# Operators and Functions

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Operators and Functions is a research report published by Ken Iverson in 1978, collecting a set of operators and functions he had developed over the preceding years. Released two years before Iverson left IBM for I.P. Sharp over differences regarding the direction of APL, it offers precursors for many of the ideas later developed in SHARP APL. Its primitives were used more directly in NARS, which influenced Dyalog APL and in this way shaped much of present-day APL development.

Functions:

`<` Enclose
`>` Disclose
`∪` Nub Union
`∩` Ordered Nub Intersection
${\displaystyle \cup \!\!\!\!-}$ Distribution
${\displaystyle \cap \!\!\!\!-}$ Ordered Distribution
`~` Set Difference
`⊆` Inclusion
`⊇` Inclusion
`⊂` Strict inclusion
`⊃` Strict inclusion
`⌷` Indexing

Operators:

`f⍣B` Power
`f⍣∘` Identity function (e.g. `+` to `×`)
`f⍨` Commute
`̈∆` Domain
`f⍤a` Nuax
`f⍥a` Coax
`f⍢g` Dual
`f¨g` Composition
`f/` (Windowed) Reduction
`f\` (Windowed) Scan
`f⌿` (Windowed) Reduction
`f⍀` (Windowed) Scan
`f∆` Derivative Difference
`̄:` Variant
${\displaystyle \vee \!\!\!\!\wedge }$ Boolean