🧮 Mathic

A programming language with built-in symbolic algebra, powered by LLVM/MLIR

Features

• Symbolic expressions — first-class symbolic algebra: declare symbolic variables, compose expressions with +, -, *, /, and evaluate with concrete values at runtime.
• JIT compilation — programs are compiled on-the-fly via MLIR/LLVM and executed natively.
• MLIR-powered — a custom MLIR dialect (symbolic) represents symbolic expressions, lowered to arith + func for native codegen.
• Statically typed — type-checked at compile time.

Example

df main() i32 {
    sym x: expr<i32>;

    let a: expr<i32> = x + 5;
    let r1: i32 = eval(a, x, 10);

    let b: expr<i32> = 3 * x;
    let r2: i32 = eval(b, x, 10);

    let c: expr<i32> = 2 * x + 1;
    let r3: i32 = eval(c, x, 10);

    return r1 + r2 + r3;
}

Declares symbolic variables (sym), composes expressions with arithmetic, and evaluates them with concrete values at runtime.

Prerequisites

LLVM/MLIR 21 is required. After installing, set:

export LLVM_SYS_211_PREFIX=/path/to/llvm-21
export MLIR_SYS_210_PREFIX=/path/to/llvm-21
export TABLEGEN_210_PREFIX=/path/to/llvm-21

Installing LLVM/MLIR (click to expand)

macOS (Homebrew)

brew install llvm@21
export LLVM_SYS_211_PREFIX=$(brew --prefix llvm@21)
export MLIR_SYS_210_PREFIX=$(brew --prefix llvm@21)
export TABLEGEN_210_PREFIX=$(brew --prefix llvm@21)

You may also need:

export LIBRARY_PATH=/opt/homebrew/lib

Building from source

Requires ~6 GB RAM and ~20 GB disk space.

git clone https://github.com/llvm/llvm-project.git
cd llvm-project
git checkout llvmorg-21.1.7
cmake -G Ninja ../llvm \
    -DLLVM_ENABLE_PROJECTS="mlir" \
    -DCMAKE_BUILD_TYPE=RelWithDebInfo \
    -DLLVM_ENABLE_ASSERTIONS=On \
    -DLLVM_BUILD_LLVM_DYLIB=On \
    -DLLVM_LINK_LLVM_DYLIB=On \
    -DMLIR_BUILD_MLIR_C_DYLIB=On \
    -DLLVM_TARGETS_TO_BUILD=host \
    -DCMAKE_INSTALL_PREFIX=/opt/llvm-21 \
    -DLLVM_USE_LINKER=mold   # optional, faster with mold
ninja install

Installation

cargo install mathic

Make sure LLVM_SYS_211_PREFIX, MLIR_SYS_210_PREFIX and TABLEGEN_210_PREFIX are set before building.

Usage

euler <file>.mth

Project

See docs/ for the full project structure and pipeline. See docs/dialects/Symbolic.md for the symbolic dialect reference.

Status

Early development. Features are added incrementally. The symbolic dialect and its lowering passes are functional but evolving.

Built with ❤️ and 🦀 Rust