Compose

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Compose (∘) or Composition is the most common name for the primitive dyadic operator denoted with a Jot (∘) introduced by NARS and included in the Dyalog APL family. On the APL Wiki, Compose is divided into its two cases, Beside when both operands are functions, and Bind when one is a function and the other an array.

Composition assembles functions and arguments to form derived functions. This provides the glue with which to put together functions and arguments so that operator's arguments can be more complex than single functions.[1]

In Ken Iverson's designs Rationalized APL, A Dictionary of APL, and the J language, the composition (⍤) or Compose (&) refers to a different kind of composition, the Over operator.

More recently, the term "composition" is used in Dyalog APL to refer to any of a family of operators including Beside and Bind (∘), Commute and Constant (⍨), Atop (⍤), and Over (⍥).[2] Extended Dyalog APL and dzaima/APL add to this list the operators Under (⍢) and Reverse Compose (⍛).

References

  1. ↑ Carl M. Cheney. APL*PLUS Nested Arrays System (NARS reference manual). STSC. 1981.
  2. ↑ Marshall Lochbaum. Tacit Techniques with Dyalog version 18.0 Operators (slides) at Dyalog '19.
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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