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Only [[dzaima/APL]] allows <source lang=apl inline>(A h)</source>, which it treats as <source lang=apl inline>A∘h</source>.<ref>dzaima/APL: [https://github.com/dzaima/APL/blob/ceea05e25687988ed0980a4abf4b9249b736543f/docs/differences.txt#L19 Differences from Dyalog APL]. Retrieved 09 Jan 2020.</ref> | Only [[dzaima/APL]] allows <source lang=apl inline>(A h)</source>, which it treats as <source lang=apl inline>A∘h</source>.<ref>dzaima/APL: [https://github.com/dzaima/APL/blob/ceea05e25687988ed0980a4abf4b9249b736543f/docs/differences.txt#L19 Differences from Dyalog APL]. Retrieved 09 Jan 2020.</ref> See [[Bind]]. | ||
== Examples == | == Examples == | ||
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=== Fractions === | === Fractions === | ||
We can convert decimal numbers to fractions. For example, we can convert <math>2.625</math> to the improper fraction <math>21 | We can convert decimal numbers to fractions. For example, we can convert <math>2.625</math> to the improper fraction <math>\tfrac{21}{8}</math> with | ||
<source lang=apl> | <source lang=apl> | ||
(1∧⊢,÷)2.625 | (1∧⊢,÷)2.625 | ||
21 8 | 21 8 | ||
</source> | </source> | ||
Alternatively, we can convert it to the mixed fraction <math>2{5 | Alternatively, we can convert it to the mixed fraction <math>2\tfrac{5}{8}</math> with a mixed fraction: | ||
<source lang=apl> | <source lang=apl> | ||
(1∧0 1∘⊤,÷)2.625 | (1∧0 1∘⊤,÷)2.625 | ||
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0 0 2 | 0 0 2 | ||
</source> | </source> | ||
For a more parallel comparison of the notations, see the [[Comparison_with_traditional_mathematics#Practical_example|comparison with traditional mathematics]]. | For a more parallel comparison of the notations, see the [[Comparison_with_traditional_mathematics#Practical_example|comparison with traditional mathematics]]. | ||
===The Number of the Beast=== | |||
The following expression for computing the [[wikipedia:666 (number)|number of the Beast]] (and of [[I.P. Sharp]]'s APL-based email system, [[666 BOX]]) nicely illustrates how to read a train. | |||
<source lang=apl> | |||
((+.×⍨⊢~∘.×⍨)1↓⍳)17 ⍝ Accursed train | |||
666 | |||
</source> | |||
First, <source lang=apl inline>((+.×⍨⊢~∘.×)1↓⍳)</source> is supplied with only one argument <source lang=apl inline>17</source> and is thus interpreted monadically. | |||
Second, <source lang=apl inline>(+.×⍨⊢~∘.×⍨)1↓⍳</source> is a 4-train: reading right-to-left, the last 3 components are interpreted as the fork <source lang=apl inline>1↓⍳</source> and the 4-train is interpreted as the atop <source lang=apl inline>(+.×⍨⊢~∘.×⍨)(1↓⍳)</source>. | |||
Similarly, <source lang=apl inline>(+.×⍨⊢~∘.×⍨)</source> is also a 4-train and interpreted as the atop <source lang=apl inline>+.×⍨(⊢~∘.×⍨)</source>. | |||
Thus the accursed train is interpreted as <source lang=apl inline>((+.×⍨(⊢~∘.×⍨))(1↓⍳))17</source>. Having read the train, we now evaluate it monadically. | |||
<source lang=apl> | |||
((+.×⍨(⊢~∘.×⍨))(1↓⍳))17 ⍝ Accursed train as an atop over a fork atop a fork | |||
+.×⍨(⊢~∘.×⍨)1↓⍳17 ⍝ Atop evalution | |||
+.×⍨(⊢1↓⍳17)~∘.×⍨1↓⍳17 ⍝ Fork evalution | |||
+.×⍨(1↓⍳17)~∘.×⍨1↓⍳17 ⍝ ⊢ evaluation | |||
+.×⍨2 3 5 7 11 13 15 17 ⍝ numbers 2 through 17 without those appearing in their multiplication table are primes | |||
666 ⍝ the sum of the squares of the primes up to 17 | |||
</source> | |||
Note that <source lang=apl inline>((⊢⍨∘.×⍨)1↓⍳)</source> is a train computing primes up to the given input. | |||
A more satisfying variation of the accursed train is the following. | |||
<source lang=apl> | |||
(⍎⊢,⍕∘≢)'((+.×⍨⊢~∘.×⍨)1↓⍳)' ⍝ Accursed train 2.0 | |||
⍎(⊢,⍕∘≢)'((+.×⍨⊢~∘.×⍨)1↓⍳)' ⍝ 4-train intepreted as an atop | |||
⍎(⊢'((+.×⍨⊢~∘.×⍨)1↓⍳)'),⍕∘≢'((+.×⍨⊢~∘.×⍨)1↓⍳)' ⍝ fork evaluation | |||
⍎'((+.×⍨⊢~∘.×⍨)1↓⍳)','17' ⍝ ⊢ evaluation and ⍕∘≢ evaluation | |||
⍎'((+.×⍨⊢~∘.×⍨)1↓⍳)17' ⍝ , evaluation | |||
666 ⍝ ⍎ executes original Accursed train | |||
</source> | |||
== External links == | == External links == | ||
== Tutorials == | === Tutorials === | ||
* Dyalog: [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm version 14.0 release notes] | * Dyalog: [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm version 14.0 release notes] | ||
* APL Cultivation: [https://chat.stackexchange.com/rooms/52405/conversation/lesson-23-transcribing-to-and-reading-trains Transcribing to and reading trains] | * [[APL Cultivation]]: [https://chat.stackexchange.com/rooms/52405/conversation/lesson-23-transcribing-to-and-reading-trains Transcribing to and reading trains] | ||
* APLtrainer: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code] (video) | * [[APLtrainer]]: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code] (video) | ||
* APLtrainer: [https://www.youtube.com/watch?v=A2LqqBosvY0 Function trains in APL] (video) | * [[APLtrainer]]: [https://www.youtube.com/watch?v=A2LqqBosvY0 Function trains in APL] (video) | ||
* Dyalog | * [[Dyalog webinar]]: [https://www.youtube.com/watch?v=Enlh5qwwDuY?t=440 Train Spotting in Dyalog APL] (video) | ||
* Dyalog '13: [https://www.youtube.com/watch?v=7-93GzDqC08 Train Spotting in Version 14.0] (video) | * [[Dyalog '13]]: [https://www.youtube.com/watch?v=7-93GzDqC08 Train Spotting in Version 14.0] (video) | ||
== Documentation == | === Documentation === | ||
* [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm Announcement] | * [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm Announcement] | ||
* [http://help.dyalog.com/latest/Content/Language/Introduction/Trains.htm Dyalog] | * [http://help.dyalog.com/latest/Content/Language/Introduction/Trains.htm Dyalog] | ||
==References== | == References == | ||
<references/> | <references/> | ||
{{APL syntax}}[[Category:Tacit programming| | |||
{{APL syntax}}[[Category:Tacit programming| ]] |