Epsil

Epsil is a programming language for scientific computing, built on the Compute Engine.

Experimental

Epsil is available as an experimental entry point. Its syntax and semantics may change between releases while the language is being exercised in notebooks and other applications.

Epsil is embedded from JavaScript through the @cortex-js/compute-engine/epsil entry point:

import { ComputeEngine, executeEpsil } from "@cortex-js/compute-engine/epsil";

const ce = new ComputeEngine();
const { value, diagnostics } = executeEpsil(ce, "1 + 2");

Here is "Hello World" in Epsil. Edit the code and press Run (or ⌘/Ctrl+Enter) — the result is the value of the last statement, shown as an Epsil value and as its underlying MathJSON.

"Hello World"

⌘/Ctrl + Enter

Epsil is symbolic by default: expressions stay exact unless you ask for a numeric approximation with N().

Simplify(2 + 3x^3 + 2x^2 + x^3 + 1)

⌘/Ctrl + Enter

Values have a type, and strings support \(…) interpolation:

let x = 2^11 - 1 "\(x) has type \(Type(x))"

⌘/Ctrl + Enter

Errors are ordinary values, so a program never throws to its host — a problem surfaces as an ["Error", …] value or a diagnostic:

const answer = 42 answer = 0

⌘/Ctrl + Enter

Start Here

Follow the five-minute getting-started guide — try the REPL, run a source file, and embed Epsil in JavaScript.

Explore complete Epsil programs for symbolic computation, collections, calculus, linear algebra, strings, and more.

Use the CLI and interactive REPL from a terminal.

Coming from Python? Translate your idioms — and learn the three reflexes that silently do the wrong thing.

Coming from Mathematica? Most of the mental model carries over; here is what changes.

Writing Epsil with an LLM? Give it the language card for AI agents — a condensed, machine-verified reference.

Connect ChatGPT, Claude, or another AI assistant to Epsil with the built-in MCP server — exact math as a tool call.

Language Reference

Read more about the formal syntax of Epsil — statements, primaries, calls and indexing.

Literals — numbers, strings, symbols, and $…$ LaTeX islands.

Operators — arithmetic, logic, relational, and the pipeline operator.

Control flow — if/else, match, loops, blocks, and functions.

Declarations — binding names with let and const.

Types — annotations, named types, effects, and absence values.

Comments — line and block comments.

Pragmas — parser directives embedded in the code.

Collections

Epsil has literal syntax for the Compute Engine's collections.

Lists are ordered and 1-indexed with xs[i]:

[3, 5, 7, 11]

⌘/Ctrl + Enter

Sets are unordered collections of unique elements:

{3, 5, 7, 11}

⌘/Ctrl + Enter

Dictionaries are sets of key/value pairs. The empty dictionary is {->}:

{one -> 1, two -> 2}

⌘/Ctrl + Enter

Read more about lists, sets, tuples and dictionaries.

Future Directions

Several keywords are reserved but not designed — they are held so that a future version of Epsil can introduce them without breaking existing programs, and using one as an ordinary name today is an error. None of the following are part of the language yet:

• Modules and imports — import, export, module.
• Error-handling keywords — try, catch, throw. In Epsil, errors are ordinary values, so these are not needed for the current design.
• Concurrency — async, await, parallel.
• Macros and compile-time metaprogramming.

If you need a symbol whose name collides with one of these reserved words, use the verbatim form (`match`).