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 Prefix m\  u\  _ 0 _ Infix

 u\y has #y items resulting from applying u to each of the prefixes k{.y , for k from 1 to #y . m\y applies successive verbs from the gerund m to the prefixes of y , extending m cyclically as required. If x>:0 , the items of x u\ y result from applying u to each infix of length x . If x<0 , u is applied to non-overlapping infixes of length |x , including any final shard. x m\ y applies successive verbs from the gerund m to the infixes of y , extending m cyclically as required.

```   +/\a=: 1 2 4 8 16                     NB. Subtotals, or partial sums
1 3 7 15 31

*/\a                                  NB. Partial products
1 2 8 64 1024

<\a
+-+---+-----+-------+----------+
|1|1 2|1 2 4|1 2 4 8|1 2 4 8 16|
+-+---+-----+-------+----------+

<\i.3 4
+-------+-------+---------+
|0 1 2 3|0 1 2 3|0 1  2  3|
|       |4 5 6 7|4 5  6  7|
|       |       |8 9 10 11|
+-------+-------+---------+

(+/\^:_1 +/\ a) ,: */\^:_1 a
1 2 4 8 16
1 2 2 2  2
```
The following examples illustrate the use of the dyad infix:
```   (2 -/\ ])  a                          NB. Backward differences
_1 _2 _4 _8
(2 -~/\ ]) a                          NB. Forward  differences
1 2 4 8

3  <\ 'abcdefgh'
+---+---+---+---+---+---+
|abc|bcd|cde|def|efg|fgh|
+---+---+---+---+---+---+
_3 <\ 'abcdefgh'
+---+---+--+
|abc|def|gh|
+---+---+--+
```

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