Commute: Difference between revisions

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(f x) g (h x) ⍝ the last ⍨ is being used dyadically, i.e. Swap
(f x) g (h x) ⍝ the last ⍨ is being used dyadically, i.e. Swap
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== History ==
The Commute operator was defined in [[Operators and Functions]] in 1978, and taken up by [[NARS]] as a result. [[Dyalog]], influenced by NARS, included the operator early on. While it didn't appear in [[SHARP APL]], it was included in [[J]] as "Reflex/Passive" (<source lang=j inline>~</source>).


== External links ==
== External links ==

Revision as of 01:56, 2 May 2022

⍨

Commute (⍨) is a monadic operator that takes a dyadic function as operand and modifies how the argument(s) of its derived functions are used. If the derived function is used monadically, the argument is also used as left argument. This usage is also known as Self or, more informally, Selfie. If the derived function is used dyadically, the arguments are swapped. This usage is also known as Swap. The glyph is also used for Constant.

Examples

This decrements from the vector: 

      1 -⍨ 1 2 3
0 1 2
Works in: Dyalog APL, dzaima/APL, NARS2000

Double: 

      +⍨1 2 3
2 4 6
Works in: Dyalog APL, dzaima/APL, NARS2000

Commute can be used to emulate a monadic f g h Fork when combined with Compose (note the following code is not workable APL, but a series of evaluations): 

g⍨∘f⍨∘h⍨ x   
x g⍨∘f⍨∘h x ⍝ the last ⍨ is being used monadically, i.e. Selfie
x g⍨∘f⍨ h x
(h x) g⍨∘f x ⍝ the last ⍨ is being used dyadically, i.e. Swap
(h x) g⍨ (f x) 
(f x) g (h x) ⍝ the last ⍨ is being used dyadically, i.e. Swap

History

The Commute operator was defined in Operators and Functions in 1978, and taken up by NARS as a result. Dyalog, influenced by NARS, included the operator early on. While it didn't appear in SHARP APL, it was included in J as "Reflex/Passive" (~).

External links

Lessons

Documentation


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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