Ambivalent function: Difference between revisions
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In [[APL syntax]], a [[function]] is '''ambivalent''' | In [[APL syntax]], a [[function]] is '''ambivalent''' (sometimes '''variadic''' or '''nomadic'''), if it can be called with either [[monadic]] or [[dyadic]] [[valence]]. While every non-[[niladic]] function can be written with one or two arguments, some functions give a [[SYNTAX ERROR]] when called with two arguments (these functions are called monadic) or with only one (these are called dyadic). Ambivalent functions do not give a [[SYNTAX ERROR]] immediately in either case. | ||
Being ambivalent, or not, is an inherent property of a function. This contrasts with the terms "monadic" and "dyadic" which may refer either to the function's inherent properties as described above or to the context in which it is used. When an ambivalent function is invoked it has either one argument or two: we would say for example it is an ambivalent function ''called monadically''. | Being ambivalent, or not, is an inherent property of a function. This contrasts with the terms "monadic" and "dyadic" which may refer either to the function's inherent properties as described above or to the context in which it is used. When an ambivalent function is invoked it has either one argument or two: we would say for example it is an ambivalent function ''called monadically''. | ||
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=== Tradfns === | === Tradfns === | ||
In some APLs, for example [[APL*PLUS]], [[tradfn]]s that declare a left argument in the [[function header]] are always ambivalent, and the code needs to check whether a left argument was supplied by the left argument name's [[name class]]; < | In some APLs, for example [[APL*PLUS]], [[tradfn]]s that declare a left argument in the [[function header]] are always ambivalent, and the code needs to check whether a left argument was supplied by the left argument name's [[name class]]; <syntaxhighlight lang=apl inline>0 ≠ ⎕NC 'leftArg'</syntaxhighlight>. Other APLs, for example [[Dyalog APL]], will not allow calling such a function monadically, unless the header has curly braces around the left argument name to indicate that it is optional; <syntaxhighlight lang=apl inline> result ← {leftArg} FnName rightArg</syntaxhighlight>. Then too, they need to query the name class, or, unique for Dyalog APL, use a specialised ''Called Monadically'' [[I-beam]], <syntaxhighlight lang=apl inline>900⌶⍬</syntaxhighlight>.<ref>[[Dyalog APL]] Language Reference Guide > The I-Beam Operator > [https://help.dyalog.com/latest/#Language/I%20Beam%20Functions/Called%20Monadically.htm Called Monadically]</ref> | ||
=== Dfns === | === Dfns === | ||
[[Dfn]]s are always ambivalent, even if they reference < | [[Dfn]]s are always ambivalent, even if they reference <syntaxhighlight lang=apl inline>⍺</syntaxhighlight>. (This is in contrast with [[dop]]s which have a fixed [[operator valence]] determined by the presence of an unquoted <syntaxhighlight lang=apl inline>⍵⍵</syntaxhighlight> in their code.) Like tradfns, the dfn can check the name class (<syntaxhighlight lang=apl inline>0 ≠ ⎕NC '⍺'</syntaxhighlight>). | ||
However, most APLs that support dfns also allow a statement of the structure < | However, most APLs that support dfns also allow a statement of the structure <syntaxhighlight lang=apl inline>⍺ ← defaultValue</syntaxhighlight> which skipped if the function was called dyadically.<ref>[[Dyalog APL]] Programming Reference Guide > Defined Functions & Operators > Direct Functions & Operators > [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Default%20Left%20Argument.htm Default Left Argument]</ref> This syntax also allows assigning a function, or even an operator, to <syntaxhighlight lang=apl inline>⍺</syntaxhighlight>, thus streamlining many ambivalent definitions. For example, we can create a Nth root function which defaults to being the square root when used monadically: | ||
[https://tio.run/##SyzI0U2pTMzJT///Pyg/v@RR24RqLgUgeNS7C8g2grK3KmgpHN4OFOOqhahTMDQw4DJWADONzAE Try it online!] | [https://tio.run/##SyzI0U2pTMzJT///Pyg/v@RR24RqLgUgeNS7C8g2grK3KmgpHN4OFOOqhahTMDQw4DJWADONzAE Try it online!] | ||
< | <syntaxhighlight lang=apl> | ||
Root←{ | Root←{ | ||
⍺←2 | ⍺←2 | ||
⍵ * ÷⍺ | ⍵ * ÷⍺ | ||
} | } | ||
</ | </syntaxhighlight> | ||
We can also define the [[Over]] operator with < | We can also define the [[Over]] operator with <syntaxhighlight lang=apl inline>⍺</syntaxhighlight> defaulting to be an operator that skips its operand: | ||
[https://tio.run/##SyzI0U2pTMzJT///378stehR24RqLgUgeNS7C8R@1LtV4VF3C5jbu6sWLKUBFASL9@7ShEogiW3V5Kr9/19XAWSagsbh6Y96V2gqGHOZKqAJmQAA Try it online!] | [https://tio.run/##SyzI0U2pTMzJT///378stehR24RqLgUgeNS7C8R@1LtV4VF3C5jbu6sWLKUBFASL9@7ShEogiW3V5Kr9/19XAWSagsbh6Y96V2gqGHOZKqAJmQAA Try it online!] | ||
< | <syntaxhighlight lang=apl> | ||
Over←{ | Over←{ | ||
⍺←{⍵ ⋄ ⍺⍺} | ⍺←{⍵ ⋄ ⍺⍺} | ||
(⍵⍵ ⍺) ⍺⍺ (⍵⍵ ⍵) | (⍵⍵ ⍺) ⍺⍺ (⍵⍵ ⍵) | ||
} | } | ||
</ | </syntaxhighlight> | ||
== External links == | == External links == | ||
| Line 36: | Line 36: | ||
=== Documentation === | === Documentation === | ||
* [http://microapl.com/apl_help/ch_020_010_070.htm APLX] | * [http://microapl.com/apl_help/ch_020_010_070.htm APLX] | ||
* [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/Model%20Syntax.htm Dyalog] | * [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/TradFns/Model%20Syntax.htm Dyalog] | ||
== References == | == References == | ||
Latest revision as of 22:17, 10 September 2022
In APL syntax, a function is ambivalent (sometimes variadic or nomadic), if it can be called with either monadic or dyadic valence. While every non-niladic function can be written with one or two arguments, some functions give a SYNTAX ERROR when called with two arguments (these functions are called monadic) or with only one (these are called dyadic). Ambivalent functions do not give a SYNTAX ERROR immediately in either case.
Being ambivalent, or not, is an inherent property of a function. This contrasts with the terms "monadic" and "dyadic" which may refer either to the function's inherent properties as described above or to the context in which it is used. When an ambivalent function is invoked it has either one argument or two: we would say for example it is an ambivalent function called monadically.
Tradfns
In some APLs, for example APL*PLUS, tradfns that declare a left argument in the function header are always ambivalent, and the code needs to check whether a left argument was supplied by the left argument name's name class; 0 ≠ ⎕NC 'leftArg'. Other APLs, for example Dyalog APL, will not allow calling such a function monadically, unless the header has curly braces around the left argument name to indicate that it is optional; result ← {leftArg} FnName rightArg. Then too, they need to query the name class, or, unique for Dyalog APL, use a specialised Called Monadically I-beam, 900⌶⍬.[1]
Dfns
Dfns are always ambivalent, even if they reference ⍺. (This is in contrast with dops which have a fixed operator valence determined by the presence of an unquoted ⍵⍵ in their code.) Like tradfns, the dfn can check the name class (0 ≠ ⎕NC '⍺').
However, most APLs that support dfns also allow a statement of the structure ⍺ ← defaultValue which skipped if the function was called dyadically.[2] This syntax also allows assigning a function, or even an operator, to ⍺, thus streamlining many ambivalent definitions. For example, we can create a Nth root function which defaults to being the square root when used monadically:
Root←{
⍺←2
⍵ * ÷⍺
}
We can also define the Over operator with ⍺ defaulting to be an operator that skips its operand:
Over←{
⍺←{⍵ ⋄ ⍺⍺}
(⍵⍵ ⍺) ⍺⍺ (⍵⍵ ⍵)
}
External links
Tutorials
- John 'Jake' Jacob. Pervasion of Ambivalence in APL Functions. Optima Systems. July 9, 2020.
Documentation
References
- ↑ Dyalog APL Language Reference Guide > The I-Beam Operator > Called Monadically
- ↑ Dyalog APL Programming Reference Guide > Defined Functions & Operators > Direct Functions & Operators > Default Left Argument