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Adverbs

Adverbs are high order constructions that modify the way a verb is applied to data.

Each monad

Applies monadic in the left argument to each element of the right structure.

o){x+1}'4 5 6
5 6 7
o)

Each dyad

Applies dyad to each pair of left and right arguments' elements or pair with one item.

o)1 2 3 +' 4 5 6
5 7 9
o)10+'1 2 3
11 12 13
o)

Each prior

Applies dyad to subsequent pairs of right argument structure.

o)+':1 2 3
1 3 5
o)

... beware of edge cases though:

o){y}':,1
,0N
o){y}':1 2
0N 1
o)

In lambdas, implicit an argument x - current item, y - prior item.

Each prior with initial value

Same as above, but the left argument defines initial value.

o)10*':1 2 2
10 2 4
o)

Each right

Applies dyad to each pair of the left argument and right argument elements.

o)10 100+/:1 2 3
11 101
12 102
13 103
o)

Each left

Applies dyad to each pair of the left argument elements and right argument.

o)10 100+\:1 2 3
11 12 13
101 102 103
o)

Over aka fold

Reduces right argument structure using left dyad. Initial value is different for some verbs.

o)+/1 2 3
6
o){0N!x,y; x+y}/10 3 2 1
10 3
13 2
15 1
16
o)

Boolean vectors behave as vectors of long for some verbs:

o)+/101b
2
o)


o)+/0#0
0
o)

However:

o)*/0#0
1
o):/0#0
0N
o)

Over with initial value

Folds right argument structure using left dyad. Initial value is given explicitly:

o)10*/1 2 2
40
o)

Over "converge"/"fixedpoint"

Repeatedly applies monadic function the left argument until result stops changing:

o){x%2}/100
0
o)

If over with a lambda is applied to a vector, and there is no implicit argument y in the lambda, then the entire vector is taken as one argument. 
    o) // !!! infinite loop !!!
    o) {0N!x; x+1}/1 2 3
    2 3 4
    3 4 5
    ...
In this line, x will change infinitely. 

o){0N!x; (1+x*3)%4}/2 5 3 1
2 5 3 1
1 4 2 1
1 3 1 1
1 2 1 1
1 1 1 1
1 1 1 1
o)

Scan

Acts pretty much the same as "over", but rеturns a structure of the same size.

o)+\1 2 3
1 3 6
o)+\011b
0 1 2
o)

Scan with initial value

"Scan" but with explicitly given initial value.

o)10*\1 2 2
10 20 40
o)

Scan "converge"/"fixedpoint"

Repeatedly applies monadic function in the left argument to the right one, until result stops changing and accumulates all intermediate results:

o){x%2}\100
100 50 25 12 6 3 1 0
o)

If scan with a lambda is applied to a vector, and there is no implicit argument y in the lambda, then the entire vector is taken as one argument. 
    o) // !!! infinite loop !!!
    o) {x+1}\1 2 3
    2 3 4
    3 4 5
    ...
In this line, x will change infinitely. 

o){(1+x*3)%4}\2 5 3 1
2 5 3 1
1 4 2 1
1 3 1 1
1 2 1 1
1 1 1 1
1 1 1 1
o)

"For" loop

Applies monadic verb to the right argument left argument times.

o)5{x+1}/10
15
o)

"While" loop

Applies monadic verb to the right argument while the left argument rеturns true value.

o){x<100}{x*2}/1
128
o)

Scan "For" loop

Applies monadic verb to the right argument left argument times.

o)5{x+1}\10
10 11 12 13 14 15
o)

Scan "While" loop

Applies monadic verb to the right argument while the left argument rеturns true value.

o){x<100}{x*2}\1
1 2 4 8 16 32 64 128
o)

Commute

~ transforms dyadic to have its left and right argument swapped.

Amend/dmend also support commute dyads:

o)a:!5
0 1 2 3 4
o).[a;();~[_];-2]
0 1 2
o)