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Function-operator overloading (view source)

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In [[APL syntax]], '''function-operator overloading''' (sometimes '''schizophrenia''' in reference to [[wikipedia:split personality|split personality]]) is the practice of using a single [[glyph]] for both a [[primitive function]] and a [[primitive operator]]. Dialects with this feature include [[Dyalog APL]], [[NARS2000]], [[A+]], and [[GNU APL]]. Most commonly it refers to one of the slash glyphs (such as <source lang=apl inline>/</source> for [[Replicate]] or [[Reduce]]), but [[assignment]] may also be handled in a similar manner because ordinary assignment has the form of a [[dyadic function]] while [[modified assignment]] works like a [[monadic operator]] applied dyadically. It may apply only to the glyphs themselves, or to their values as well: for example, in [[Dyalog APL]] the assignments <source lang=apl inline>r←/</source> and even <source lang=apl inline>r←/[3]</source> create variables <source lang=apl inline>r</source> which exhibit overloading.
In [[APL syntax]], '''function-operator overloading''' (sometimes '''schizophrenia'''<ref>The term ''schizophrenia'' used to be associated with [[wikipedia:split personality|''split personality'']] by the general population but that usage went into decline when it became known as a separate disorder. The term was used for duality of programming language constructs as early 1978, for example in [https://dl.acm.org/doi/10.1145/800025.1198354 the transcript] of [[Alan Perlis]]'s [[HOPL]] I entry on [[wikipedia:ALGOL 58|ALGOL 58]]. The informal usage has lived on in APL circles when referring to the "split personality" exhibited in primitives affected by function-operator overloading.</ref>) is the practice of using a single [[glyph]] for both a [[primitive function]] and a [[primitive operator]], which is then characterised as a '''hybrid''' primitive. Dialects with this feature include [[Dyalog APL]], [[NARS2000]], [[A+]], and [[GNU APL]]. Most commonly it refers to one of the slash glyphs <source lang=apl inline>/⌿\⍀</source> (for example, <source lang=apl inline>/</source> is both [[Replicate]] and [[Reduce]]), and dialects [[APL2]] and [[APLX]], which [[Replicate#Operator or function?|define Replicate and Expand to be operators]], don't use it. [[Assignment]] may also be handled in a similar manner because ordinary assignment has the form of a [[dyadic function]] while [[modified assignment]] works like a [[monadic operator]] applied dyadically. Overloading may apply only to the glyphs themselves, or to their values and derivations as well: for example, in [[Dyalog APL]] the assignments <source lang=apl inline>r←/</source> and even <source lang=apl inline>r←/[3]</source> cause <source lang=apl inline>r</source> to exhibit overloading.
 
== Occurrence ==
The following glyphs may be subject to function-operator overloading:
The following glyphs may be subject to function-operator overloading:
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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 it requires an extra set of parentheses.
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)|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, [[Beside]] or [[Commute]] can be used instead, but they require 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
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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]]}}
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.


== References ==
== References ==
<references />
<references />
 
== External links ==
{{APL syntax}}
* GNU APL: Design Decisions — [https://www.gnu.org/software/apl/apl.html#APL-symbols-that-can-be-functions-or-operators APL symbols that can be functions or operators]
* Dyalog APL: Function Trains — [https://help.dyalog.com/latest/#Language/Introduction/Trains.htm#bindstr Binding Strengths]
{{APL syntax}}[[Category:Syntactic elements]][[Category:Function characteristics]]
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