KlongPy: A High-Performance Array Language with Autograd

KlongPy is a Python adaptation of the Klong array language, offering high-performance vectorized operations. It prioritizes compatibility with Python, thus allowing seamless integration of Python's expansive ecosystem while retaining Klong's succinctness.

KlongPy backends include NumPy and optional PyTorch (CPU, CUDA, and Apple MPS). When PyTorch is enabled, automatic differentiation (autograd) is supported; otherwise, numeric differentiation is the default.

Full documentation: https://klongpy.org

New to v0.7.0, KlongPy now brings gradient-based programming to an already-succinct array language, so you can differentiate compact array expressions directly. It's also a batteries-included system with IPC, DuckDB-backed database tooling, web/websocket support, and other integrations exposed seamlessly from the language.

Backends include NumPy and optional PyTorch (CPU, CUDA, and Apple MPS). When PyTorch is enabled, gradients use autograd; otherwise numeric differentiation is the default.

PyTorch gradient descent (10+ lines):

import torch
x = torch.tensor(5.0, requires_grad=True)
optimizer = torch.optim.SGD([x], lr=0.1)
for _ in range(100):
    loss = x ** 2
    optimizer.zero_grad()
    loss.backward()
    optimizer.step()
print(x)  # ~0

KlongPy gradient descent (2 lines):

f::{x^2}; s::5.0
{s::s-(0.1*f:>s)}'!100   :" s -> 0"

Array languages like APL, K, and Q revolutionized finance by treating operations as data transformations, not loops. KlongPy brings this philosophy to machine learning: gradients become expressions you compose, not boilerplate you maintain. The result is a succint mathematical-like notation that is automatically extended to machine learning.

Quick Install

# REPL + NumPy backend (pick one option below)
pip install "klongpy[repl]"
kgpy

# Enable torch backend (autograd + GPU)
pip install "klongpy[torch]"
kgpy --backend torch

# Everything (web, db, websockets, torch, repl)
pip install "klongpy[all]"

REPL

$ kgpy
Welcome to KlongPy REPL v0.7.0
Author: Brian Guarraci
Web: http://klongpy.org
Backend: torch (mps)
]h for help; Ctrl-D or ]q to quit

$>

Why KlongPy?

For Quants and Traders

Optimize portfolios with gradients in a language designed for arrays:

:" Portfolio optimization: gradient of Sharpe ratio"
returns::[0.05 0.08 0.03 0.10]      :" Annual returns per asset"
vols::[0.15 0.20 0.10 0.25]         :" Volatilities per asset"
w::[0.25 0.25 0.25 0.25]            :" Portfolio weights"

sharpe::{(+/x*returns)%((+/((x^2)*(vols^2)))^0.5)}
sg::sharpe:>w                       :" Gradient of Sharpe ratio"
.d("sharpe gradient="); .p(sg)
sharpe gradient=[0.07257738709449768 0.032256484031677246 0.11693036556243896 -0.22176480293273926]

For ML Researchers

Neural networks in pure array notation:

:" Single-layer neural network with gradient descent"
.bkf(["exp"])
sigmoid::{1%(1+exp(0-x))}
forward::{sigmoid((w1*x)+b1)}
X::[0.5 1.0 1.5 2.0]; Y::[0.2 0.4 0.6 0.8]
w1::0.1; b1::0.1; lr::0.1
loss::{+/((forward'X)-Y)^2}

:" Train with multi-param gradients"
{grads::loss:>[w1 b1]; w1::w1-(lr*grads@0); b1::b1-(lr*grads@1)}'!1000
.d("w1="); .d(w1); .d(" b1="); .p(b1)
w1=1.74 b1=-2.17

For Scientists

Express mathematics directly:

:" Gradient of f(x,y,z) = x^2 + y^2 + z^2 at [1,2,3]"
f::{+/x^2}
f:>[1 2 3]
[2.0 4.0 6.0]

The Array Language Advantage

Array languages express what you want, not how to compute it. This enables automatic optimization:

Operation	Python	KlongPy
Sum an array	sum(a)	+/a
Running sum	np.cumsum(a)	+\a
Dot product	np.dot(a,b)	+/a*b
Average	sum(a)/len(a)	(+/a)%#a
Gradient	10+ lines	f:>x
Multi-param grad	20+ lines	loss:>[w b]
Jacobian	15+ lines	x∂f
Optimizer	10+ lines	{w::w-(lr*f:>w)}

KlongPy inherits from the APL family tree (APL → J → K/Q → Klong), adding Python integration and automatic differentiation.

Performance

Run the included benchmark on any backend:

kgpy --backend torch --device cpu examples/bench_compiler.kg
kgpy --backend numpy examples/bench_compiler.kg

Expression Compiler Benchmark (Apple M1 Mac Studio)

Both backends include an expression compiler that converts Klong ASTs to a backend-neutral IR, then generates platform-specific Python functions. Expressions compile once and are cached — subsequent calls pay only execution cost.

Times are per-call averages over 1000 iterations.

Operation	Elements	NumPy	Torch CPU
Arithmetic
a+b	100K	0.066 ms	0.155 ms
a*2+b	100K	0.091 ms	0.276 ms
(a+b)*(a-b)	100K	0.124 ms	0.390 ms
(a*2+b*3)%(a+1)-(b*c)	100K	0.218 ms	0.870 ms
Lambdas
{x+y}(a;b)	100K	0.074 ms	0.156 ms
{(x+y)*(x-y)}(a;b)	100K	0.129 ms	0.390 ms
{+/x*y}(a;b)	100K	0.098 ms	0.285 ms
Reduce
+/a	100K	0.065 ms	0.150 ms
+/a*b	100K	0.095 ms	0.293 ms
Scan
+\ts cumsum	10K	0.083 ms	0.054 ms
`	\ts` running max	10K	24.63 ms
`(	\ts)-ts` drawdown	10K	24.65 ms
`	/(	\ts)-ts` max drawdown	10K
Real-world
(+/p*s)%+/s VWAP	100K	0.151 ms	0.512 ms
vwap::{(+/x*y)%+/y}; vwap(p;s)	100K	0.151 ms	0.489 ms
a-(+/a)%#a de-mean	100K	0.088 ms	0.292 ms

NumPy is faster for element-wise and reduce operations on CPU. Torch excels at scan operations where it compiles to native tensor methods (cummax, cumsum) — running max is 362x faster than NumPy's interpreter fallback. Torch's full advantage appears on GPU (--device cuda or --device mps).

Complete Feature Set

KlongPy is a batteries-included platform with kdb+/Q-inspired features:

Core Language

• Vectorized Operations: NumPy/PyTorch-powered bulk array operations
• Automatic Differentiation: Native :> operator for exact gradients
• GPU Acceleration: CUDA and Apple MPS support via PyTorch
• Python Integration: Import any Python library with .py() and .pyf()

Data Infrastructure (kdb+/Q-like)

• Fast Columnar Database: Zero-copy DuckDB integration for SQL on arrays
• Inter-Process Communication: Build ticker plants and distributed systems
• Table & Key-Value Store: Persistent storage for tables and data
• Web Server: Built-in HTTP server for APIs and dashboards
• WebSockets: Connect to WebSocket servers and handle messages in KlongPy
• Timers: Scheduled execution for periodic tasks

Documentation

• Quick Start Guide: Get running in 5 minutes
• PyTorch Backend & Autograd: Complete autograd reference
• Operator Reference: All language operators
• Performance Guide: Optimization tips

Full documentation: https://briangu.github.io/klongpy

Typing Special Characters

KlongPy uses Unicode operators for mathematical notation. Here's how to type them:

Symbol	Name	Mac	Windows	Description
∇	Nabla	Option + v then select, or Character Viewer	Alt + 8711 (numpad)	Numeric gradient
∂	Partial	Option + d	Alt + 8706 (numpad)	Jacobian operator

Mac Tips:

• Option + d types ∂ directly
• For ∇, open Character Viewer with Ctrl + Cmd + Space, search "nabla"
• Or simply copy-paste: ∇ ∂

Alternative: Use the function equivalents that don't require special characters:

3∇f           :" Using nabla"
.jacobian(f;x) :" Instead of x∂f"

Syntax Cheat Sheet

Functions take up to 3 parameters, always named x, y, z:

:" Operators (right to left evaluation)"
5+3*2           :" 11 (3*2 first, then +5)"
+/[1 2 3]       :" 6  (sum: + over /)"
*/[1 2 3]       :" 6  (product: * over /)"
#[1 2 3]        :" 3  (length)"
3|5             :" 5  (max)"
3&5             :" 3  (min)"

:" Functions"
avg::{(+/x)%#x}         :" Monad (1 arg)"
dot::{+/x*y}            :" Dyad (2 args)"
clip::{(x|y)&z}         :" Triad (3 args): min(max(x,y),z)"

:" Adverbs (modifiers)"
f::{x^2}
f'[1 2 3]               :" Each: apply f to each -> [1 4 9]"
+/[1 2 3]               :" Over: fold/reduce -> 6"
+\[1 2 3]               :" Scan: running fold -> [1 3 6]"
{x@0}@'[10 20 30]       :" Each-Index: enumerate -> [0 1 2]"

:" Evaluated arrays (expressions evaluated at construction)"
a::10; b::20
[;a;b;a+b]              :" -> [10 20 30]"

:" Autograd"
f::{x^2}
3∇f                     :" Numeric gradient at x=3 -> ~6.0"
f:>3                    :" Autograd (exact with torch) at x=3 -> 6.0"
f::{+/x^2}             :" Redefine f as sum-of-squares"
f:>[1 2 3]              :" Gradient -> [2 4 6]"

:" Multi-parameter gradients"
w::2.0; b::3.0
loss::{(w^2)+(b^2)}
loss:>[w b]             :" Gradients for both -> [4.0 6.0]"

:" Jacobian (for vector functions)"
g::{x^2}                :" Element-wise square"
[1 2]∂g                 :" Jacobian matrix -> [[2 0] [0 4]]"

Examples

1. Basic Array Operations

?> a::[1 2 3 4 5]
[1 2 3 4 5]
?> a*a                    :" Element-wise square"
[1 4 9 16 25]
?> +/a                    :" Sum"
15
?> (*/a)                  :" Product"
120
?> avg::{(+/x)%#x}        :" Define average"
:monad
?> avg(a)
3.0

2. Gradient Descent

Minimize f(x) = (x-3)^2

(with PyTorch's autograd)

$ rlwrap kgpy --backend torch
?> f::{(x-3)^2}
:monad
?> s::10.0; lr::0.1
0.1
?> {s::s-(lr*f:>s); s}'!10
[8.600000381469727 7.4800004959106445 6.584000587463379 5.8672003746032715 5.293760299682617 4.835008144378662 4.468006610870361 4.174405097961426 3.9395241737365723 3.751619338989258]

(Numerical differentiation)

$ rlwrap kgpy
?> f::{(x-3)^2}
:monad
?> s::10.0; lr::0.1
0.1
?> {s::s-(lr*f:>s); s}'!10
[8.60000000104776 7.480000001637279 6.584000001220716 5.867200000887465 5.2937600006031005 4.835008000393373 4.4680064002611175 4.174405120173077 3.939524096109306 3.7516192768605094]

3. Linear Regression

:" Data: y = 2*x + 3 + noise"
X::[1 2 3 4 5]
Y::[5.1 6.9 9.2 10.8 13.1]

:" Model parameters"
w::0.0; b::0.0

:" Loss function"
mse::{(+/(((w*X)+b)-Y)^2)%#X}

:" Train with multi-parameter gradients"
lr::0.01
{grads::mse:>[w b]; w::w-(lr*grads@0); b::b-(lr*grads@1)}'!1000

.d("Learned: w="); .d(w); .d(" b="); .p(b)
Learned: w=2.01 b=2.97

4. Database Operations

?> .py("klongpy.db")
?> t::.table([[\"name\" [\"Alice\" \"Bob\" \"Carol\"]] [\"age\" [25 30 35]]])
name  age
Alice  25
Bob    30
Carol  35
?> db::.db(:{},\"T\",t)
?> db(\"SELECT * FROM T WHERE age > 27\")
name  age
Bob    30
Carol  35

5. IPC: Distributed Computing

Server:

?> avg::{(+/x)%#x}
:monad
?> .srv(8888)
1

Client:

?> f::.cli(8888)              :" Connect to server"
remote[localhost:8888]:fn
?> myavg::f(:avg)             :" Get remote function reference"
remote[localhost:8888]:fn:avg:monad
?> myavg(!1000000)            :" Execute on server"
499999.5

6. Web Server

.py("klongpy.web")
data::!10
index::{x; "Hello from KlongPy! Data: ",data}
get:::{}; get,"/",index
post:::{}
h::.web(8888;get;post)
.p("Server ready at http://localhost:8888")

$ curl http://localhost:8888
['Hello from KlongPy! Data: ' 0 1 2 3 4 5 6 7 8 9]

Installation Options

Basic Runtime (NumPy only)

pip install klongpy

REPL Support

pip install "klongpy[repl]"

With PyTorch Autograd (Recommended)

pip install "klongpy[torch]"
kgpy --backend torch          # Enable torch backend

Web / DB / WebSockets Extras

pip install "klongpy[web]"
pip install "klongpy[db]"
pip install "klongpy[ws]"

Full Installation (REPL, DB, Web, WebSockets, Torch)

pip install "klongpy[all]"

Lineage and Inspiration

KlongPy stands on the shoulders of giants:

• APL (1966): Ken Iverson's revolutionary notation
• J: ASCII-friendly APL successor
• K/Q/kdb+: High-performance time series and trading systems
• Klong: Nils M Holm's elegant, accessible array language
• NumPy: The "Iverson Ghost" in Python's scientific stack
• PyTorch: Automatic differentiation and GPU acceleration

KlongPy combines Klong's simplicity with Python's ecosystem and PyTorch's autograd creating something new: an array language where gradients are first-class citizens.

Use Cases

• Quantitative Finance: Self-optimizing trading strategies, risk models, portfolio optimization
• Machine Learning: Neural networks, gradient descent, optimization in minimal code
• Scientific Computing: Physics simulations, numerical methods, data analysis
• Time Series Analysis: Signal processing, feature engineering, streaming data
• Rapid Prototyping: Express complex algorithms in few lines, then optimize

Status

KlongPy is a superset of the Klong array language, passing all Klong integration tests plus additional test suites. The PyTorch backend provides GPU acceleration (CUDA, MPS) and automatic differentiation.

Ongoing development:

• Expanded torch backend coverage
• Additional built-in tools and integrations
• Improved error messages and debugging

Related Projects

• Klupyter - KlongPy in Jupyter Notebooks
• VS Code Syntax Highlighting
• Advent of Code Solutions

Development

git clone https://github.com/briangu/klongpy.git
cd klongpy
pip install -e ".[dev]"   # Install in editable mode with dev dependencies
python3 -m pytest tests/  # Run tests

Issues

This project does not accept direct issue submissions.

Please start with a GitHub Discussion. Maintainers will promote validated discussions to Issues.

Active contributors may be invited to open issues directly.

Contributors

See CONTRIBUTING.md for contribution workflow, discussion-first policy, and code standards.

Documentation

# Install docs tooling
pip install -e ".[docs]"

# Build the site into ./site
mkdocs build

# Serve locally with live reload
mkdocs serve

Acknowledgements

Huge thanks to Nils M Holm for creating Klong and writing the Klong Book, which made this project possible.