Tacit programming: Difference between revisions

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Move some material to a dedicated page on trains

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-Tacit functions apply to implicit arguments following a small set of rules. This is in contrast to the explicit use of arguments in [[dfns]] (<source inline lang=apl>⍺ ⍵</source>) and [[tradfns]] (which have named arguments). Known dialects which implement trains are [[Dyalog APL]], [[dzaima/APL]], [[ngn/apl]] and [[NARS2000]].
+'''Tacit programming''', also called '''[[wikipedia:Tacit_programming|point-free style]]''', refers to usage of tacit [[function]]s that are defined in terms of implicit [[argument]]s. This is in contrast to the explicit use of arguments in [[dfn]]s (<source inline lang=apl>⍺ ⍵</source>) and [[tradfn]]s (which have named arguments). Some APL dialects allow to combine functions into [[train]]s following a small set of rules. This allows creating complex [[derived function]]s without specifying any arguments explicitly.
+Dialects which implement trains include [[Dyalog APL]], [[dzaima/APL]], [[ngn/apl]] and [[NARS2000]].
 == Primitives ==
@@ Line 32: / Line 34: @@
 == Trains ==
-A train is a series of functions in isolation. An isolated function is either surrounded by parentheses or named. Below, <source lang=apl inline>⍺</source> and <source lang=apl inline>⍵</source> refer to the arguments of the train. <source lang=apl inline>f</source>, <source lang=apl inline>g</source>, and <source lang=apl inline>h</source> are functions (which themselves can be tacit or not), and <source lang=apl inline>A</source> is an array. The arguments are processed by the following rules:
+A [[train]] is a series of functions in isolation. An isolated function is either surrounded by parentheses or named.
-A 2-train is an ''atop'':
+These rules are used for 3-trains:
-{|
-|<source lang=apl>  (g h) ⍵</source>|| {{←→}} ||<source lang=apl>g (  h ⍵)</source>
-|-
-|<source lang=apl>⍺ (g h) ⍵</source>|| {{←→}} ||<source lang=apl>g (⍺ h ⍵)</source>
-|}
-A 3-train is a ''fork'':
 {|
 |<source lang=apl>  (f g h) ⍵</source>|| {{←→}} ||<source lang=apl>(  f ⍵) g (  h ⍵)</source>
@@ Line 48: / Line 44: @@
 The ''left tine'' of a fork can be an array:
 {|
-|<source lang=apl>  (A g h)</source>|| {{←→}} ||<source lang=apl>A g (  h ⍵)</source>
+|<source lang=apl>  (A g h) ⍵</source>|| {{←→}} ||<source lang=apl>A g (  h ⍵)</source>
 |-
 |<source lang=apl>⍺ (A g h) ⍵</source>|| {{←→}} ||<source lang=apl>A g (⍺ h ⍵)</source>
 |}
-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>
+In APL (but not [[J]]), these rules are used for 2-trains:
+{|
+|<source lang=apl>  (g h) ⍵</source>|| {{←→}} ||<source lang=apl>g (  h ⍵)</source>
+|-
+|<source lang=apl>⍺ (g h) ⍵</source>|| {{←→}} ||<source lang=apl>g (⍺ h ⍵)</source>
+|}
+== Debugging ==
+In [[Dyalog APL]], analysis of trains is assisted by a [[user command]] <source lang=apl inline>]Boxing on</source>. This is achieved by executing the command <source lang=apl inline>]Boxing on</source> and then entering a train without any parameters. A structure of the train will be displayed.
+For example, the "accursed train" from the section below can be analysed like this:
+<source lang=apl>
+      ]Boxing on
+Was OFF
+      ((+.×⍨⊢~∘.×⍨)1↓⍳)     ⍝ the train to be analysed
+┌───────────────────────────────┬───────┐
+│┌───────────┬─────────────────┐│┌─┬─┬─┐│
+││┌───────┬─┐│┌─┬─┬───────────┐│││1│↓│⍳││
+│││┌─┬─┬─┐│⍨│││⊢│~│┌───────┬─┐│││└─┴─┴─┘│
+││││+│.│×││ │││ │ ││┌─┬─┬─┐│⍨││││       │
+│││└─┴─┴─┘│ │││ │ │││∘│.│×││ ││││       │
+││└───────┴─┘││ │ ││└─┴─┴─┘│ ││││       │
+││           ││ │ │└───────┴─┘│││       │
+││           │└─┴─┴───────────┘││       │
+│└───────────┴─────────────────┘│       │
+└───────────────────────────────┴───────┘
+</source>
+Alternatively, a train can be represented in form of a tree:
+<source lang=apl>
+      ]Boxing on -trains=tree
+Was ON -trains=box
+      ((+.×⍨⊢~∘.×⍨)1↓⍳)     ⍝ the train to be analysed
+     ┌───┴───┐
+   ┌─┴─┐   ┌─┼─┐
+   ⍨ ┌─┼─┐ 1 ↓ ⍳
+ ┌─┘ ⊢ ~ ⍨
+ .     ┌─┘
+┌┴┐    .
++ ×   ┌┴┐
+      ∘ ×
+</source>
+Or fully parenthesised:
+<source lang=apl>
+      ]Boxing on -trains=parens
+Was OFF -trains=box
+      ((+.×⍨⊢~∘.×⍨)1↓⍳)     ⍝ the train to be analysed
+(((+.×)⍨)(⊢~((∘.×)⍨)))(1↓⍳)
+</source>
+=== Conversion to dfns ===
+It can help understanding to convert a tacit function to a dfn. For many tacit functions, it is not immediately clear if the intention of the function is to be used monadically or dyadically, or even both. Such knowledge can be conveyed by comments, but sometimes it is possible to spot patterns that are exclusively monadic or dyadic: A function with a bound argument (for example <source lang=apl inline>+∘1</source>) can indicate a monadic function, and in some contexts, <source lang=apl inline>=</source>, which can only be used dyadically, would indicate a monadic function. The website [https://tacit.help tacit.help] provides automated translation of most tacit functions, into both monadic and dyadic, fully parenthesised dfns.
 == Examples ==
 One of the major benefits of tacit programming is the ability to convey a short, well-defined idea as an isolated expression. This aids both human readability ([[semantic density]]) and the computer's ability to interpret code, potentially executing special code for particular [[idiom]]s.
@@ Line 75: / Line 121: @@
 === Fractions ===
-We can convert decimal numbers to fractions. For example, we can convert <math>2.625</math> to the improper fraction <math>21\over 8</math> with
+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>
        (1∧⊢,÷)2.625
 8
 </source>
-Alternatively, we can convert it to the mixed fraction <math>2{5\over 8}</math> with
+Alternatively, we can convert it to the mixed fraction <math>2\tfrac{5}{8}</math> with a mixed fraction:
-A mixed fraction:
 <source lang=apl>
        (1∧0 1∘⊤,÷)2.625
@@ Line 118: / Line 163: @@
 0 2
 </source>
 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
+</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 17    ⍝ numbers 2 through 17 without those appearing in their multiplication table are primes
+                           ⍝ 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
+                                                  ⍝ ⍎ executes original Accursed train
+</source>
+== See also ==
+* [[Function composition]]
 == External links ==
-== Tutorials ==
+=== Tutorials ===
-* Dyalog: [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm version 14.0 release notes]
+<div style="column-width:30em">
-* APL Cultivation: [https://chat.stackexchange.com/rooms/52405/conversation/lesson-23-transcribing-to-and-reading-trains Transcribing to and reading trains]
+==== In text form ====
-* APLtrainer: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code] (video)
+* [[Learning APL]]: [https://xpqz.github.io/learnapl/tacit.html Trainspotting]
-* APLtrainer: [https://www.youtube.com/watch?v=A2LqqBosvY0 Function trains in APL] (video)
+* [[Documentation_suites#Dyalog_APL|Dyalog documentation]]: [https://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm version 14.0 release notes]
-* Dyalog Webinar: [https://www.youtube.com/watch?v=Enlh5qwwDuY?t=440 Train Spotting in Dyalog APL] (video)
+* [[Dfns workspace]]: [https://dfns.dyalog.com/n_tacit.htm Translation of <nowiki>[dfns]</nowiki> into tacit form]
-* Dyalog '13: [https://www.youtube.com/watch?v=7-93GzDqC08 Train Spotting in Version 14.0] (video)
+* [[APL Cultivation]]: [https://chat.stackexchange.com/rooms/52405/conversation/lesson-23-transcribing-to-and-reading-trains Transcribing to and reading trains]
+* gitonthescene: [https://gist.github.com/gitonthescene/666c77ee3ed0ae0a79cf8e057584b7fd Forks: Spoon fed]
+* gitonthescene: [https://gist.github.com/gitonthescene/5e9c25ab9edd2f2ce0d5ad38d8a8b2b4 Training day]
-== Documentation ==
+==== Videos ====
-* [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm Announcement]
+* [[APLtrainer]]: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code]
-* [http://help.dyalog.com/latest/Content/Language/Introduction/Trains.htm Dyalog]
+* [[APLtrainer]]: [https://www.youtube.com/watch?v=A2LqqBosvY0 Function trains in APL]
+* [[Dyalog webinar]]: [https://www.youtube.com/watch?v=Enlh5qwwDuY?t=440 Train Spotting in Dyalog APL]
+* [[Dyalog '13]]: [https://www.youtube.com/watch?v=7-93GzDqC08 Train Spotting in Version 14.0]
+</div>
-==References==
+== References ==
 <references/>
 {{APL syntax}}[[Category:Tacit programming| ]]

Tacit programming: Difference between revisions

Tacit programming (view source)

Revision as of 15:31, 8 August 2022

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