Reverse Compose: Difference between revisions

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(April implemented this (as Before) before Kap actually)
(aka "behind")
 
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{{Built-in|Reverse Compose|⍛}} or '''Before''' is a [[primitive operator]] closely related to [[Beside]] (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>), which appears in [[Extended Dyalog APL]], [[dzaima/APL]], [[April]] and [[Kap]]. Called [[dyad|dyadically]] with function operands <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>f</syntaxhighlight> [[monad|monadically]] to pre-processes the left argument before applying <syntaxhighlight lang=apl inline>g</syntaxhighlight> between the pre-processed left argument and the given right argument. <syntaxhighlight lang=apl inline>X f⍛g Y</syntaxhighlight> is thus equivalent to <syntaxhighlight lang=apl inline>(f X) g Y</syntaxhighlight>. The operator can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</syntaxhighlight>. This dyadic definition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]].
{{Built-in|Reverse Compose|⍛}}, '''Before''' or '''Behind''' is a [[primitive operator]] closely related to [[Beside]] (<syntaxhighlight lang=apl inline>∘</syntaxhighlight>), which appears in [[Extended Dyalog APL]], [[dzaima/APL]], [[April]] and [[Kap]]. Called [[dyad|dyadically]] with function operands <syntaxhighlight lang=apl inline>f</syntaxhighlight> and <syntaxhighlight lang=apl inline>g</syntaxhighlight>, it uses <syntaxhighlight lang=apl inline>f</syntaxhighlight> [[monad|monadically]] to pre-processes the left argument before applying <syntaxhighlight lang=apl inline>g</syntaxhighlight> between the pre-processed left argument and the given right argument. <syntaxhighlight lang=apl inline>X f⍛g Y</syntaxhighlight> is thus equivalent to <syntaxhighlight lang=apl inline>(f X) g Y</syntaxhighlight>. The operator can be defined as the [[dop]] <syntaxhighlight lang=apl inline>{(⍺⍺ ⍺) ⍵⍵ ⍵}</syntaxhighlight>. This dyadic definition matches the [[hook]] function Before, represented as <code>⊸</code> in [[BQN]].


Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], <syntaxhighlight lang=apl inline>f⍛g Y</syntaxhighlight> evaluated to <syntaxhighlight lang=apl inline>g Y</syntaxhighlight>, but the later [[Dyalog APL Vision]], as well as [[April]] and [[Kap]], define it to be <syntaxhighlight lang=apl inline>(f Y) g Y</syntaxhighlight>, matching Before. This later definition might also be written <syntaxhighlight lang=apl inline>f⍛g</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>f⍛g⍨⍨</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</syntaxhighlight>. In [[dzaima/APL]] the monadic case is simply an error.
Unlike Before, the [[monad]]ic case of Reverse Compose has differed across implementations. When introduced by [[Extended Dyalog APL]], <syntaxhighlight lang=apl inline>f⍛g Y</syntaxhighlight> evaluated to <syntaxhighlight lang=apl inline>g Y</syntaxhighlight>, but the later [[Dyalog APL Vision]], as well as [[April]] and [[Kap]], define it to be <syntaxhighlight lang=apl inline>(f Y) g Y</syntaxhighlight>, matching Before. This later definition might also be written <syntaxhighlight lang=apl inline>f⍛g</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>f⍛g⍨⍨</syntaxhighlight>{{←→}}<syntaxhighlight lang=apl inline>g⍨∘f⍨</syntaxhighlight>. In [[dzaima/APL]] the monadic case is simply an error.

Latest revision as of 13:57, 28 June 2024

⍛

Reverse Compose (⍛), Before or Behind is a primitive operator closely related to Beside (∘), which appears in Extended Dyalog APL, dzaima/APL, April and Kap. Called dyadically with function operands f and g, it uses f monadically to pre-processes the left argument before applying g between the pre-processed left argument and the given right argument. X f⍛g Y is thus equivalent to (f X) g Y. The operator can be defined as the dop {(⍺⍺ ⍺) ⍵⍵ ⍵}. This dyadic definition matches the hook function Before, represented as ⊸ in BQN.

Unlike Before, the monadic case of Reverse Compose has differed across implementations. When introduced by Extended Dyalog APL, f⍛g Y evaluated to g Y, but the later Dyalog APL Vision, as well as April and Kap, define it to be (f Y) g Y, matching Before. This later definition might also be written f⍛g f⍛g⍨⍨ g⍨∘f⍨. In dzaima/APL the monadic case is simply an error.

Common usage

Its plain usage is to pre-process left arguments without needing one or more applications of Commute (⍨). For example, the square of the left argument minus the right argument can be expressed as:

Try it online!

      3×⍨⍛-2
7
Works in: dzaima/APL, Extended Dyalog APL, Kap

It can also be combined with Beside to create the split-compose construct. Here, we take the sign of the left argument and apply it to (that is, multiply it with) the absolute value of the right argument:

Try it online!

      3 ¯1 4×⍛×∘|¯2 ¯7 1
2 ¯7 1
Works in: dzaima/APL, Extended Dyalog APL, Kap

External links

Documentation

Publications

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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