Scalar function: Difference between revisions
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A scalar function is one of a class of primitive | A '''scalar function''' is one of a class of [[primitive function]]s that apply to [[argument]]s 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 model|nested]] array languages, scalar functions [[pervasion|pervade]] any [[nested array]]s by [[recursion|recursively]] descending into them until reaching [[simple scalars]]; in [[Flat array model|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 <source lang=apl inline>~</ | Only a particular [[valence]] of a function is labelled "scalar". The scalar monad [[Not]] usually shares the glyph <source lang=apl inline>~</source> with non-scalar dyad [[Without]], and similarly scalar [[Roll]] and non-scalar [[Deal]] are both written <source lang=apl inline>?</source>. | ||
== Standard scalar functions == | == Standard scalar functions == | ||
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Most APLs use a set of scalar functions that was worked out fairly early in APL's development. These are listed in this section. | Most APLs use a set of scalar functions that was worked out fairly early in APL's development. These are listed in this section. | ||
{| class=wikitable | |||
! Monadic function !! Glyph !! Dyadic function | |||
{| | |||
|- | |- | ||
| <source lang=apl inline> | | [[Conjugate]] || <source lang=apl inline>+</source> || [[Plus]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Negate]] || <source lang=apl inline>-</source> || [[Minus]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Signum]] or Direction || <source lang=apl inline>×</source> || [[Times]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Reciprocal]] || <source lang=apl inline>÷</source> || [[Divide]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Floor]] || <source lang=apl inline>⌊</source> || [[Minimum]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Ceiling]] || <source lang=apl inline>⌈</source> || [[Maximum]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Exponential]] || <source lang=apl inline>*</source> || [[Power function]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Natural Logarithm]] || <source lang=apl inline>⍟</source> || [[Logarithm]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Magnitude]] or Absolute value || <source lang=apl inline>|</source> || [[Residue]] | ||
|- | |- | ||
| <source lang=apl inline>○</ | | [[Pi Times]] || <source lang=apl inline>○</source> || [[Circle function]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Factorial]] || <source lang=apl inline>!</source> || [[Binomial]] coefficient or combination function | ||
|- | |- | ||
| [[Roll]] || <source lang=apl inline>?</source> || | |||
| <source lang=apl inline> | |||
|- | |- | ||
| <source lang=apl inline> | | [[Not]] || <source lang=apl inline>~</source> || | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>∧</source> || [[Logical And]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>∨</source> || [[Logical Or]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>⍲</source> || [[Nand]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>⍱</source> || [[Nor]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline><</source> || [[Less than]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>≤</source> || [[Less than or equal to]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>=</source> || [[Equal to]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>≥</source> || [[Greater than or equal to]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>></source> || [[Greater than]] | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>≠</source> || [[Not equal to]] | ||
|} | |||
== Additional scalar functions == | |||
Very few additional scalar functions have been added later in various dialects: | |||
{| class=wikitable | |||
! Monadic function !! Glyph !! Dyadic function | |||
|- | |- | ||
| <source lang=apl inline> | | [[Square Root]] || <source lang=apl inline>√</source> || [[Nth Root]] | ||
|- | |- | ||
| <source lang=apl inline> | | [[Type]] || <source lang=apl inline>∊</source> or <source lang=apl inline>⊤</source> || | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>∧</source> || [[Lowest Common Multiple]] (LCM) | ||
|- | |- | ||
| <source lang=apl inline> | | || <source lang=apl inline>∨</source> || [[Greatest Common Divisor]] (GCD) | ||
|- | |- | ||
|} | |} | ||
== External links == | |||
* [https://www.sacrideo.us/apl-a-day-7-scalar-functions/ Scalar Functions] (part of [https://www.sacrideo.us/tag/apl-a-day/ APL a Day]) | |||
* [https://forums.dyalog.com/viewtopic.php?f=30&t=1621 Scalar functions] by [[Roger Hui]] | |||
{{APL features}}[[Category:Kinds of functions]][[Category:Scalar functions| ]] |
Revision as of 10:29, 4 May 2020
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 pervade any nested arrays by recursively descending into them until reaching 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 function | Glyph | Dyadic function |
---|---|---|
Conjugate | + |
Plus |
Negate | - |
Minus |
Signum or Direction | × |
Times |
Reciprocal | ÷ |
Divide |
Floor | ⌊ |
Minimum |
Ceiling | ⌈ |
Maximum |
Exponential | * |
Power function |
Natural Logarithm | ⍟ |
Logarithm |
Magnitude or Absolute value | | |
Residue |
Pi Times | ○ |
Circle function |
Factorial | ! |
Binomial coefficient or combination function |
Roll | ? |
|
Not | ~ |
|
∧ |
Logical And | |
∨ |
Logical Or | |
⍲ |
Nand | |
⍱ |
Nor | |
< |
Less than | |
≤ |
Less than or equal to | |
= |
Equal to | |
≥ |
Greater than or equal to | |
> |
Greater than | |
≠ |
Not equal to |
Additional scalar functions
Very few additional scalar functions have been added later in various dialects:
Monadic function | Glyph | Dyadic function |
---|---|---|
Square Root | √ |
Nth Root |
Type | ∊ or ⊤ |
|
∧ |
Lowest Common Multiple (LCM) | |
∨ |
Greatest Common Divisor (GCD) |
External links
- Scalar Functions (part of APL a Day)
- Scalar functions by Roger Hui
APL features [edit] | |
---|---|
Built-ins | Primitives (functions, operators) ∙ Quad name |
Array model | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |
Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |
Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search |
Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |