# `↦` — Range / To

Function. Keys: `Alt-l`. Ranks: `0` monadic, `0 0` dyadic

`X↦Y` counts from `X` to `Y` in steps of 1. It counts down when `Y` is
less than `X`. Two characters count through the code points between
them.

``` bpl
2↦5          ⍝ 2 3 4 5
5↦2          ⍝ 5 4 3 2
'a'↦'e'      ⍝ "abcde"
```

The last item is the last step that doesn’t pass `Y`. The number of
steps counts as whole within comparison tolerance.

``` bpl
0.5↦3        ⍝ 0.5 1.5 2.5
0↦0.3÷0.1    ⍝ 0 1 2 3
```

Each item is `X` plus or minus an exact count: `0ₓ`, `1ₓ`, `2ₓ` and so
on. The result’s type therefore follows `X`. `Y` sets only how many
items there are.

``` bpl
1ₓ↦5         ⍝ [1 2 3 4 5]ₓ
1↦5ₓ         ⍝ 1 2 3 4 5
```

`↦N` counts from `1` up to `N`, or from `¯1` down to `N` when `N` is
negative. It has `⌊|N` items. `↦0` is empty. The result’s type follows
`N`.

``` bpl
↦4           ⍝ 1 2 3 4
↦¯3          ⍝ ¯1 ¯2 ¯3
↦0           ⍝ ⍬
```

On a vector, `↦` applies to each item, as [Rank](jot-diaeresis.qmd)
does. Fill pads the results to a common length.

``` bpl
↦2 3         ⍝ [1 2 0⋄1 2 3]
```

## Errors

- `DOMAIN`: a complex number, a character with a number, or an infinite
  end
- `LIMIT`: more items than an array can hold