### Quick - `ƒ` - Reduce With Starting Value

Characters: `ƒ`

Tags: array

The resulting link is dyadic, meaning it takes two arguments. Note that the arity refers to that of the resulting link, not the number of links this quick consumes.

##### Functionality

Reduce or n-wise reduce a list starting at the right argument.

##### Details

If a nilad appears right before `ƒ`, this does n-wise reduce. For positive `n`, split the list into chunks of length `n` (identical to `s` (Split (Length))) and reduce each sublist. For negative `n`, instead of reducing each sublist, slice and remove chunks of length `-n`. For example, `5R ;-2ƒ0` returns `[[0, 3, 4, 5], [0, 1, 2, 5], [0, 1, 2, 3, 4]]` - in the first list, `[1, 2]` is removed, in the second list, `[3, 4]` is removed, and in the last list, `[5]` is removed.

To a reduce a list, begin with the right argument, and then for each element, apply the link to the current accumulator and the incoming value. `a,b,c,... ×ƒ y` is equivalent to `y × a × b × c × ...`. The link must be a dyad; if you want to apply a monad to the two elements, you can use the idiom `,F¥` for some monad `F`, which first pairs the elements and then calls `F` on the result.

##### Syntax
• `<dyad>ƒ` - reduce
• `<dyad><nilad>ƒ` - n-wise reduce