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Function-operator overloading: Difference between revisions
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Function-operator overloading (view source)
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This form of overloading relies on the fact that an expression like <source lang=apl inline>a / b</source> can be disambiguated based on whether <source lang=apl inline>a</source> is a function or not: if so, <source lang=apl inline>/</source> should be an operator. This assumption is violated when [[function train]]s are part of the syntax, because a train such as <source lang=apl inline>= / +</source> could be interpreted either as the two-train <source lang=apl inline>(=/) +</source>, [[Equals]] [[reduction]] [[atop]] [[Plus]], or as a three train [[Equals]] [[Compress]] [[Plus]]. No interpretation can always give the result the user wants, but dialects with overloading always choose the first interpretation, in which the overloaded value is treated as an operator. | This form of overloading relies on the fact that an expression like <source lang=apl inline>a / b</source> can be disambiguated based on whether <source lang=apl inline>a</source> is a function or not: if so, <source lang=apl inline>/</source> should be an operator. This assumption is violated when [[function train]]s are part of the syntax, because a train such as <source lang=apl inline>= / +</source> could be interpreted either as the two-train <source lang=apl inline>(=/) +</source>, [[Equals]] [[reduction]] [[atop]] [[Plus]], or as a three train [[Equals]] [[Compress]] [[Plus]]. No interpretation can always give the result the user wants, but dialects with overloading always choose the first interpretation, in which the overloaded value is treated as an operator. | ||
The [[Atop operator]] provides a way to obtain the other interpretation: <source lang=apl inline>⊢⍤/</source> is identical to <source lang=apl inline>/</source> as a function, but forces the function-operator overloading to be resolved in favor of a function because there is a [[dyadic operator]] to its left.<ref>[[Marshall Lochbaum|Lochbaum, Marshall]]. [https://dyalog.tv/Dyalog19/?v=czWC4tjwzOQ "Tacit Techniques with Dyalog version 18.0 Operators"]. [[Dyalog '19]].</ref> When the Atop operator is not available, [[Compose]] can be used instead, but | Function-operator overloading works by checking to the left of a potential function or operator to see if it is a function. This includes [[derived function]]s: for instance, the snippet <source lang=apl inline>-⍨/</source> is treated as a [[reduction]] with operand <source lang=apl inline>-⍨</source>. In [[A+]], only a small set of [[scalar dyadic]] functions can be used as operands to [[Reduce]] and [[Scan]], and the language simply checks whether these glyphs appear immediately to the left of the slash. Thus, parenthesizing or assigning a name to these functions will cause overloading resolution to fail, resulting in a valence error. | ||
==Mitigation== | |||
The [[Atop operator]] provides a way to obtain the other interpretation: <source lang=apl inline>⊢⍤/</source> is identical to <source lang=apl inline>/</source> as a function, but forces the function-operator overloading to be resolved in favor of a function because there is a [[dyadic operator]] to its left.<ref>[[Marshall Lochbaum|Lochbaum, Marshall]]. [https://dyalog.tv/Dyalog19/?v=czWC4tjwzOQ "Tacit Techniques with Dyalog version 18.0 Operators"]. [[Dyalog '19]].</ref> When the Atop operator is not available, [[Compose]] or [[Commute]] can be used instead, but they requires an extra set of parentheses. Alternatively, the function behaviour can be forced by encapsulating the hybrid primitive in a [[dfn]]. | |||
<source lang=apl> | <source lang=apl> | ||
(2=2 1) / (2+2 1) ⍝ Desired result | (2=2 1) / (2+2 1) ⍝ Desired result | ||
| Line 27: | Line 29: | ||
4 | 4 | ||
2 (= (/∘⊢) +) 2 1 ⍝ Resolved with Compose | 2 (= (/∘⊢) +) 2 1 ⍝ Resolved with Compose | ||
4 | |||
2 (= (/⍨⍨) +) 2 1 ⍝ Resolved with Commute | |||
4 | |||
2 (= {⍺/⍵} +) 2 1 ⍝ Resolved with dfn | |||
4 | 4 | ||
</source>{{Works in|[[Dyalog APL]], with version [[Dyalog APL 18.0|18.0]] for [[Atop]]}} | </source>{{Works in|[[Dyalog APL]], with version [[Dyalog APL 18.0|18.0]] for [[Atop]]}} | ||
== References == | == References == | ||
<references /> | <references /> | ||
{{APL syntax}} | {{APL syntax}} | ||