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Tacit programming: Difference between revisions
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'''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 (<syntaxhighlight inline lang=apl>⍺ ⍵</ | '''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 (<syntaxhighlight inline lang=apl>⍺ ⍵</syntaxhighlight>) 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]]. | Dialects which implement trains include [[Dyalog APL]], [[dzaima/APL]], [[ngn/apl]] and [[NARS2000]]. | ||
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6 times 3 plus 5 | 6 times 3 plus 5 | ||
48 | 48 | ||
</ | </syntaxhighlight> | ||
== Derived functions == | == Derived functions == | ||
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3 1 4 dot 2 7 1 | 3 1 4 dot 2 7 1 | ||
17 | 17 | ||
</ | </syntaxhighlight> | ||
== Derived operators == | == Derived operators == | ||
A dyadic operator with its right operand forms a tacit monadic operator: | A dyadic operator with its right operand forms a tacit monadic operator: | ||
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1 +Twice 10 | 1 +Twice 10 | ||
12 | 12 | ||
</ | </syntaxhighlight> | ||
== Trains == | == Trains == | ||
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These rules are used for 3-trains: | These rules are used for 3-trains: | ||
{| | {| | ||
|<syntaxhighlight lang=apl> (f g h) ⍵</ | |<syntaxhighlight lang=apl> (f g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>( f ⍵) g ( h ⍵)</syntaxhighlight> | ||
|- | |- | ||
|<syntaxhighlight lang=apl>⍺ (f g h) ⍵</ | |<syntaxhighlight lang=apl>⍺ (f g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>(⍺ f ⍵) g (⍺ h ⍵)</syntaxhighlight> | ||
|} | |} | ||
The ''left tine'' of a fork can be an array: | The ''left tine'' of a fork can be an array: | ||
{| | {| | ||
|<syntaxhighlight lang=apl> (A g h) ⍵</ | |<syntaxhighlight lang=apl> (A g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>A g ( h ⍵)</syntaxhighlight> | ||
|- | |- | ||
|<syntaxhighlight lang=apl>⍺ (A g h) ⍵</ | |<syntaxhighlight lang=apl>⍺ (A g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>A g (⍺ h ⍵)</syntaxhighlight> | ||
|} | |} | ||
In APL (but not [[J]]), these rules are used for 2-trains: | In APL (but not [[J]]), these rules are used for 2-trains: | ||
{| | {| | ||
|<syntaxhighlight lang=apl> (g h) ⍵</ | |<syntaxhighlight lang=apl> (g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g ( h ⍵)</syntaxhighlight> | ||
|- | |- | ||
|<syntaxhighlight lang=apl>⍺ (g h) ⍵</ | |<syntaxhighlight lang=apl>⍺ (g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g (⍺ h ⍵)</syntaxhighlight> | ||
|} | |} | ||
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{| | {| | ||
|<syntaxhighlight lang=apl>(f g h) ⍵</ | |<syntaxhighlight lang=apl>(f g h) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g⍨∘f⍨∘h⍨ ⍵</syntaxhighlight> | ||
|- | |- | ||
|<syntaxhighlight lang=apl>(f g f) ⍵</ | |<syntaxhighlight lang=apl>(f g f) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g⍥f⍨ ⍵</syntaxhighlight> | ||
|- | |- | ||
|<syntaxhighlight lang=apl>(⊢ g f) ⍵</ | |<syntaxhighlight lang=apl>(⊢ g f) ⍵</syntaxhighlight>|| {{←→}} ||<syntaxhighlight lang=apl>g∘f⍨ ⍵</syntaxhighlight> | ||
|} | |} | ||
== Debugging == | == Debugging == | ||
In [[Dyalog APL]], analysis of trains is assisted by a [[user command]] <syntaxhighlight lang=apl inline>]Boxing on</ | In [[Dyalog APL]], analysis of trains is assisted by a [[user command]] <syntaxhighlight lang=apl inline>]Boxing on</syntaxhighlight>. This is achieved by executing the command <syntaxhighlight lang=apl inline>]Boxing on</syntaxhighlight> 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: | For example, the "accursed train" from the section below can be analysed like this: | ||
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│└───────────┴─────────────────┘│ │ | │└───────────┴─────────────────┘│ │ | ||
└───────────────────────────────┴───────┘ | └───────────────────────────────┴───────┘ | ||
</ | </syntaxhighlight> | ||
Alternatively, a train can be represented in form of a tree: | Alternatively, a train can be represented in form of a tree: | ||
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+ × ┌┴┐ | + × ┌┴┐ | ||
∘ × | ∘ × | ||
</ | </syntaxhighlight> | ||
Or fully parenthesised: | Or fully parenthesised: | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
| Line 108: | Line 108: | ||
((+.×⍨⊢~∘.×⍨)1↓⍳) ⍝ the train to be analysed | ((+.×⍨⊢~∘.×⍨)1↓⍳) ⍝ the train to be analysed | ||
(((+.×)⍨)(⊢~((∘.×)⍨)))(1↓⍳) | (((+.×)⍨)(⊢~((∘.×)⍨)))(1↓⍳) | ||
</ | </syntaxhighlight> | ||
=== Conversion to dfns === | === 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 <syntaxhighlight lang=apl inline>+∘1</ | 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 <syntaxhighlight lang=apl inline>+∘1</syntaxhighlight>) can indicate a monadic function, and in some contexts, <syntaxhighlight lang=apl inline>=</syntaxhighlight>, which can only be used dyadically, would indicate a dyadic function. The website [https://tacit.help tacit.help] provides automated translation of most tacit functions, into both monadic and dyadic, fully parenthesised dfns. | ||
== Examples == | == 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. | 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. | ||
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5 (+,-) 2 ⍝ 5±2 | 5 (+,-) 2 ⍝ 5±2 | ||
7 3 | 7 3 | ||
</ | </syntaxhighlight> | ||
=== Arithmetic mean === | === Arithmetic mean === | ||
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(+⌿÷≢) 5 4⍴⍳4 ⍝ Mean of columns in a matrix | (+⌿÷≢) 5 4⍴⍳4 ⍝ Mean of columns in a matrix | ||
1 2 3 4 | 1 2 3 4 | ||
</ | </syntaxhighlight> | ||
=== Fractions === | === Fractions === | ||
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(1∧⊢,÷)2.625 | (1∧⊢,÷)2.625 | ||
21 8 | 21 8 | ||
</ | </syntaxhighlight> | ||
Alternatively, we can convert it to the mixed fraction <math>2\tfrac{5}{8}</math> with a mixed fraction: | Alternatively, we can convert it to the mixed fraction <math>2\tfrac{5}{8}</math> with a mixed fraction: | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
(1∧0 1∘⊤,÷)2.625 | (1∧0 1∘⊤,÷)2.625 | ||
2 5 8 | 2 5 8 | ||
</ | </syntaxhighlight> | ||
=== Is it a palindrome? === | === Is it a palindrome? === | ||
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(⌽≡⊢)'racecat' | (⌽≡⊢)'racecat' | ||
0 | 0 | ||
</ | </syntaxhighlight> | ||
=== Split delimited text === | === Split delimited text === | ||
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│space│delimited│text│ | │space│delimited│text│ | ||
└─────┴─────────┴────┘ | └─────┴─────────┴────┘ | ||
</ | </syntaxhighlight> | ||
=== Component of a vector in the direction of another vector === | === Component of a vector in the direction of another vector === | ||
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3 5 2 InDirOf 0 0 1 ⍝ Trivial example | 3 5 2 InDirOf 0 0 1 ⍝ Trivial example | ||
0 0 2 | 0 0 2 | ||
</ | </syntaxhighlight> | ||
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]]. | ||
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((+.×⍨⊢~∘.×⍨)1↓⍳)17 ⍝ Accursed train | ((+.×⍨⊢~∘.×⍨)1↓⍳)17 ⍝ Accursed train | ||
666 | 666 | ||
</ | </syntaxhighlight> | ||
First, <syntaxhighlight lang=apl inline>((+.×⍨⊢~∘.×)1↓⍳)</ | First, <syntaxhighlight lang=apl inline>((+.×⍨⊢~∘.×)1↓⍳)</syntaxhighlight> is supplied with only one argument <syntaxhighlight lang=apl inline>17</syntaxhighlight> and is thus interpreted monadically. | ||
Second, <syntaxhighlight lang=apl inline>(+.×⍨⊢~∘.×⍨)1↓⍳</ | Second, <syntaxhighlight lang=apl inline>(+.×⍨⊢~∘.×⍨)1↓⍳</syntaxhighlight> is a 4-train: reading right-to-left, the last 3 components are interpreted as the fork <syntaxhighlight lang=apl inline>1↓⍳</syntaxhighlight> and the 4-train is interpreted as the atop <syntaxhighlight lang=apl inline>(+.×⍨⊢~∘.×⍨)(1↓⍳)</syntaxhighlight>. | ||
Similarly, <syntaxhighlight lang=apl inline>(+.×⍨⊢~∘.×⍨)</ | Similarly, <syntaxhighlight lang=apl inline>(+.×⍨⊢~∘.×⍨)</syntaxhighlight> is also a 4-train and interpreted as the atop <syntaxhighlight lang=apl inline>+.×⍨(⊢~∘.×⍨)</syntaxhighlight>. | ||
Thus the accursed train is interpreted as <syntaxhighlight lang=apl inline>((+.×⍨(⊢~∘.×⍨))(1↓⍳))17</ | Thus the accursed train is interpreted as <syntaxhighlight lang=apl inline>((+.×⍨(⊢~∘.×⍨))(1↓⍳))17</syntaxhighlight>. Having read the train, we now evaluate it monadically. | ||
<syntaxhighlight lang=apl> | <syntaxhighlight lang=apl> | ||
((+.×⍨(⊢~∘.×⍨))(1↓⍳))17 ⍝ Accursed train as an atop over a fork atop a fork | ((+.×⍨(⊢~∘.×⍨))(1↓⍳))17 ⍝ Accursed train as an atop over a fork atop a fork | ||
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+.×⍨2 3 5 7 11 13 17 ⍝ numbers 2 through 17 without those appearing in their multiplication table are primes | +.×⍨2 3 5 7 11 13 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 | 666 ⍝ the sum of the squares of the primes up to 17 | ||
</ | </syntaxhighlight> | ||
Note that <syntaxhighlight lang=apl inline>((⊢⍨∘.×⍨)1↓⍳)</ | Note that <syntaxhighlight lang=apl inline>((⊢⍨∘.×⍨)1↓⍳)</syntaxhighlight> is a train computing primes up to the given input. | ||
A more satisfying variation of the accursed train is the following. | A more satisfying variation of the accursed train is the following. | ||
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⍎'((+.×⍨⊢~∘.×⍨)1↓⍳)17' ⍝ , evaluation | ⍎'((+.×⍨⊢~∘.×⍨)1↓⍳)17' ⍝ , evaluation | ||
666 ⍝ ⍎ executes original Accursed train | 666 ⍝ ⍎ executes original Accursed train | ||
</ | </syntaxhighlight> | ||
== External links == | == External links == | ||