apiel

Apiel is a subset of the APL programming language implemented in Rust.

The project exports a macro (apl!) for evaluating APL expressions from Rust code, and a CLI (apiel-cli) for interactive use.

Array Languages

APL was the first language in an "Array programming" or "Iversonian" paradigm. These languages are closer to mathematical notation than to C-like programming languages. The concepts proposed by APL inspired many similar languages, influenced the development of the functional programming paradigm, and had a giant impact on programming as a whole.

Approach

The project utilizes Yacc (Yet-Another-Compiler-Compiler) implementation in Rust through grmtools to build the lexer and parser.

apiel.l contains the tokens for the lexer, apiel.y describes the Yacc grammar. The build.rs generates Rust code for the lexer and parser. The evaluator in parse/eval.rs is a recursive match over the Expr AST.

Function trains are handled via token-level preprocessing: parenthesized groups of function references are detected by the lexer and rewritten to dfn expressions before parsing.

Usage

CLI

cargo run -p apiel-cli

or RUST_LOG=debug cargo run -p apiel-cli for debugging output.

Library

use apiel::apl;

let result = apl!("+/ ⍳ 10").unwrap();  // [55.0]

// Pass data from Rust
let result = apl!("⍺ × ⍵", alpha: &[10.0], omega: &[1.0, 2.0, 3.0]).unwrap();

// Persistent environment
let mut env = apiel::Env::new();
apl!("data←⍳ 10", &mut env).unwrap();
apl!("+/ data", &mut env).unwrap();  // [55.0]

Supported Glyphs and Operations

Scalar Functions

Glyph	Monadic operation	Impl.	Dyadic operation	Impl.
+	Conjugate	✅*	Addition	✅
-	Negate	✅	Subtraction	✅
×	Direction (signum)	✅	Multiplication	✅
÷	Reciprocal	✅	Division	✅
*	Exponential	✅	Power	✅
⍟	Natural logarithm	✅	Logarithm	✅
○	Pi multiple	✅	Circular functions	✅
!	Factorial	✅	Binomial	✅
?	Roll	✅	Deal	✅
|	Magnitude	✅	Residue	✅
⌈	Ceiling	✅	Maximum	✅
⌊	Floor	✅	Minimum	✅
⌹	Matrix inverse	✅	Matrix divide	✅

* Not implemented for complex numbers

Array Functions

Glyph	Monadic operation	Impl.	Dyadic operation	Impl.
⍳	Index generate	✅	Index of	✅
⍸	Where	✅	Interval index	✅
⍴	Shape	✅	Reshape	✅
,	Ravel	✅	Catenate	✅
⌽	Reverse	✅	Rotate	✅
⍉	Transpose	✅	Dyadic transpose	✅
↑	Mix	✅	Take	✅
↓	Split	✅	Drop	✅
⍋	Grade Up	✅	-	-
⍒	Grade Down	✅	-	-
⊂	Enclose	✅	Partitioned enclose	✅
⊃	First / Disclose	✅	-	-
⊆	-	-	Partition	✅
⌷	-	-	Index	✅
⍷	-	-	Find	✅

Selection and Set Functions

Glyph	Monadic operation	Impl.	Dyadic operation	Impl.
∪	Unique	✅	Union	✅
∩	-	-	Intersection	✅
~	Not	✅	Without	✅
⊣	Same (identity)	✅	Left	✅
⊢	Same (identity)	✅	Right	✅
≡	Depth	✅	Match	✅
≢	Tally	✅	Not Match	✅

Comparison and Logic

Glyph	Monadic operation	Impl.	Dyadic operation	Impl.
=	-	-	Equal	✅
≠	-	-	Not Equal	✅
<	-	-	Less Than	✅
>	-	-	Greater Than	✅
≤	-	-	Less or Equal	✅
≥	-	-	Greater or Equal	✅
∧	-	-	And	✅
∨	-	-	Or	✅
⍲	-	-	Nand	✅
⍱	-	-	Nor	✅

Encoding

Glyph	Monadic operation	Impl.	Dyadic operation	Impl.
⊥	-	-	Decode	✅
⊤	-	-	Encode	✅

Operators (Higher-Order)

Glyph	Name	Impl.	Description
f/	Reduce	✅	Right fold: +/ 1 2 3 = 6
f\	Scan	✅	Cumulative fold: +\ 1 2 3 = 1 3 6
∘.f	Outer Product	✅	All pairs: 1 2 ∘.× 3 4
f.g	Inner Product	✅	Generalized matrix multiply
f¨	Each	✅	Apply to each element
f⍨	Commute / Selfie	✅	A f⍨ B = B f A; f⍨ B = B f B
f⍣n	Power	✅	Apply f n times
{f}∘{g}	Compose	✅	f(g(⍵))
{f}⍥{g}	Over	✅	Monadic: f(g(⍵)); Dyadic: (g ⍺) f (g ⍵)
{f}⍤k	Rank	✅	Apply f to each rank-k cell
{f}@i	At	✅	Apply f at specified indices
{f}⌸	Key	✅	Group-by: apply f to each group
(f g h)	Fork (3-train)	✅	(f ⍵) g (h ⍵) -- e.g. (+/ ÷ ≢) for average
(f g)	Atop (2-train)	✅	f (g ⍵)

Reduce, scan, outer product, inner product, and each work with all 20 primitive operators.

Language Features

Feature	Impl.	Description
← Assignment	✅	Variable binding
x+←1 Modified assignment	✅	x←x+1 shorthand, works with all operators
x[i]←v Indexed assignment	✅	Modify elements at 1-based indices
{⍵} Dfns (lambdas)	✅	Anonymous functions with ⍵ (right) and ⍺ (left) args
f←{⍵} Named functions	✅	Store and call functions by name
∇ Self-reference	✅	Recursive calls within dfns
⋄ : Guards / Statements	✅	Multi-branch conditionals and sequential execution
¯ High minus	✅	Negative number literals
'...' Strings	✅	Character vectors
Nested arrays	✅	Arrays containing arrays via ⊂
N-dimensional arrays	✅	Any rank via ⍴ reshape
Scalar extension	✅	Auto-broadcast scalars to arrays

Examples

>>> (+/ ÷ ≢) 2 4 6 8 10
6
>>> (⌈/ - ⌊/) 3 1 4 1 5 9
8
>>> +⍨ 1 2 3
2 4 6
>>> {⍵+1}⍣3 ⍳ 5
4 5 6 7 8
>>> 2 3 ⍴ ⍳ 6
1 2 3 4 5 6
>>> ⍴ 2 3 ⍴ ⍳ 6
2 3
>>> ⌽ 1 2 3 4 5
5 4 3 2 1
>>> 1 2 3 = 1 3 3
1 0 1
>>> {⍵<2: ⍵ ⋄ (∇ ⍵-1)+∇ ⍵-2} 10
55
>>> ∧/ 1 1 1 0
0
>>> {≢⍵}⌸ 1 1 2 3 3 3
2 1 3

Affiliation

This was implemented as my capstone project for the rustcamp, a Rust bootcamp organized by the Ukrainian Rust Community (website, linked in, telegram, github, youtube, twitter).