A+: Difference between revisions

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! Glyph                                !! Dyadic                                        !! Monadic
! Glyph                                !! Dyadic                                        !! Monadic
|-
|-
| <source lang=apl inline>+</source>  || [[Add]]                                      || [[Conjugate|Identity]]
| <syntaxhighlight lang=apl inline>+</source>  || [[Add]]                                      || [[Conjugate|Identity]]
|-
|-
| <source lang=apl inline>-</source>  || [[Subtract]]                                  || [[Negate]]
| <syntaxhighlight lang=apl inline>-</source>  || [[Subtract]]                                  || [[Negate]]
|-
|-
| <source lang=apl inline>×</source>  || [[Multiply]]                                  || [[Sign]]
| <syntaxhighlight lang=apl inline>×</source>  || [[Multiply]]                                  || [[Sign]]
|-
|-
| <source lang=apl inline>÷</source>  || [[Divide]]                                    || [[Reciprocal]]
| <syntaxhighlight lang=apl inline>÷</source>  || [[Divide]]                                    || [[Reciprocal]]
|-
|-
| <source lang=apl inline>*</source>  || [[Power]]                                    || [[Exponential]]
| <syntaxhighlight lang=apl inline>*</source>  || [[Power]]                                    || [[Exponential]]
|-
|-
| <source lang=apl inline>⍟</source>  || [[Log]]                                      || [[Natural log]]
| <syntaxhighlight lang=apl inline>⍟</source>  || [[Log]]                                      || [[Natural log]]
|-
|-
| <source lang=apl inline>|</source>  || [[Residue]]                                  || [[Absolute value]]
| <syntaxhighlight lang=apl inline>|</source>  || [[Residue]]                                  || [[Absolute value]]
|-
|-
| <source lang=apl inline>⊥</source>  || [[Decode]]                                    || Pack
| <syntaxhighlight lang=apl inline>⊥</source>  || [[Decode]]                                    || Pack
|-
|-
| <source lang=apl inline>⊤</source>  || [[Encode]]                                    || Unpack
| <syntaxhighlight lang=apl inline>⊤</source>  || [[Encode]]                                    || Unpack
|-
|-
| <source lang=apl inline>?</source>  || [[Deal]]                                      || [[Roll]]
| <syntaxhighlight lang=apl inline>?</source>  || [[Deal]]                                      || [[Roll]]
|-
|-
| <source lang=apl inline>○</source>  || [[Circle function|Circle]] (sin, cos, ...)    || [[Pi times]]
| <syntaxhighlight lang=apl inline>○</source>  || [[Circle function|Circle]] (sin, cos, ...)    || [[Pi times]]
|-
|-
| <source lang=apl inline>⌹</source>  || [[Solve]]                                    || [[Matrix Inverse]]
| <syntaxhighlight lang=apl inline>⌹</source>  || [[Solve]]                                    || [[Matrix Inverse]]
|-
|-
| <source lang=apl inline>⌈</source>  || [[Max]]                                      || [[Ceiling]]
| <syntaxhighlight lang=apl inline>⌈</source>  || [[Max]]                                      || [[Ceiling]]
|-
|-
| <source lang=apl inline>⌊</source>  || [[Min]]                                      || [[Floor]]
| <syntaxhighlight lang=apl inline>⌊</source>  || [[Min]]                                      || [[Floor]]
|-
|-
| <source lang=apl inline><</source>  || [[Less than]]                                || [[Enclose]]
| <syntaxhighlight lang=apl inline><</source>  || [[Less than]]                                || [[Enclose]]
|-
|-
| <source lang=apl inline>≤</source>  || [[Less than or Equal to]]                    ||
| <syntaxhighlight lang=apl inline>≤</source>  || [[Less than or Equal to]]                    ||
|-
|-
| <source lang=apl inline>=</source>  || [[Equal to]]                                  ||
| <syntaxhighlight lang=apl inline>=</source>  || [[Equal to]]                                  ||
|-
|-
| <source lang=apl inline>></source>  || [[Greater than]]                              || [[Disclose]]
| <syntaxhighlight lang=apl inline>></source>  || [[Greater than]]                              || [[Disclose]]
|-
|-
| <source lang=apl inline>≥</source>  || [[Greater than or Equal to]]                  ||
| <syntaxhighlight lang=apl inline>≥</source>  || [[Greater than or Equal to]]                  ||
|-
|-
| <source lang=apl inline>≠</source>  || [[Not equal to]]                              ||
| <syntaxhighlight lang=apl inline>≠</source>  || [[Not equal to]]                              ||
|-
|-
| <source lang=apl inline>⍋</source>  || [[Bins]]                                      || [[Grade up]]
| <syntaxhighlight lang=apl inline>⍋</source>  || [[Bins]]                                      || [[Grade up]]
|-
|-
| <source lang=apl inline>⍒</source>  ||                                              || [[Grade down]]
| <syntaxhighlight lang=apl inline>⍒</source>  ||                                              || [[Grade down]]
|-
|-
| <source lang=apl inline>≡</source>  || [[Match]]                                    || [[Depth]]
| <syntaxhighlight lang=apl inline>≡</source>  || [[Match]]                                    || [[Depth]]
|-
|-
| <source lang=apl inline>⍳</source>  || [[Index Of|Find]]                                      || [[Interval]]
| <syntaxhighlight lang=apl inline>⍳</source>  || [[Index Of|Find]]                                      || [[Interval]]
|-
|-
| <source lang=apl inline>∊</source>  || [[Member]]                                    || [[Rake]] (like [[Enlist]])
| <syntaxhighlight lang=apl inline>∊</source>  || [[Member]]                                    || [[Rake]] (like [[Enlist]])
|-
|-
| <source lang=apl inline>^</source>  || [[And]]                                      || Stop
| <syntaxhighlight lang=apl inline>^</source>  || [[And]]                                      || Stop
|-
|-
| <source lang=apl inline>∨</source>  || [[Or]] or Cast                                || [[Type]]
| <syntaxhighlight lang=apl inline>∨</source>  || [[Or]] or Cast                                || [[Type]]
|-
|-
| <source lang=apl inline>⍕</source>  || [[Format]]                                    || [[Default Format]]
| <syntaxhighlight lang=apl inline>⍕</source>  || [[Format]]                                    || [[Default Format]]
|-
|-
| <source lang=apl inline>⍎</source>  || Execute in Context or Protected Execute      || [[Execute]]
| <syntaxhighlight lang=apl inline>⍎</source>  || Execute in Context or Protected Execute      || [[Execute]]
|-
|-
| <source lang=apl inline>%</source>  || Value in Context                              || Value (of a symbol)
| <syntaxhighlight lang=apl inline>%</source>  || Value in Context                              || Value (of a symbol)
|-
|-
| <source lang=apl inline>←</source>  || [[Assignment]] or [[Selective Assignment]]    || Result (returns from functions)
| <syntaxhighlight lang=apl inline>←</source>  || [[Assignment]] or [[Selective Assignment]]    || Result (returns from functions)
|-
|-
| <source lang=apl inline>⊃</source>  || [[Pick]]                                      || [[Raze]]
| <syntaxhighlight lang=apl inline>⊃</source>  || [[Pick]]                                      || [[Raze]]
|-
|-
| <source lang=apl inline>#</source>  || [[Choose]]                                    || [[Count]]
| <syntaxhighlight lang=apl inline>#</source>  || [[Choose]]                                    || [[Count]]
|-
|-
| <source lang=apl inline>[;]</source> ||colspan=2| [[Bracket Indexing]] (varying number of arguments)
| <syntaxhighlight lang=apl inline>[;]</source> ||colspan=2| [[Bracket Indexing]] (varying number of arguments)
|-
|-
| <source lang=apl inline>↑</source>  || [[Take]]                                      || [[Signal]]
| <syntaxhighlight lang=apl inline>↑</source>  || [[Take]]                                      || [[Signal]]
|-
|-
| <source lang=apl inline>↓</source>  || [[Drop]]                                      || Print
| <syntaxhighlight lang=apl inline>↓</source>  || [[Drop]]                                      || Print
|-
|-
| <source lang=apl inline>⌽</source>  || [[Rotate]]                                    || [[Reverse]]
| <syntaxhighlight lang=apl inline>⌽</source>  || [[Rotate]]                                    || [[Reverse]]
|-
|-
| <source lang=apl inline>⍉</source>  || [[Dyadic transpose|Transpose Axes]]          || [[Transpose]]
| <syntaxhighlight lang=apl inline>⍉</source>  || [[Dyadic transpose|Transpose Axes]]          || [[Transpose]]
|-
|-
| <source lang=apl inline>!</source>  || [[Restructure]]                              || [[Item Ravel]]
| <syntaxhighlight lang=apl inline>!</source>  || [[Restructure]]                              || [[Item Ravel]]
|-
|-
| <source lang=apl inline>⊂</source>  || Partition (a little like [[Split]])          || Partition Count
| <syntaxhighlight lang=apl inline>⊂</source>  || Partition (a little like [[Split]])          || Partition Count
|-
|-
| <source lang=apl inline>⍴</source>  || [[Reshape]]                                  || [[Shape]]
| <syntaxhighlight lang=apl inline>⍴</source>  || [[Reshape]]                                  || [[Shape]]
|-
|-
| <source lang=apl inline>⊣</source>  || [[Left]]                                      || Null (returns <source lang=apl inline>()</source>)
| <syntaxhighlight lang=apl inline>⊣</source>  || [[Left]]                                      || Null (returns <syntaxhighlight lang=apl inline>()</source>)
|-
|-
| <source lang=apl inline>⊢</source>  ||                                              || [[Right]]
| <syntaxhighlight lang=apl inline>⊢</source>  ||                                              || [[Right]]
|-
|-
| <source lang=apl inline>∪</source>  || Combine Symbols                              || Separate Symbols
| <syntaxhighlight lang=apl inline>∪</source>  || Combine Symbols                              || Separate Symbols
|-
|-
| <source lang=apl inline>,</source>  || [[Catenate]]                                  || [[Ravel]]
| <syntaxhighlight lang=apl inline>,</source>  || [[Catenate]]                                  || [[Ravel]]
|-
|-
| <source lang=apl inline>~</source>  || [[Laminate]]                                  || [[Not]]
| <syntaxhighlight lang=apl inline>~</source>  || [[Laminate]]                                  || [[Not]]
|-
|-
| <source lang=apl inline>/</source>  || [[Replicate]]                                || [[Reduce]] (+ × ⌈ ⌊ ∧ ∨)
| <syntaxhighlight lang=apl inline>/</source>  || [[Replicate]]                                || [[Reduce]] (+ × ⌈ ⌊ ∧ ∨)
|-
|-
| <source lang=apl inline>\</source>  || [[Expand]]                                    || [[Scan]] (+ × ⌈ ⌊ ∧ ∨)
| <syntaxhighlight lang=apl inline>\</source>  || [[Expand]]                                    || [[Scan]] (+ × ⌈ ⌊ ∧ ∨)
|-
|-
| <source lang=apl inline>.</source>  || [[Inner Product]] (+.×  ⌈.+  ⌊.+)          ||
| <syntaxhighlight lang=apl inline>.</source>  || [[Inner Product]] (+.×  ⌈.+  ⌊.+)          ||
|-
|-
| <source lang=apl inline>∘.</source>  || [[Outer Product]] (+ - × ÷ | ⌈ ⌊ < ≤ = ≥ > ≠) ||
| <syntaxhighlight lang=apl inline>∘.</source>  || [[Outer Product]] (+ - × ÷ | ⌈ ⌊ < ≤ = ≥ > ≠) ||
|-
|-
| <source lang=apl inline>@</source>  || [[Rank operator|Rank]]                        ||
| <syntaxhighlight lang=apl inline>@</source>  || [[Rank operator|Rank]]                        ||
|-
|-
| <source lang=apl inline>¨</source>  ||                                              || [[Each]] or Apply
| <syntaxhighlight lang=apl inline>¨</source>  ||                                              || [[Each]] or Apply
|-
|-
| <source lang=apl inline>⍨</source>  ||                                              || Bitwise
| <syntaxhighlight lang=apl inline>⍨</source>  ||                                              || Bitwise
|}
|}


Revision as of 21:10, 10 September 2022

This page is about the Morgan Stanley dialect. For the project based on APL 90 (dialect) and presented at APL90, which replaced functions with first-class blocks, see A+ (Girardot).

A+ is an extension of the A language. A was created in 1985 by Arthur Whitney, then of Morgan Stanley. At the time, various departments had a significant investment in APL applications and talent, APL being a language well-suited to the manipulation of large arrays of numbers. As technology was moving from the mainframe to distributed systems, there was a search for a suitable APL implementation to run on SunOS, the distributed platform of the period, and this prompted Whitney to create A as a statically typed dialect of APL with various novelties like symbols as a simple scalar type and the Rank operator.

Over the course of the next few years, various extensions were made to the language, culminating in A+ in 1988, with "+" referring to the graphical user interface. While an A+ development group was formally in 1992, presented the very first version of K that very same year, and by 1994, K became the official successor of A+. In 2001, the source code was made public, and various volunteers took over development until 2008. From then until 2014 it was maintained by Robert Lefkowitz.

Primitives

Glyph Dyadic Monadic
<syntaxhighlight lang=apl inline>+</source> Add Identity
<syntaxhighlight lang=apl inline>-</source> Subtract Negate
<syntaxhighlight lang=apl inline>×</source> Multiply Sign
<syntaxhighlight lang=apl inline>÷</source> Divide Reciprocal
<syntaxhighlight lang=apl inline>*</source> Power Exponential
<syntaxhighlight lang=apl inline>⍟</source> Log Natural log
</source> Residue Absolute value
<syntaxhighlight lang=apl inline>⊥</source> Decode Pack
<syntaxhighlight lang=apl inline>⊤</source> Encode Unpack
<syntaxhighlight lang=apl inline>?</source> Deal Roll
<syntaxhighlight lang=apl inline>○</source> Circle (sin, cos, ...) Pi times
<syntaxhighlight lang=apl inline>⌹</source> Solve Matrix Inverse
<syntaxhighlight lang=apl inline>⌈</source> Max Ceiling
<syntaxhighlight lang=apl inline>⌊</source> Min Floor
<syntaxhighlight lang=apl inline><</source> Less than Enclose
<syntaxhighlight lang=apl inline>≤</source> Less than or Equal to
<syntaxhighlight lang=apl inline>=</source> Equal to
<syntaxhighlight lang=apl inline>></source> Greater than Disclose
<syntaxhighlight lang=apl inline>≥</source> Greater than or Equal to
<syntaxhighlight lang=apl inline>≠</source> Not equal to
<syntaxhighlight lang=apl inline>⍋</source> Bins Grade up
<syntaxhighlight lang=apl inline>⍒</source> Grade down
<syntaxhighlight lang=apl inline>≡</source> Match Depth
<syntaxhighlight lang=apl inline>⍳</source> Find Interval
<syntaxhighlight lang=apl inline>∊</source> Member Rake (like Enlist)
<syntaxhighlight lang=apl inline>^</source> And Stop
<syntaxhighlight lang=apl inline>∨</source> Or or Cast Type
<syntaxhighlight lang=apl inline>⍕</source> Format Default Format
<syntaxhighlight lang=apl inline>⍎</source> Execute in Context or Protected Execute Execute
<syntaxhighlight lang=apl inline>%</source> Value in Context Value (of a symbol)
<syntaxhighlight lang=apl inline>←</source> Assignment or Selective Assignment Result (returns from functions)
<syntaxhighlight lang=apl inline>⊃</source> Pick Raze
<syntaxhighlight lang=apl inline>#</source> Choose Count
<syntaxhighlight lang=apl inline>[;]</source> Bracket Indexing (varying number of arguments)
<syntaxhighlight lang=apl inline>↑</source> Take Signal
<syntaxhighlight lang=apl inline>↓</source> Drop Print
<syntaxhighlight lang=apl inline>⌽</source> Rotate Reverse
<syntaxhighlight lang=apl inline>⍉</source> Transpose Axes Transpose
<syntaxhighlight lang=apl inline>!</source> Restructure Item Ravel
<syntaxhighlight lang=apl inline>⊂</source> Partition (a little like Split) Partition Count
<syntaxhighlight lang=apl inline>⍴</source> Reshape Shape
<syntaxhighlight lang=apl inline>⊣</source> Left Null (returns <syntaxhighlight lang=apl inline>()</source>)
<syntaxhighlight lang=apl inline>⊢</source> Right
<syntaxhighlight lang=apl inline>∪</source> Combine Symbols Separate Symbols
<syntaxhighlight lang=apl inline>,</source> Catenate Ravel
<syntaxhighlight lang=apl inline>~</source> Laminate Not
<syntaxhighlight lang=apl inline>/</source> Replicate Reduce (+ × ⌈ ⌊ ∧ ∨)
<syntaxhighlight lang=apl inline>\</source> Expand Scan (+ × ⌈ ⌊ ∧ ∨)
<syntaxhighlight lang=apl inline>.</source> Inner Product (+.× ⌈.+ ⌊.+)
<syntaxhighlight lang=apl inline>∘.</source> Outer Product (+ - × ÷ | ⌈ ⌊ < ≤ = ≥ > ≠)
<syntaxhighlight lang=apl inline>@</source> Rank
<syntaxhighlight lang=apl inline>¨</source> Each or Apply
<syntaxhighlight lang=apl inline>⍨</source> Bitwise

External links

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
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