BasedPL, the Based-array Programming Language, is an array language derived from APL, with ideas from J and BQN. Its notation aims to be simple and consistent. Most of this documentation calls it BPL. BPL is written in Rust and comes as a native executable, a Jupyter kernel and a Python API.
For APL users, the main choices are:
- Based arrays, as in BQN: numbers, characters and functions are atoms; enclosure always adds a layer.
- Vectors in brackets, and grouping by spaces.
[a b c]is a vector, anda+b × c+dis(a+b)×(c+d). A run that ends in a function is a train. For example,+/÷≢ xis the mean ofx, and2×doubles its argument.0⌷vandv₀both select the first item ofv. - Leading-axis broadcasting, including expansion of length-1 axes, plus string keys and names on axes.
- Exact integers and rationals alongside approximate real and complex numbers.
- Dfns, trains and operators, with additions such as Under, iteration histories, windows and function arrays.
Positions and axes count from 0, as in BQN and Python. Approximate comparisons use tolerance 1E¯14. See the language principles for why BPL works this way, the glyph reference for Dyalog differences and Arrays for the array model.
pip install basedpl
bplAt the prompt, define a mean and apply it:
avg←+/÷≢
avg 2 4 95
Use bpl -e 'avg←+/÷≢ ⋄ avg 2 4 9' for a shell command. The command-line guide covers source files and pipes.
In the REPL, type a backtick followed by a glyph name. For example, `iota becomes ⍳ when you press Tab or type a non-letter. Abbreviations and Alt-key shortcuts are available. ]help + shows help for +. •prefs changes display settings, such as boxes and how much of a large array shows. See REPL and the glyph reference, which lists each glyph’s key.
In Jupyter, select the installed BasedPL kernel. Cells share definitions and support completion, Shift-Tab help and interruption. You can also use %%bpl cells in a Python notebook. See Using BPL notebooks.
APL is a language built around operations on whole arrays and notation for combining functions. Here is a taste of that style in BPL.
Numbers separated by spaces form a vector. Arithmetic applies to every element:
10+1 2 311 12 13
Operators modify or combine functions. Reduce (/) turns addition into summation. ⍳10 generates 0…9:
+/⍳1045
Functions can also be combined without naming their arguments. In avg←+/÷≢, sum (+/) divided by tally (≢) defines the mean:
avg 1 2 3 42.5
To see how these ideas express an algorithm, start from “a prime has exactly two positive divisors”. Form all remainders of 1 to 50 (|⊗⍨1+⍳50), count the zeros down each column (+⌿0=), and find the positions (⍸) whose count is two. Positions count from 0. 1+ turns each position back into its number:
1+⍸2=+⌿0=|⊗⍨1+⍳502 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Getting started builds a primes function from the same divisor count, step by step, and displays the divisibility matrix along the way.
Bare numbers are approximate. Use ₓ for exact integers and r for exact fractions:
1r3+1r61ᵣ2
Complex numbers use j between real and imaginary parts. Functions such as square root extend into the complex domain:
√¯40ⱼ2
See Numbers for conversion and mixed arithmetic.
Write matrix rows directly in an array literal. Leading-axis agreement lets a vector supply one offset per row:
m←[1 2 3
4 5 6]
m+10 2011 12 13
24 25 26
See array notation and broadcasting.
Axes can have names, and positions along them can have string keys. Describe the axes once, then select by key or reduce by axis name:
axes←["city":["NY" "LA"] "month":["Jan" "Feb" "Mar"]]
sales←axes:[10 20 30 ⋄ 40 50 60]
"LA" "Feb"⌷sales
+/⍠"month" sales50
["city":2]⍴["NY":60 "LA":150]
Keys and names travel with axes through operations such as transpose. Arithmetic aligns matching names and keys. See Axis keys.
A vector of counts keeps the history: one state for each count, where count 0 is the initial value. Here, double up to four times:
2×⍣(⍳5) 11 2 4 8 16
Under (⌾) transforms the argument, applies a function, then reverses the transformation. Scale by ten, floor, and scale back to round down to tenths:
⌊⌾ 10× 1.25 2.781.2 2.7
Explore iteration and inverses, Under, windows and function selection.
Primes and factorisation are built in:
⨸360ₓ[2 2 2 3 3 5]ₓ
Polynomials support coefficients, roots and evaluation. Polynomial functions can be differentiated: for f(x) = 1 + 2x + 3x², f′(2) = 14.
f←[1 2 3]ₓ⌻ ⋄ f∂2ₓ14ₓ
Probability distributions provide sampling, density, CDF and quantiles. Two fair coin tosses give these probabilities for 0, 1 and 2 heads:
coin←2 0.5 •distribution "binomial"
coin.density 0 1 20.25 0.5 0.25
Matrix division handles linear systems and least squares.
JSON objects become keyed arrays, with dot access to their fields:
order←•json "{""price"":10.5,""qty"":2}"
order.price×order.qty21
CSV headers likewise name column vectors. Files, CSV and JSON covers reading, transforming and writing data. Regex supplies matching, captures and replacement through Rust’s regex engine.
•plot draws charts from arrays. Keys label the axes and name the lines. See Plots.
["legend":"end"]•plot sales
Build SVG from element functions and keyed attributes. Notebooks display the picture directly. The same element trees serialize to XML. See XML and SVG.
circle←•element "circle"
text←•element "text"
c←["cx":50 "cy":40 "r":25 "fill":"orange"]circle ""
t←["x":50 "y":85 "text-anchor":"middle"]text "Hello, SVG"
["width":240 "height":240]•svg [c t]
BPL functions are Python callables:
from basedpl import fn
mean = fn('+/÷≢')
mean([1, 2, 3])Arrays have .py, .np and .df conversions for Python values, NumPy and pandas. Functions also have Python names and composition operators. See the Python tutorial.
For other frontends, the process interfaces provide JSON messages and interruptible workers. The BPL library contains more algorithms, codecs, interpreters and puzzles.
Requires Python 3.10 or later and Rust 1.98 or later. On x86-64, it also requires a CPU with AVX2 (x86-64-v3). In your Python environment:
git clone https://github.com/AnswerDotAI/basedpl.git
cd basedpl
pip install .For a standalone executable without Python, run cargo install --path .. Cargo installs it in its bin directory, normally ~/.cargo/bin. Put that directory on your PATH.
Install the development and documentation tools with pip install -e '.[dev]'. That also builds the extension and installs it in the editable package. The main commands are:
cargo t
python scripts/develop.py
bpl -e '2×3+4'
cargo fastfmt
pytest
ship-rs-buildAfter Rust changes, run cargo t for the Rust tests, then python scripts/develop.py to install the extension that cargo t built. Both use one compilation of the crate. The bpl command then runs the new build. cargo t stands for cargo test --features python. Run pip install -e '.[dev]' again only when the package metadata changes. Use cargo fastfmt, not cargo fmt.
Before a release, run python scripts/prep.py from the repository root. It writes the syntax highlighters’ glyph lists and the macOS keyboard layout bundle. It then runs nbdev’s prepare to export, test and clean the notebooks and render this README.
Use lowercase j in complex literals throughout tests and examples, including adapted reference cases. Reserve uppercase J for explicit input-alias tests. Keep archived upstream source unchanged.
Write literal matrices in array notation, [10 20 30 ⋄ 40 50 60], not as a reshape, 2 3⍴10 20 30 40 50 60. Keep ⍴ where the example is about reshape.
Brackets are the usual way to write a list. A bare literal list, such as 1 2 3, is a shorthand. Write a list of names in brackets, as in [a b], even where a b would also work. End an operand with a space, not with parentheses or ⊢. After a dyadic operator and a space, the whole next run is the operand. For example, ⌊⌾ 10× x needs no parentheses. Where a literal operand would run into the argument, a vector argument goes in touching brackets: f⍤1[2 3]. A single number goes in parentheses: f⍣¯2(5). Judge each line by how it reads. Report any case where none of these forms works.
A name applied to a literal touches it, as a glyph does: fib10 and 1+⌽f5. Write it that way where it’s shorter and needs no new parentheses. Keep the space where the literal would join the next part of the expression, or where a subject before the name is its left argument.
Read a selection with ⌷, as in [⍋v]⌷v. Write one literal position with a subscript, as in v₁ and v₁←0. Use . for other assignment targets, such as v.[i]←0, for record fields, such as T.name, and wherever ⌷ would be longer.