Variant

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Variant (⍠, ⎕OPT) or Custom (: in A Dictionary of APL[1]) and Fit in J, is a special dyadic operator which takes a function as its left operand and modifies its behaviour as specified by the array right operand.

Since ⍠ was not in Dyalog's atomic vector when the feature was added, a system operator alternative was provided in form of ⎕OPT.

History

Variant dates back all the way to Iverson notation where a subscript was used to indicate which index origin a primitive would operate under. This system was dropped in APL\360. Instead, the system command )ORIGIN was provided for controlling the interpreter's global setting. This was then supplemented with a system variable to control the global state. Though this feature is still present in many APL systems, together with numerous other system variables for controlling other aspects of the system, for example comparison tolerance, these global settings were recognised as an unfortunate design in that every programmer would be forced to set and localise every system variable that could affect the given code. Later, Ken Iverson envisioned a return to a per-invocation setting, similar to the original notation, but this time in the form of a dyadic operator that would customise primitive functions.

Although SHARP APL didn't implement Iverson's idea, J did. Later Dyalog APL 13.0 (2011) repurposed it as a way of providing auxilliary arguments to system functions and functions derived from system operators, but not for primitives.

Usage =

The Dyalog system operator ⎕S takes as operands a text be search for and what to return for each match (with & meaning the matched text): 

      ('abra'⎕S'&')'Abrabrabra'
 abra
Works in: Dyalog APL

Only one match is found, because ⎕S defaults to being case sensitive and disallow overlapping matches. The variant operator can be used to enable case insensitivity: 

      ('abra'⎕S'&'⍠1)'Abrabrabra'
 Abra  abra
Works in: Dyalog APL

This usage with a simple scalar right operand is in line with Iverson's design: 

   1 = 1+1e_14         NB. equivalent to 1 =  1+1e¯14 in Dictionary APL
1
   1 (= !. 0) 1+1e_14  NB. equivalent to 1 (= : 0) 1+1e¯14 in Dictionary APL
0
Works in: J

However, Dyalog also allows a wikipedia:name–value pair, or a vector of name–value pairs. The above example can be spelled using the IC (for Insensitive Case) setting name: 

      ('abra'⎕S'&'⍠'IC'1)'Abrabrabra'
 Abra  abra
Works in: Dyalog APL

Multiple settings can either be specified with multiple applications of variant, or by using a vector of name–value pairs. Here, OM (for Overlapping Matches) is enabled in addition to IC: 

      ('abra'⎕S'&'⍠'IC'1⍠'OM'1)'Abrabrabra'
 Abra  abra  abra 
      ('abra'⎕S'&'⍠('IC'1)('OM'1))'Abrabrabra'
 Abra  abra  abra
Works in: Dyalog APL

External links

Tutorials

Documentation

References

  1. ↑ Ken Iverson. A Dictionary of APL. Custom. APL Quote Quad, Volume 18, Number 1, 1987-09.


APL built-ins [edit]
Primitives (Timeline) Functions
Scalar
Monadic Conjugate ∙ Negate ∙ Signum ∙ Reciprocal ∙ Magnitude ∙ Exponential ∙ Natural Logarithm ∙ Floor ∙ Ceiling ∙ Factorial ∙ Not ∙ Pi Times ∙ Roll ∙ Type ∙ Imaginary ∙ Square Root ∙ Round
Dyadic Add ∙ Subtract ∙ Times ∙ Divide ∙ Residue ∙ Power ∙ Logarithm ∙ Minimum ∙ Maximum ∙ Binomial ∙ Comparison functions ∙ Boolean functions (And, Or, Nand, Nor) ∙ GCD ∙ LCM ∙ Circular ∙ Complex ∙ Root
Non-Scalar
Structural Shape ∙ Reshape ∙ Tally ∙ Depth ∙ Ravel ∙ Enlist ∙ Table ∙ Catenate ∙ Reverse ∙ Rotate ∙ Transpose ∙ Raze ∙ Mix ∙ Split ∙ Enclose ∙ Nest ∙ Cut (K) ∙ Pair ∙ Link ∙ Partitioned Enclose ∙ Partition
Selection First ∙ Pick ∙ Take ∙ Drop ∙ Unique ∙ Identity ∙ Stop ∙ Select ∙ Replicate ∙ Expand ∙ Set functions (Intersection ∙ Union ∙ Without) ∙ Bracket indexing ∙ Index ∙ Cartesian Product ∙ Sort
Selector Index generator ∙ Grade ∙ Index Of ∙ Interval Index ∙ Indices ∙ Deal ∙ Prefix and suffix vectors
Computational Match ∙ Not Match ∙ Membership ∙ Find ∙ Nub Sieve ∙ Encode ∙ Decode ∙ Matrix Inverse ∙ Matrix Divide ∙ Format ∙ Execute ∙ Materialise ∙ Range
Operators Monadic Each ∙ Commute ∙ Constant ∙ Replicate ∙ Expand ∙ Reduce ∙ Windowed Reduce ∙ Scan ∙ Outer Product ∙ Key ∙ I-Beam ∙ Spawn ∙ Function axis ∙ Identity (Null, Ident)
Dyadic Bind ∙ Compositions (Compose, Reverse Compose, Beside, Withe, Atop, Over) ∙ Inner Product ∙ Determinant ∙ Power ∙ At ∙ Under ∙ Rank ∙ Depth ∙ Variant ∙ Stencil ∙ Cut ∙ Direct definition (operator) ∙ Identity (Lev, Dex)
Quad names Index origin ∙ Comparison tolerance ∙ Migration level ∙ Atomic vector
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