@). By “immutable” in this context we mean non-destructive – it creates a new array, rather than mutating in place. Immutability is a good thing.
+Let’s look at the powerful immutable array update operator, At (@). By “immutable”, in this context, we mean non-destructive – it creates a new array, rather than mutating in place. Immutability is a good thing.
The dyadic @ operator has a lot of moving parts, and we won’t cover all possible combinations here.
References for @:
Was OFF
-@ can take both functions and arrays as either operand. In its simplest form, the left operand specifies values, and the right operand indexes:
+@ can take both functions and arrays as either operand. In its simplest form, the left operand specifies values, and the right operand indices:
0@1 2 3⊢1 1 1 1 1 1 1
@@ -481,7 +481,7 @@ The At operator:
]dinput
-_At_←{ ⍝ Partial @ - left and right operands must be functions, and the right arg a vector
+_At_ ← { ⍝ Partial @ - left and right operands must be functions, and the right arg a vector
mutator ← ⍺⍺ ⍝ Left operand -- function only
selector ← ⍵⍵ ⍝ Right operand -- function only
data ← ⍵ ⍝ Derived function right argument -- vector only. Note: copy
@@ -509,7 +509,7 @@ The At operator:
]dinput
-_At_←{ ⍝ Partial @ - left and right operands must be functions, and the right arg a vector
+_At_ ← { ⍝ Partial @ - left and right operands must be functions, and the right arg a vector
data ← ⍵
(mask/data) ← ⍺⍺ (mask←⍵⍵ ⍵)/⍵
data
@@ -528,16 +528,16 @@ The At operator: 5 1 7 3 9 5 11 7 13 9 15 11
-We used leading and trailing underscores when naming our operator to indicate visually that it’s a dyad, as suggested by the unofficial style guide.
+We used leading and trailing underscores when naming our operator to indicate visually that it’s a dyad, as suggested by Adám Brudzewsky’s unofficial style guide.
Higher rank: choose and reach¶
The real @ has many more tricks up its sleeve, of course. It can also be applied to arrays of any rank, not just vectors.
-If we look at Dyalog’s specification of @ we have
+If we look at Dyalog’s specification of @ we have
R←{X}(f@g)Y
-If g is a simple vector, it chooses major cells in Y. If g is nested, it specifies indices for choose or reach indexing. What does that mean, then? One way to think of it is that the g vector behaves just as if it had been inserted between square brackets.
-The first case is straight-forward: the major cells of an array is basically those given by the first axis of the shape. In the case of a 2-D matrix, its rows:
+If g is a simple vector, it chooses major cells in Y. If g is nested, it specifies indices for choose or reach indexing. What does that mean, then? One way to think of it is that the g vector behaves just as if it had been inserted between square brackets.
+The first case is straightforward: the major cells of an array are those given by the first axis of the shape. In the case of a 2D matrix, its rows:
-@0 2 ⊢ 3 3⍴1 2 3 4 5 6 7 8 9 ⍝ Negate rows 0 and 2: major cells
@@ -563,11 +563,11 @@ Higher rank: choose and reachindexing section:
+
We can also access elements that are deeply nested using reach indexing, which we met briefly in the indexing section:
-⊢G←2 3⍴('Adam' 1)('Bob' 2)('Carl' 3)('Danni' 4)('Eve' 5)('Frank' 6)
-'***' ¯999@((0 0)0)((1 2)1) ⊢ G
+⎕ ← G ← 2 3⍴('Adam' 1)('Bob' 2)('Carl' 3)('Danni' 4)('Eve' 5)('Frank' 6)
+'***' ¯999@((0 0)0)((1 2)1)⊢G
@@ -599,7 +599,7 @@ Examples