Tacit programming
Tacit functions apply to implicit arguments following a small set of rules. This is in contrast to the explicit use of arguments in dfns (⍺ ⍵) and tradfns (which have named arguments). Known dialects which implement trains are Dyalog APL, dzaima/APL, ngn/apl and NARS2000.
Primitives
All primitive functions are tacit. Some APLs allow primitive functions to be named.
plus ← +
times ← ×
6 times 3 plus 5
48
Derived functions
Functions derived from an operator and operand are tacit.
sum ← +/
sum ⍳10
55
Trains
A train is a series of functions in isolation. An isolated function is either surrounded by parentheses or named. Arguments are processed by the following rules:
A 2-train is an atop:
(g h) ⍵ ⬄ g ( h ⍵) ⍺ (g h) ⍵ ⬄ g (⍺ h ⍵)
A 3-train is a fork:
(f g h) ⍵ ⬄ ( f ⍵) g ( h ⍵) ⍺ (f g h) ⍵ ⬄ (⍺ f ⍵) g (⍺ h ⍵)
The left tine of a fork (but not an atop) can be an array:
(A g h) ⍵ ⬄ A g ( h ⍵) ⍺ (A g h) ⍵ ⬄ A g (⍺ h ⍵)
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 idioms.
Plus and minus
(+,-)2
2 ¯2
1 2 3 (+,-) 4
5 6 7 ¯3 ¯2 ¯1
(2 3⍴0) (+,-) 1
1 1 1 ¯1 ¯1 ¯1
1 1 1 ¯1 ¯1 ¯1
Arithmetic mean
(+⌿÷≢) ⍳10 ⍝ Mean of the first ten integers
5.5
(+⌿÷≢) 5 4⍴⍳4 ⍝ Mean of columns in a matrix
1 2 3 4
Top-heavy fraction as decimal
(1∧⊢,÷) 1.125 9 8
Is it a palindrome?
(⌽≡⊢)'racecar'
1
(⌽≡⊢)'racecat'
0
Split delimited text
','(≠⊆⊢)'comma,delimited,text'
┌─────┬─────────┬────┐
│comma│delimited│text│
└─────┴─────────┴────┘
' '(≠⊆⊢)'space delimited text'
┌─────┬─────────┬────┐
│space│delimited│text│
└─────┴─────────┴────┘
Component of a vector in the direction of another vector
Sometimes a train can make an expression nicely resemble its equivalent definition in traditional mathematical notation. As an example, here is a program to compute the component of a vector a in the direction of another vector b.
Sqrt ← *∘.5 ⍝ Square root
Norm ← Sqrt+.×⍨ ⍝ Magnitude (norm) of numeric vector in Euclidean space
Unit ← ÷∘Norm⍨ ⍝ Unit vector in direction of vector ⍵
InDirOf ← (⊢×+.×)∘Unit ⍝ Component of vector ⍺ in direction of vector ⍵
3 5 2 InDirOf 0 0 1 ⍝ Trivial example
0 0 2
In particular, the definition of InDirOf resembles the definition in traditional mathematical notation:
| Traditional notation | APL |
|---|---|
(Sqrt+.×⍨) b | |
(÷∘Norm⍨) b | |
a +.× b | |
a (⊢×+.×)∘Unit b |
| APL features [edit] | |
|---|---|
| Built-ins | Primitives (functions, operators) ∙ Quad name |
| Array model | Shape ∙ Rank ∙ Depth ∙ Bound ∙ Index (Indexing) ∙ Axis ∙ Ravel ∙ Ravel order ∙ Element ∙ Scalar ∙ Vector ∙ Matrix ∙ Simple scalar ∙ Simple array ∙ Nested array ∙ Cell ∙ Major cell ∙ Subarray ∙ Empty array ∙ Prototype |
| Data types | Number (Boolean, Complex number) ∙ Character (String) ∙ Box ∙ Namespace ∙ Function array |
| Concepts and paradigms | Conformability (Scalar extension, Leading axis agreement) ∙ Scalar function (Pervasion) ∙ Identity element ∙ Complex floor ∙ Array ordering (Total) ∙ Tacit programming (Function composition, Close composition) ∙ Glyph ∙ Leading axis theory ∙ Major cell search ∙ First-class function |
| Errors | LIMIT ERROR ∙ RANK ERROR ∙ SYNTAX ERROR ∙ DOMAIN ERROR ∙ LENGTH ERROR ∙ INDEX ERROR ∙ VALUE ERROR ∙ EVOLUTION ERROR |