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:
| Glyph | Monadic | Dyadic |
|---|---|---|
< |
Enclose | |
> |
Disclose | |
∪ |
Nub | Union |
∩ |
Ordered Nub | Intersection |
| Distribution | ||
| Ordered Distribution | ||
~ |
Set Difference | |
⊆ |
Inclusion | |
⊇ |
Inclusion | |
⊂ |
Strict inclusion | |
⊃ |
Strict inclusion | |
⌷ |
Indexing |
Operators:
| Syntax | Monadic call | Dyadic call |
|---|---|---|
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/ |
Dyadic Reduction (Windowed Reduction) | |
f\ |
Dyadic Scan | |
f⌿ |
Dyadic Reduction (Windowed Reduction) | |
f⍀ |
Dyadic Scan | |
f∆ |
Derivative | Difference |
̄: |
Variant | |
| Boolean | ||
External links
- Jsoftware: Operators and Functions (digitised)
| APL dialects [edit] | |
|---|---|
| Maintained | APL+Win ∙ APL2 ∙ APL64 ∙ APL\iv ∙ Aplette ∙ April ∙ Co-dfns ∙ Dyalog APL ∙ Dyalog APL Vision ∙ dzaima/APL ∙ GNU APL ∙ Kap ∙ NARS2000 ∙ Pometo ∙ TinyAPL |
| Historical | A Programming Language ∙ A+ (A) ∙ APL# ∙ APL2C ∙ APL\360 ∙ APL/700 ∙ APL\1130 ∙ APL\3000 ∙ APL.68000 ∙ APL*PLUS ∙ APL.jl ∙ APL.SV ∙ APLX ∙ Extended Dyalog APL ∙ Iverson notation ∙ IVSYS/7090 ∙ NARS ∙ ngn/apl ∙ openAPL ∙ Operators and Functions ∙ PAT ∙ Rowan ∙ SAX ∙ SHARP APL ∙ Rationalized APL ∙ VisualAPL (APLNext) ∙ VS APL ∙ York APL |
| Derivatives | AHPL ∙ BQN ∙ CoSy ∙ ELI ∙ Glee ∙ I ∙ Ivy ∙ J ∙ Jelly ∙ K (Goal, Klong, Q) ∙ KamilaLisp ∙ Lang5 ∙ Lil ∙ Nial ∙ RAD ∙ Uiua |
| Overviews | Comparison of APL dialects ∙ Timeline of array languages ∙ Timeline of influential array languages ∙ Family tree of array languages |