Mixed Functions

Mixed rank functions and special symbols are summarised in Table 1. For convenience, they are sub-divided into five classes:

Table 1: Mixed rank functions and special symbols
Structural These functions change the structure of the arguments in some way.
Selection These functions select elements from an argument.
Selector These functions identify specific elements by a Boolean map or by an ordered set of indices.
Miscellaneous These functions transform arguments in some way, or provide information about the arguments.
Special These symbols have special properties.

In general, the structure of the result of a mixed primitive function is different from that of its arguments.

Scalar extension may apply to some, but not all, dyadic mixed functions.

Mixed primitive functions are not pervasive. The function is applied to elements of the arguments, not necessarily independently.

Examples

      'CAT' 'DOG' 'MOUSE'⍳⊂'DOG'
2 
      3↑ 1 'TWO' 3 'FOUR'
1  TWO  3

In the following tables, note that:

  • [] Implies axis specification is optional
  • $ This function is in another class
Table 2: Structural Primitive Functions
Symbol Monadic Dyadic
⍴ $ Reshape
, Ravel [] Catenate/Laminate []
⍪ Table Catenate First / Laminate []
⌽ Reverse [] Rotate []
⊖ Reverse First [] Rotate First []
⍉ Transpose Transpose
↑ Mix / Disclose [] $
↓ Split [] $
⊂ Enclose [] Partitioned Enclose []
⊆ Nest Partition []
∊ Enlist (See Type ) $
Table 3: Selection Primitive Functions
Symbol Monadic Dyadic
⊃ Disclose / Mix Pick
↑ $ Take []
↓ $ Drop []
/   Replicate []
⌿   Replicate First []
\   Expand []
⍀   Expand First []
~ $ Without (Excluding)
∩   Intersection
∪ Unique Union
⊣ Same Left
⊢ Same Right
⌷ Materialise Index
≠ Unique Mask  
Table 4: Selector Primitive Functions
Symbol Monadic Dyadic
⍳ Index Generator Index Of
⍸ Where Interval Index
∊ $ Membership
⍋ Grade Up Grade Up
⍒ Grade Down Grade Down
? $ Deal
⍷   Find
Table 5: Miscellaneous Primitive Functions
Symbol Monadic Dyadic
⍴ Shape $
≡ Depth Match
≢ Tally Not Match
⍎ Execute Execute
⍕ Format Format
⊥   Decode (Base)
⊤   Encode (Representation)
⌹ Matrix Inverse Matrix Divide
Table 6: Special Syntax
Symbol Monadic Dyadic
→ Abort  
→ Branch  
←   Assignment
[I]←   Assignment(Indexed)
(I)←   Assignment(Selective)
[]   Indexing