Classic Edition: the symbol ⌸ is not available in Classic Edition, and the Key operator is instead represented by ⎕U2338.

f may be any dyadic function that returns a result.

If X is specified, it is an array whose major cells specify keys for corresponding major cells of Y. The Key operator ⌸ applies the function f to each unique key in X and the major cells of Y having that key.

If X is omitted, Y is an array whose major cells represent keys. In this case, the Key operator applies the function f to each unique key in Y and the elements of ⍳≢Y having that key. f⌸Y is the same as Y f⌸⍳≢Y.

The elements of R appear in the order in which they first appear in Y.

Key is similar to the GROUP BY clause in SQL.

⎕CT and ⎕DCT are implicit arguments of the Key operator.

#### Example

In this example, both arrays are vectors so their major cells are their elements. The function {⍺':'⍵} is applied between the unique elements in suits ('Spades' 'Hearts' 'Clubs') and the elements in cards grouped according to their corresponding elements in suits, that is, ('2' 'Ace'), ('Queen' 'Jack') and (,'4').

cards←'2' 'Queen' 'Ace' '4' 'Jack' suits←'Spades' 'Hearts' 'Spades' 'Clubs' 'Hearts' suits,[1.5]cards Spades 2 Hearts Queen Spades Ace Clubs 4 Hearts Jack suits {⍺':'⍵}⌸ cards Spades : 2 Ace Hearts : Queen Jack Clubs : 4

#### Monadic Examples

{⍺ ⍵} ⌸ suits ⍝ indices of unique major cells Spades 1 3 Hearts 2 5 Clubs 4 {⍺,≢⍵} ⌸ suits ⍝ count of unique major cells Spades 2 Hearts 2 Clubs 1

letters←'zabayza' {⍺(≢⍵)}⌸letters z 2 a 3 b 1 y 1

#### Further Examples

x is a vector of stock codes, y is a corresponding matrix of values.

⍴x 10 ⍴y 10 2 x,y IBM 13 75 AAPL 45 53 GOOG 21 4 GOOG 67 67 AAPL 93 38 MSFT 51 83 IBM 3 5 AAPL 52 67 AAPL 0 38 IBM 6 41

If we apply the function {⍺ ⍵} to x and y using the ⌸ operator, we can see how the rows (its major cells) of y are grouped according to the corresponding elements (its major cells) of x.

x{⍺ ⍵}⌸y IBM 13 75 3 5 6 41 AAPL 45 53 93 38 52 67 0 38 GOOG 21 4 67 67 MSFT 51 83

More usefully, we can apply the function {⍺(+⌿⍵)}, which delivers the stock codes and the corresponding totals in y:

x{⍺(+⌿⍵)}⌸y IBM 22 121 AAPL 190 196 GOOG 88 71 MSFT 51 83

There is no need for the function to use its left argument. So to obtain just the totals in y grouped by the stock codes in x:

x{+⌿⍵}⌸y 22 121 190 196 88 71 51 83

#### Defined Function Example

This example appends the data for a stock into a component file named by the symbol.

∇ r←stock foo data;fid;file [1] file←⊃stock [2] :Trap 0 [3] fid←file ⎕FTIE 0 [4] file ⎕FERASE fid [5] :EndTrap [6] fid←file ⎕FCREATE 0 [7] r←data ⎕FAPPEND fid [8] ⎕FUNTIE fid ∇

x foo⌸y 1 1 1 1

#### Example

{⍺ ⍵} ⌸ suits ⍝ indices of unique major cells Spades 1 3 Hearts 2 5 Clubs 4 {⍺,≢⍵} ⌸ suits ⍝ count of unique major cells Spades 2 Hearts 2 Clubs 1

#### Another Example

Given a list of names and scores., the problem is to sum the scores for each unique name. A solution is presented first without using the Key operator, and then with the Key operator.

names ⍝ 12, some repeat Pete Jay Bob Pete Pete Jay Jim Pete Pete Jim Pete Pete (∪names)∘.≡names 1 0 0 1 1 0 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 scores 66 75 71 100 22 10 67 77 55 42 1 78 b←↓(∪names)∘.≡names ]disp b/¨⊂⍳12 ┌→──────────────┬───┬─┬────┐ │1 4 5 8 9 11 12│2 6│3│7 10│ └~─────────────→┴~─→┴→┴~──→┘ +/¨b/¨⊂scores 399 85 71 109 ]disp {⊂⍵}⌸ names ┌→──────────────┬───┬─┬────┐ │1 4 5 8 9 11 12│2 6│3│7 10│ └~─────────────→┴~─→┴→┴~──→┘ names {+/⍵}⌸ scores 399 85 71 109