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'''Mnemonics''' can assist with remembering the meaning of APL [[glyph]]s where on they keyboard they are found for [[typing glyphs|typing them]]. Both of these skills are essential for an effective APL programmer. This article currently provides examples such aide-mémoires, but will be completed in due time.
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'''Mnemonics''' can assist with [[learning resources|learning]] the meaning of APL [[glyph]]s and where on they keyboard they are found for [[typing glyphs|typing them]]. Both of these skills are essential for an effective APL programmer. This article provides such aide-mémoires.
== Pairing glyphs with their meaning ==
 
Many glyphs have meaning [[Comparison_with_traditional_mathematics#Identical|identical to their mathematical counterparts]].
 
<source lang=apl inline>⋄</source> (Diamond) separates statements. That is, no functions or operators can break through <source lang=apl inline>⋄</source>, just as diamonds are virtually indestructible.
 
<source lang=apl inline>⌺</source> looks like a <source lang=apl inline>⋄</source>-shaped [[Stencil]] laid on a piece of paper, <source lang=apl inline>⎕</source>.
 
<source lang=apl inline>!</source> is [[Binomial]] in addition to [[Factorial]], as the two are closely related.
 
[[File:I beam HEB 100.png|thumb|[[I-beam]] <source lang=apl inline>⌶</source> does look like an [[wikipedia:I-beam|I-beam]]]]
<source lang=apl inline>⌶</source> ([[I-beam]]) calls system services. APL was originally developed at [[IBM]], so system services were also IBM services. <source lang=apl inline>⌶</source> is an [[wikipedia:I-beam|I-beam]] and ''I-beam'' is pronounced almost identically to ''IBM''.
 
<source lang=apl inline>@</source> applies a function or substitutes elements ''[[at]]'' specific locations.


[[File:Bristol Type 223 top-view silhouette.png|thumb|right|The [[Grade]] glyphs look like [[wikipedia:supersonic transport|supersonic transport]]s]]
[[File:Bristol Type 223 top-view silhouette.png|thumb|The [[Grade]] glyphs <source lang=apl inline>⍋</source> and <source lang=apl inline>⍒</source> look like [[wikipedia:supersonic transport|supersonic transport]]s.]]
== Pairing glyphs with their meaning ==
<source lang=apl inline>⍋</source> and <source lang=apl inline>⍒</source> give the indices ([[grade]]s) needed to sort ascending and descending respectively, and look like an ascending and descending supersonic transport, respectively.
<source lang=apl inline>⍋</source> and <source lang=apl inline>⍒</source> give the indices ([[grade]]s) needed to sort ascending and descending respectively, and look like an ascending and descending supersonic transport, respectively.


<source lang=apl inline>⌽</source>, <source lang=apl inline>⊖</source>, and <source lang=apl inline>⍉</source> [[reverse]] or [[transpose]] an array over a given [[axis]]. The <source lang=apl inline>○</source> part of the glyphs symbolise the array, while the line component (<source lang=apl inline>|</source>, <source lang=apl inline>\</source>, or <source lang=apl inline>-</source>) indicates the line across which the reversal/transposal is done.
<source lang=apl inline>⌽</source>, <source lang=apl inline>⊖</source>, and <source lang=apl inline>⍉</source> [[reverse]] or [[transpose]] an array over a given [[axis]]. The <source lang=apl inline>○</source> part of the glyphs symbolise the array, while the line component (<source lang=apl inline>|</source>, <source lang=apl inline>\</source>, or <source lang=apl inline>-</source>) indicates the line across which the reversal/transposal is done.
[[File:TreeLog.jpg|thumb|The [[Log]] glyph <source lang=apl inline>⍟</source> looks like a tree log.]]
<source lang=apl inline>⍟</source> looks like the cross-section of a tree [[log]]
<source lang=apl inline>⍱</source> and <source lang=apl inline>⍲</source> ([[Nor]] and [[Nand]]) have the [[Not]] glyph <source lang=apl inline>~</source> on top of or overlaid on the [[Or]] glyph <source lang=apl inline>∨</source> and [[And]] glyph <source lang=apl inline>∧</source> respectively.
<source lang=apl inline>×</source> can be seen as an <math>x</math> when monadic, indicating the unknown [[sign]] to be determined.
<source lang=apl inline>+</source> negates the imaginary part (that is, it [[conjugate]]s) by analogy to monadic <source lang=apl inline>-</source> which negates both the real and the imaginary parts.
<source lang=apl inline>÷</source> takes a default left argument of <source lang=apl inline>1</source> (thus computing the [[reciprocal]]), that being the [[identity element]] of [[division]].


<source lang=apl inline>⌹</source> is [[matrix divide]] with a <source lang=apl inline>⎕</source> symbolising a matrix and an inscribed <source lang=apl inline>÷</source> for "divide".
<source lang=apl inline>⌹</source> is [[matrix divide]] with a <source lang=apl inline>⎕</source> symbolising a matrix and an inscribed <source lang=apl inline>÷</source> for "divide".
<source lang=apl inline>?</source> symbolises the unknown, and thus [[roll]]s dice and [[deal]]s cards randomly.
<source lang=apl inline>⍺</source> and <source lang=apl inline>⍵</source> are the leftmost and rightmost letters of the [[wikipedia:Greek alphabet|Greek alphabet]]. They therefore denote the left and right arguments of [[dfn]]s, respectively.
<source lang=apl inline>∊</source> is the Greek letter [[Epsilon]] which corresponds to the letter ''E'' for [[Enlist]] and [[Element of]].
<source lang=apl inline>⍴</source> is the Greek letter [[Rho]] which corresponds to the letter ''R'' for [[Reshape]].
<source lang=apl inline>~</source> is [[Not]] when monadic, but its dyadic form, [[Without]], can also be remembered as ''but not''.
<source lang=apl inline>⍨</source> is a monadic operator that looks like a face. When its derived function is applied monadically, it can be called ''[[self]]ie'', in that it applies the operand function to the argument with the argument itself as left argument too.
<source lang=apl inline>↑</source> and <source lang=apl inline>↓</source> ([[Mix]] and [[Split]]) increase and decrease rank (if possible) when used monadically.
<source lang=apl inline>↓</source> [[drop]]s elements, and so it points down, the direction in which things are dropped. Take uses <source lang=apl inline>↑</source> by analogy.
<source lang=apl inline>⍳</source> is the Greek letter [[Iota]] which corresponds to the letter ''I'' for [[Index generator]] and [[Index of]].
<source lang=apl inline>⍸</source> is also the Greek letter [[Iota]] which corresponds to the letter ''I'' for [[Indices]] and [[Interval Index]].
<source lang=apl inline>○</source> is a circle for [[Circular]] functions and the ratio between the circumference and the diameter of a circle, [[Pi times|Pi]].
<source lang=apl inline>⍥</source> and <source lang=apl inline>⍤</source> ([[Over]] and [[Atop]]) both apply the left operand after the right operand. However, <source lang=apl inline>⍥</source> has a larger "circle of influence" in that it applies its right operand twice (once on each argument) while <source lang=apl inline>⍤</source> only applies it once (between the arguments).
<source lang=apl inline>*</source> and <source lang=apl inline>⍣</source> repeatedly apply multiplication and a function, respectively. The star symbolises [[power (function)]]/[[power (operator)]].
<source lang=apl inline>←</source> [[assign]]s by putting the value on its right into the name on its left.
<source lang=apl inline>→</source> points at the destination it is [[branch]]ing to.
<source lang=apl inline>⍬</source> ([[Zilde]]) is a combination of <source lang=apl inline>~</source> for [[Without]] and <source lang=apl inline>0</source> indicating numbers. Indeed, it is the "vector without numbers", equivalent to <source lang=apl inline>0~0</source>.
<source lang=apl inline>⊣</source> and <source lang=apl inline>⊢</source> point a finger towards the [[left]] and [[right]], which are exactly the argument they, respectively, return.
[[File:Computer console.jpg|thumb|The [[Quad]] glyph <source lang=apl inline>⎕</source> looks like a console.]]
<source lang=apl inline>⎕</source> is the prefix for all [[system name]]s, and also also manages input from the console as well as output to the console. For that, it is a stylised console. <source lang=apl inline>⍞</source> looks like a <source lang=apl inline>⎕</source> with a quote <source lang=apl inline>'</source> indicating [[string]] input and message output.
<source lang=apl inline>⌈</source> and <source lang=apl inline>⌊</source> are pictograms of a wall with a piece of [[ceiling]] and [[floor]], respectively.
<source lang=apl inline>⌈</source> and <source lang=apl inline>⌊</source> can also be seen as indicators on a vertical number line, pointing at the [[maximum]] and [[minimum]], respectively.
<source lang=apl inline>∇</source> is an upside-down Greek [[Delta]], which corresponds to the letter ''D'' for [[Defined function]] or (own) definition (for recursion).
<source lang=apl inline>⌸</source> ([[Key]]) applies a function for each collection of all elements that are [[equal]] (<source lang=apl inline>⌸</source>).
<source lang=apl inline>≡</source> can be see as a stack of layers. When used monadically, it finds the [[depth]] of an array.
<source lang=apl inline>≢</source> looks like a [[tally]] mark. It being sideways can be justified by it counting the length of the leading axis; the vertical axis of a matrix.
<source lang=apl inline>⊂</source> [[enclose]]s its argument in a layer of nesting, and [[Disclose]] uses <source lang=apl inline>⊃</source> by analogy. <source lang=apl inline>⊆</source> is exactly like <source lang=apl inline>⊂</source> except that it only does a [[conditional enclose]], namely only if the argument is [[simple]].
<source lang=apl inline>⊂</source> and <source lang=apl inline>⊆</source> enclose at specific locations, per a specification, so their dyadic forms are [[Partitioned enclose]] and [[Partition]], respectively.
<source lang=apl inline>∪</source> is a styled letter ''U'' for [[Unique]] or [[Union]] if used dyadically.
<source lang=apl inline>⊥</source> looks like the [[base]] of a pillar. [[Antibase]] uses <source lang=apl inline>⊤</source> by analogy.
[[File:Lamp bulb.png|thumb|The [[Lamp]] glyph <source lang=apl inline>⍝</source> looks like a a lamp bulb filament.]]
<source lang=apl inline>⍝</source> looks like a [[wikipedia:filament lamp|filament lamp]] and provides enlightenment by indicating [[comment]]s.
<source lang=apl inline>,</source> [[concatenate]]s arrays, much like the common punctuation symbol concatenates phrases. <source lang=apl inline>⍪</source> has an added styled row, indicating that for matrices, it concatenates additional rows.
<source lang=apl inline>.</source> is just a low dot, but performs the same operation (though generalised) as [[traditional mathematics]]' [[wikipedia:dot product|dot product]].


<source lang=apl inline>/</source> and <source lang=apl inline>⌿</source> are also called "by" which can be remembered as reduce by.
<source lang=apl inline>/</source> and <source lang=apl inline>⌿</source> are also called "by" which can be remembered as reduce by.


== Pairing glyphs/functionality with their keyboard locations ==
== Pairing glyphs/functionality with their keyboard locations ==
:''This list is incomplete; you can help by [{{fullurl:{{FULLPAGENAME}}|action=edit&section=2}} expanding it].''
Below is a US English APL keyboard layout (from [[Dyalog APL]]), annotated with short mnemonics. Some of the mnemonics are then fully explained.
Below is a US English APL keyboard layout (from [[Dyalog APL]]), annotated with short mnemonics. Some of the mnemonics are then fully explained.


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<source lang=apl inline>¨</source> applies a function to each 1 of the argument elements, so it is on <kbd>APL</kbd>+<kbd>1</kbd>.<br>
<source lang=apl inline>¨</source> applies a function to each 1 of the argument elements, so it is on <kbd>APL</kbd>+<kbd>1</kbd>.<br>
<source lang=apl inline>⌶</source> looks like a [[wikipedia:Roman numerals|Roman numeral]] 1, so it also lives on the <kbd>1</kbd>.
<source lang=apl inline>⌶</source> looks like a [[wikipedia:Roman numerals|Roman numeral]] 1, so it also lives on the <kbd>1</kbd>.
<source lang=apl inline>¯</source>, <source lang=apl inline><</source>, <source lang=apl inline>≤</source>, <source lang=apl inline>=</source>, <source lang=apl inline>≥</source>, <source lang=apl inline>></source>, and <source lang=apl inline>≠</source> form a block. The number line 1–9 (because 0 on the far right) is split into two [[equal]] halves by <kbd>5</kbd> so that gives <source lang=apl inline>=</source>. <kbd>4</kbd> and <kbd>6</kbd> are slightly less and more, respectively, so they give <source lang=apl inline>≤</source> and <source lang=apl inline>≥</source>. <kbd>3</kbd> and <kbd>7</kbd> are much less and more, respectively, so they give <source lang=apl inline><</source> and <source lang=apl inline>></source>. Finally, <kbd>2</kbd> is so much less that it is negative, giving the negative sign <source lang=apl inline>¯</source>, and <kbd>8</kbd> is so much greater that it is completely [[not equal|unequal]], <source lang=apl inline>≠</source>.
{{APL development}}{{APL glyphs}}
{{APL development}}{{APL glyphs}}
[[Category:APL character set]]
[[Category:APL character set]]

Revision as of 23:17, 26 April 2022

Mnemonics can assist with learning the meaning of APL glyphs and where on they keyboard they are found for typing them. Both of these skills are essential for an effective APL programmer. This article provides such aide-mémoires.

Pairing glyphs with their meaning

Many glyphs have meaning identical to their mathematical counterparts.

(Diamond) separates statements. That is, no functions or operators can break through , just as diamonds are virtually indestructible.

looks like a -shaped Stencil laid on a piece of paper, .

! is Binomial in addition to Factorial, as the two are closely related.

I-beam does look like an I-beam

(I-beam) calls system services. APL was originally developed at IBM, so system services were also IBM services. is an I-beam and I-beam is pronounced almost identically to IBM.

@ applies a function or substitutes elements at specific locations.

The Grade glyphs and look like supersonic transports.

and give the indices (grades) needed to sort ascending and descending respectively, and look like an ascending and descending supersonic transport, respectively.

, , and reverse or transpose an array over a given axis. The part of the glyphs symbolise the array, while the line component (|, \, or -) indicates the line across which the reversal/transposal is done.

The Log glyph looks like a tree log.

looks like the cross-section of a tree log

and (Nor and Nand) have the Not glyph ~ on top of or overlaid on the Or glyph and And glyph respectively.

× can be seen as an when monadic, indicating the unknown sign to be determined.

+ negates the imaginary part (that is, it conjugates) by analogy to monadic - which negates both the real and the imaginary parts.

÷ takes a default left argument of 1 (thus computing the reciprocal), that being the identity element of division.

is matrix divide with a symbolising a matrix and an inscribed ÷ for "divide".

? symbolises the unknown, and thus rolls dice and deals cards randomly.

and are the leftmost and rightmost letters of the Greek alphabet. They therefore denote the left and right arguments of dfns, respectively.

is the Greek letter Epsilon which corresponds to the letter E for Enlist and Element of.

is the Greek letter Rho which corresponds to the letter R for Reshape.

~ is Not when monadic, but its dyadic form, Without, can also be remembered as but not.

is a monadic operator that looks like a face. When its derived function is applied monadically, it can be called selfie, in that it applies the operand function to the argument with the argument itself as left argument too.

and (Mix and Split) increase and decrease rank (if possible) when used monadically.

drops elements, and so it points down, the direction in which things are dropped. Take uses by analogy.

is the Greek letter Iota which corresponds to the letter I for Index generator and Index of.

is also the Greek letter Iota which corresponds to the letter I for Indices and Interval Index.

is a circle for Circular functions and the ratio between the circumference and the diameter of a circle, Pi.

and (Over and Atop) both apply the left operand after the right operand. However, has a larger "circle of influence" in that it applies its right operand twice (once on each argument) while only applies it once (between the arguments).

* and repeatedly apply multiplication and a function, respectively. The star symbolises power (function)/power (operator).

assigns by putting the value on its right into the name on its left.

points at the destination it is branching to.

(Zilde) is a combination of ~ for Without and 0 indicating numbers. Indeed, it is the "vector without numbers", equivalent to 0~0.

and point a finger towards the left and right, which are exactly the argument they, respectively, return.

The Quad glyph looks like a console.

is the prefix for all system names, and also also manages input from the console as well as output to the console. For that, it is a stylised console. looks like a with a quote ' indicating string input and message output.

and are pictograms of a wall with a piece of ceiling and floor, respectively.

and can also be seen as indicators on a vertical number line, pointing at the maximum and minimum, respectively.

is an upside-down Greek Delta, which corresponds to the letter D for Defined function or (own) definition (for recursion).

(Key) applies a function for each collection of all elements that are equal ().

can be see as a stack of layers. When used monadically, it finds the depth of an array.

looks like a tally mark. It being sideways can be justified by it counting the length of the leading axis; the vertical axis of a matrix.

encloses its argument in a layer of nesting, and Disclose uses by analogy. is exactly like except that it only does a conditional enclose, namely only if the argument is simple.

and enclose at specific locations, per a specification, so their dyadic forms are Partitioned enclose and Partition, respectively.

is a styled letter U for Unique or Union if used dyadically.

looks like the base of a pillar. Antibase uses by analogy.

The Lamp glyph looks like a a lamp bulb filament.

looks like a filament lamp and provides enlightenment by indicating comments.

, concatenates arrays, much like the common punctuation symbol concatenates phrases. has an added styled row, indicating that for matrices, it concatenates additional rows.

. is just a low dot, but performs the same operation (though generalised) as traditional mathematics' dot product.

/ and are also called "by" which can be remembered as reduce by.

Pairing glyphs/functionality with their keyboard locations

This list is incomplete; you can help by expanding it.

Below is a US English APL keyboard layout (from Dyalog APL), annotated with short mnemonics. Some of the mnemonics are then fully explained.

Keyboard Mnemonics.png

begins new APL expressions just like ` button begins the main section of the keyboard.
is a modified version of , so it is Shift+.

¨ applies a function to each 1 of the argument elements, so it is on APL+1.
looks like a Roman numeral 1, so it also lives on the 1.

¯, <, , =, , >, and form a block. The number line 1–9 (because 0 on the far right) is split into two equal halves by 5 so that gives =. 4 and 6 are slightly less and more, respectively, so they give and . 3 and 7 are much less and more, respectively, so they give < and >. Finally, 2 is so much less that it is negative, giving the negative sign ¯, and 8 is so much greater that it is completely unequal, .


APL development [edit]
Interface SessionTyping glyphs (on Linux) ∙ FontsText editors
Publications IntroductionsLearning resourcesSimple examplesAdvanced examplesMnemonicsISO 8485:1989ISO/IEC 13751:2001A Dictionary of APLCase studiesDocumentation suitesBooksPapersVideosAPL Quote QuadVector journalTerminology (Chinese, German) ∙ Neural networksError trapping with Dyalog APL (in forms)
Sharing code Backwards compatibilityAPLcartAPLTreeAPL-CationDfns workspaceTatinCider
Implementation ResourcesOpen-sourceMagic functionPerformanceAPL hardware
Developers Timeline of corporationsAPL2000DyalogIBMIPSASTSC
APL glyphs [edit]
Information GlyphTyping glyphs (on Linux) ∙ UnicodeFontsMnemonicsOverstrikesMigration level
Individual glyphs Jot () ∙ Right Shoe () ∙ Up Arrow () ∙ Zilde () ∙ High minus (¯) ∙ Dot (.) ∙ Del ()