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== Pairing glyphs with their meaning == | == 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> (Diamond) separates statements. That is, no functions or operators can break through <source lang=apl inline>⋄</source>, just as diamonds are virtually indestructible. | ||
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<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> 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 lang=apl inline>!</source> is [[Binomial]] in addition to [[Factorial]], as the two are closely related. | ||
<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> ([[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. | |||
<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. | ||
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<source lang=apl inline>⍟</source> looks like the cross-section of 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> 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> | <source lang=apl inline>⍱</source> and <source lang=apl inline>⍲</source> 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". | ||
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<source lang=apl inline>?</source> symbolises the unknown, and thus [[roll]]s dice and [[deal]]s cards randomly. | <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]]. | <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 [[Epsilon]] which corresponds to the letter **E** for [[Enlist]] and [[Element of]]. | ||
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<source lang=apl inline>⍴</source> is the Greek letter [[Rho]] which corresponds to the letter **R** for [[Reshape]]. | <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 [[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 the 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. | |||
<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> 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. | |||
<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]]. | |||
<source lang=apl inline>⊥</source> looks like the [[base]] of a pillar. [[Antibase]] uses <source lang=apl inline>⊤</source> by analogy. | |||
<source lang=apl inline>⍝</source> looks like a [[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 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. | ||