# Function axis

Revision as of 02:20, 4 November 2019 by Miraheze>Adám Brudzewsky (→Functions with Axis)

In many APLs the behavior of a function may be modified using bracket notation, for example `⌽[2]`

to Rotate along the second axis. Axis specification was a feature of Iverson notation and was ubiquitous in early APLs; many newer APLs which adhere to leading axis theory reject the use of axis specification in favor of the Rank operator because it is a fully general operator while the behavior of functions with axis must be defined for each function separately.

## Functions

### Monadic functions

The following monads may allow an axis:

- Mix accepts a list of axes to specify where the axes of argument elements will be placed in the result.
- Ravel accepts a list of axes which are combined, or a single fractional number to add a length-1 axis.
- Enclose accepts a list of axes. Each subarray along these axes is enclosed.
- Split accepts a single axis, and encloses each vector along that axis.
- Reverse reverses along the specified axis.

### Dyadic functions

The following dyads may allow one:

- Scalar dyadics accept a list of axes to override conformability rules: it specifies , for each axis in the lower-rank (or left, in case of a tie) argument, which axis in the other argument it is paired with.
- Catenate combines along the selected axis, adding a new axis if a non-integer axis is given.
- Rotate rotates the right argument along the selected axis.
- Replicate and Expand work on the specified right argument axis.
- Take and Drop modify the selected right argument axes.
- Squish takes axes to specify which axis of the right argument corresponds to each left argument element.
- Partition and Partitioned Enclose have complicated and different behavior.

## Operators

The following operators may admit axis specification:

- Reduction removes the specified right argument axis.
- Scan works on the specified right argument axis.

In Dyalog APL, a slash with axis retains its function-operator overloading: it can be applied as an operator or as a dyadic function (Replicate or Expand).