Monadic function: Difference between revisions
m (Kinds of functions category) |
m (Fix a red link) |
||
| Line 11: | Line 11: | ||
1 4 9 16 25 25 16 9 4 1 | 1 4 9 16 25 25 16 9 4 1 | ||
</source> | </source> | ||
The functions <source lang=apl inline>f</source>, <source lang=apl inline>×⍨</source> ([[Times]] [[Commute]]), and <source lang=apl inline>⍳</source> ([[Iota]]) are each monadic functions: a named [[dfn]], a [[derived function]], and a [[primitive]], respectively. Evaluating them first produces the [[Index|indices]] up to 5, then multiplies each index by itself to square it, then [[catenate]]s the resulting list to its [[reverse]]. | The functions <source lang=apl inline>f</source>, <source lang=apl inline>×⍨</source> ([[Times]] [[Commute]]), and <source lang=apl inline>⍳</source> ([[Iota]]) are each monadic functions: a named [[dfn]], a [[derived function]], and a [[primitive function|primitive]], respectively. Evaluating them first produces the [[Index|indices]] up to 5, then multiplies each index by itself to square it, then [[catenate]]s the resulting list to its [[reverse]]. | ||
== External links == | == External links == | ||
Revision as of 05:24, 29 May 2020
- 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.