Tacit programming: Difference between revisions

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→‎Trains: hooks

Adám Brudzewsky

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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 [[#trains|trains]] 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 34: / Line 36: @@
 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 2-train is an ''atop'':
+=== 3-trains ===
-{|
+A 3-train is a ''fork'', so denoted because its structure resembles a three-tines fork, or a three-pronged pitchfork. The two outer functions are applied first, and their results are used as arguments to the middle function:
-|<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 53: / Line 50: @@
 |}
-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>
+=== 2-trains ===
+Most dialects define a 2-train is an ''atop'', equivalent to the function derived using the [[Atop (operator)|Atop]] operator. The left function is applied [[monadic function|monadically]] on the result of the right function:
+{|
+|<source lang=apl>  (g h) ⍵</source>|| {{←→}} ||<source lang=apl>g (  h ⍵)</source>
+|-
+|<source lang=apl>⍺ (g h) ⍵</source>|| {{←→}} ||<source lang=apl>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> See [[Bind]].
+[[J]] instead defines the 2-train as a [[hook]], equivalent to the function derived using the [[Withe]] operator. The left function is always applied [[dyadic function|dyadically]], taking as right argument, the result of applying the right function on the right argument. If there is no left argument, the sole argument is used also as left argument:
+{|
+|<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>
 == Examples ==
@@ Line 75: / Line 130: @@
 === 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 121: / Line 175: @@
 ===The Number of the Beast===
-The following expression for computing the [https://en.wikipedia.org/wiki/666_(number) Number of the Beast] nicely illustrates how to read a train.
+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
@@ Line 128: / Line 182: @@
 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↓i</source> and the 4-train is interpreted as the atop <source lang=apl inline>(+.×⍨⊢~∘.×⍨)(1↓⍳)</source>.
+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>.
@@ Line 151: / Line 205: @@
                                                   ⍝ ⍎ 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]
+* Dyalog: [https://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]
+* [[Dfns workspace]]: [https://dfns.dyalog.com/n_tacit.htm Translation of <nowiki>[dfns]</nowiki> into tacit form]
-* APLtrainer: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code] (video)
+* [[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=A2LqqBosvY0 Function trains in APL] (video)
+* [[APLtrainer]]: [https://www.youtube.com/watch?v=kt4lMZbn-so How to read trains in Dyalog APL code] (video)
-* Dyalog Webinar: [https://www.youtube.com/watch?v=Enlh5qwwDuY?t=440 Train Spotting in Dyalog APL] (video)
+* [[APLtrainer]]: [https://www.youtube.com/watch?v=A2LqqBosvY0 Function trains in APL] (video)
-* Dyalog '13: [https://www.youtube.com/watch?v=7-93GzDqC08 Train Spotting in Version 14.0] (video)
+* [[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)
-== Documentation ==
+=== Documentation ===
-* [http://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm Announcement]
+* [https://help.dyalog.com/16.0/Content/RelNotes14.0/Function%20Trains.htm Announcement]
-* [http://help.dyalog.com/latest/Content/Language/Introduction/Trains.htm Dyalog]
+* [https://help.dyalog.com/latest/Content/Language/Introduction/Trains.htm Dyalog]
-==References==
+== References ==
 <references/>
 {{APL syntax}}[[Category:Tacit programming| ]]

Tacit programming: Difference between revisions

Tacit programming (view source)

Revision as of 19:06, 1 September 2021

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