Epsil

A programming language for scientific computing

Experimental

Epsil is still being developed. Its syntax and semantics may change between releases while the language is being exercised by early adopters. Your feedback can help shape its direction.

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.

"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

Guide

The guide explains the language through examples and decisions: not only what syntax means, but when a form is useful and why you might choose it.

Take A Tour of Epsil — a one-page, example-led introduction to exact math, functions, collections, control flow, and types.

Follow Getting Started — install Epsil, try the REPL, run a source file, and embed the language 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.

Understand how Epsil evaluates — exact values, mutable bindings, lazy collections, ordinary error values, and session scope.

Tools and Integrations

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

The reference is organized by language feature. Use it when you know what you are looking for and need the complete rule, grammar, or edge case.

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 — names, let, const, destructuring, function-type annotations that bind their parameters, scopes, and named types.

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

Protocols — declaring operation sets, conforming types to them, and dispatching on the receiver.

Comments — line and block comments.

Pragmas — parser directives embedded in the code.

Inside Epsil — the JavaScript API, and the MathJSON each language form lowers to. Not needed to write Epsil.

Collections

Epsil has literal syntax for lists and dictionaries.

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

[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. None of the following are part of the language yet, and because the grammar does not claim any of them, each is still an ordinary identifier today: let import = 5 binds a variable named import. Prefer not to use them as names, so that a program keeps working when the language does claim them.

• 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.

A word the grammar DOES claim — a literal or an active keyword such as match, for or if — cannot be spelled as a plain symbol at all. Use the verbatim form for those (`match`); it works for the reserved words above too. literals.md lists which words are in which group.