4

Works in: Dyalog APL

An array's prototype is based on its first element, so the array a below has a simple numeric prototype, as does any prefix of a. This property even applies to empty arrays: the expression 0 ↑ a results in an empty array with the same prototype as a.

      ⊢a ← 5 'c' ¯2
5 c ¯2
      4 ↑ a
5 c ¯2 0
      4 ↑ 2 ↑ a
5 c 0 0
      4 ↑ 0 ↑ a
0 0 0 0

Works in: Dyalog APL

The prototype of an array may be nested. Here, we inspect the prototype of an array containing both character and numeric data. In the prototype, all characters are converted to spaces and all numbers to zeros. Thus the prototype retains type and structure information but not specific values.

      ⊢x ← ⊂'de'(3 4 5)   ⍝ A complicated scalar array
┌──────────┐
│┌──┬─────┐│
││de│3 4 5││
│└──┴─────┘│
└──────────┘
      0 1 \ x             ⍝ Its fill element is nested
┌──────────┬──────────┐
│┌──┬─────┐│┌──┬─────┐│
││  │0 0 0│││de│3 4 5││
│└──┴─────┘│└──┴─────┘│
└──────────┴──────────┘
      e ← 0 ↑ x           ⍝ An empty array based on x
      ⊃e                  ⍝ Disclosing gets the prototype
┌──┬─────┐
│  │0 0 0│
└──┴─────┘

Works in: Dyalog APL