Close composition: Difference between revisions

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In [[SHARP APL]] and [[J]], a '''close composition''' is one of the [[operator]]s [[Atop (operator)|Atop]], [[Over]], or [[Under]], defined so that the overall result has [[function rank]] equal to the right operand. In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most APLs) are provided.
In [[SHARP APL]] and [[J]], a '''close composition''' is one of the [[operator]]s [[Atop (operator)|Atop]], [[Over]], or [[Under]], defined so that the overall result has [[function rank]] equal to the right operand. In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most modern APLs) are provided.


{|class=wikitable
{|class=wikitable
! Operator !! SHARP !! J close !! J non-close
! Operator !! SHARP !! J close !! J non-close !! Modern
|-
|-
| [[Atop (operator)|Atop]] || <code>⍥</code> || <code>@</code>  || <code>@:</code>
| [[Atop (operator)|Atop]] || <source lang=apl inline>⍥</source> || <source lang=j inline>@</source>  || <source lang=j inline>@:</source> || <source lang=apl inline>⍤</source>
|-
|-
| [[Over]]                || <code>⍤</code> || <code>&</code>  || <code>&:</code>
| [[Over]]                || <source lang=apl inline>⍤</source> || <source lang=j inline>&</source>  || <source lang=j inline>&:</source> || <source lang=apl inline>⍥</source>
|-
|-
| [[Under]]                || <code>¨</code> || <code>&.</code> || <code>&.:</code>
| [[Under]]                || <source lang=apl inline>¨</source> || <source lang=j inline>&.</source> || <source lang=j inline>&.:</source> || <source lang=apl inline>⍢</source>
|}
|}


{{APL built-ins}}[[Category:Composition operators]]
{{APL built-ins}}[[Category:Composition operators]]

Revision as of 08:06, 26 April 2022

In SHARP APL and J, a close composition is one of the operators Atop, Over, or Under, defined so that the overall result has function rank equal to the right operand. In SHARP all composition operators follow this pattern, while in J, both close and non-close forms (with a result rank of infinity, matching the definition in most modern APLs) are provided.

Operator SHARP J close J non-close Modern
Atop ⍥ @ @: ⍤
Over ⍤ & &: ⍥
Under ¨ &. &.: ⍢


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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