# Monadic function

*For operators with one operand, see Monadic operator.*

A **monadic function** is a function with a single argument, written to its right. It is one of three possible function valences; the other two are dyadic and niladic. The term **prefix function** is used outside of APL to describe APL's monadic function syntax.

In APL, a single function can be both monadic and dyadic; such a function is called ambivalent or sometimes variadic. Function pages on the APL Wiki usually only describe one valence of an ambivalent function because the connection between the two may not be consistent across languages. In this case the function is described as monadic even though it may only be half of an ambivalent function.

A sequence of monadic functions is evaluated from right to left, a convention drawn from mathematics. Such a sequence can be seen in the following expression:

```
f ← {⍵,⌽⍵}
f ×⍨ ⍳ 5
1 4 9 16 25 25 16 9 4 1
```

The functions `f`

, `×⍨`

(Times Commute), and `⍳`

(Iota) are each monadic functions: a named dfn, a derived function, and a primitive, respectively. Evaluating them first produces the indices up to 5, then multiplies each index by itself to square it, then catenates the resulting list to its reverse.

## External links

APL syntax [edit]
| |
---|---|

Overview | Comparison with traditional mathematics ∙ Precedence |

Array | Numeric literal ∙ String ∙ Strand notation ∙ Object literal ∙ Array notation |

Function | Argument ∙ Function valence ∙ Derived function ∙ Function train ∙ Monadic function ∙ Dyadic function ∙ Ambivalent function |

Operator | Operand ∙ Operator valence ∙ Derived function ∙ Derived operator |

Assignment | Multiple ∙ Indexed ∙ Selective ∙ Modified |

User definition | Tradfn ∙ Dfn ∙ Tacit |

Other | Function axis ∙ Branching ∙ System command ∙ User command ∙ Keyword ∙ Dot notation |