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Jot: Difference between revisions
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{{Glyphbox|∘}} | {{Glyphbox|∘}} | ||
The [[glyph]] '''jot''' is a small circle represented by the [[Unicode]] character <code>∘</code>, "ring operator" (<code>◦</code>, "white bullet", may also be used in some dialects). Derived from the [[Iverson notation]] convention of using a circle for the top (reducing) function of an [[Inner Product]] to turn it into an [[Outer Product]], the jot now has several uses in various dialects: | The [[glyph]] '''jot''' is a small circle represented by the [[Unicode]] character <code>∘</code>, "ring operator" (<code>◦</code>, "white bullet", may also be used in some dialects). Derived from the [[Iverson notation]] convention of using a circle for the top (reducing) function of an [[Inner Product]] to turn it into an [[Outer Product]], the jot now has several uses in various dialects: | ||
* In [[APL\360]] and all other APLs, it is a "special" left operand to [[Inner Product]] (<syntaxhighlight lang=apl inline>.</ | * In [[APL\360]] and all other APLs, it is a "special" left operand to [[Inner Product]] (<syntaxhighlight lang=apl inline>.</syntaxhighlight>), so that (<syntaxhighlight lang=apl inline>∘.f</syntaxhighlight>) is an [[Outer Product]] by <syntaxhighlight lang=apl inline>f</syntaxhighlight>. | ||
* In [[SHARP APL]], <syntaxhighlight lang=apl inline>∘</ | * In [[SHARP APL]], <syntaxhighlight lang=apl inline>∘</syntaxhighlight>, named [[nil]], is the [[enclose]]d [[empty]] [[numeric]] [[vector]], which may also be written <syntaxhighlight lang=apl inline><⍳0</syntaxhighlight>. | ||
* In [[NARS]], [[Dyalog APL]], and other [[Nested array model|nested]] APLs derived from these, <syntaxhighlight lang=apl inline>∘</ | * In [[NARS]], [[Dyalog APL]], and other [[Nested array model|nested]] APLs derived from these, <syntaxhighlight lang=apl inline>∘</syntaxhighlight> is the [[Compose]] [[operator]]. | ||
* In [[NARS]] and [[NARS2000]], for an array <syntaxhighlight lang=apl inline>a</ | * In [[NARS]] and [[NARS2000]], for an array <syntaxhighlight lang=apl inline>a</syntaxhighlight>, <syntaxhighlight lang=apl inline>a∘/</syntaxhighlight> is [[Mask]] and <syntaxhighlight lang=apl inline>a∘\</syntaxhighlight> is [[Mesh]]. | ||
Thus jot may be considered either a special element of syntax as in [[APL\360]], an [[array]] as in [[SHARP APL]], or an [[operator]]. In the last case it would not normally be allowed as an [[operand]] to the [[Inner Product]] operator, and a special rule is needed to allow the [[Outer Product]] syntax. As a final option, [[APL2]] allows a jot only in the context of an Outer Product like APL\360, but documents that jot "is treated syntactically as a [[function]]."<ref>[[IBM]]. [https://www.ibm.com/downloads/cas/ZOKMYKOY "APL2 Programming: Language Reference"]. 1994. p.24.</ref> | Thus jot may be considered either a special element of syntax as in [[APL\360]], an [[array]] as in [[SHARP APL]], or an [[operator]]. In the last case it would not normally be allowed as an [[operand]] to the [[Inner Product]] operator, and a special rule is needed to allow the [[Outer Product]] syntax. As a final option, [[APL2]] allows a jot only in the context of an Outer Product like APL\360, but documents that jot "is treated syntactically as a [[function]]."<ref>[[IBM]]. [https://www.ibm.com/downloads/cas/ZOKMYKOY "APL2 Programming: Language Reference"]. 1994. p.24.</ref> | ||