# Scalar function

A scalar function is one of a class of primitive functions that apply to arguments one element at a time. Dyadic scalar functions pair elements of their arguments based on conformability rules, and thus are subject to scalar extension. In nested array languages scalar functions recursively descend into nested arrays until they can be applied to simple scalars; in flat array languages they usually do not apply inside boxes.

Only a particular valence of a function is labelled "scalar". The scalar monad Not usually shares the glyph `~`

with non-scalar dyad Without, and similarly scalar Roll and non-scalar Deal are both written `?`

.

## Standard scalar functions

Most APLs use a set of scalar functions that was worked out fairly early in APL's development. These are listed in this section.

### Monadic functions

`+` |
Conjugate |

`-` |
Negate |

`×` |
Signum or Direction |

`÷` |
Reciprocal |

`⌊` |
Floor |

`⌈` |
Ceiling |

`*` |
Exponential |

`⍟` |
Natural Logarithm |

`|` |
Magnitude |

`!` |
Factorial |

`○` |
Pi Times |

`~` |
Not |

`∊` |
Type |

### Dyadic functions

`+` |
Plus |

`-` |
Minus |

`×` |
Times |

`÷` |
Divide |

`⌊` |
Minimum |

`⌈` |
Maximum |

`*` |
Power function |

`⍟` |
Logarithm |

`|` |
Residue |

`!` |
Binomial coefficient or combination function |

`○` |
Circle function |

`∧` |
Logical And |

`∨` |
Logical Or |

`⍲` |
Nand |

`⍱` |
Nor |

`<` |
Less than |

`≤` |
Less than or equal to |

`=` |
Equal to |

`≥` |
Greater than or equal to |

`>` |
Greather than |

`≠` |
Not equal to |