infix-parser

A fast C++20 infix expression parser built on lexy. Parses mathematical expressions into a compact reverse-prefix AST suitable for stack-based evaluation and automatic differentiation.

Features

• Fast number parsing via fast-float
• Reverse-prefix encoding — binary [rhs, lhs, op], unary [child, op], ternary [else, then, cond, op]
• Rich operator set

Category	Symbols / names
Arithmetic	+ - * / ^ % |
Comparison	< > <= >= == !=
Unary	abs exp exp2 log log2 log10 sqrt cbrt erf sin cos tan asin acos atan sinh cosh tanh sigmoid square cube
Binary	aq pow min max atan2 hypot fmod
Ternary	if (soft, differentiable)

• All functions are differentiable — designed to integrate with Ceres/operon

Prerequisites

Tool	Version
CMake	≥ 3.14
C++ compiler	C++20 (GCC 12+, Clang 15+, MSVC 2022)
vcpkg	any recent

Dependencies (managed by vcpkg): lexy, fast-float, fmt. Optional (enabled via VCPKG_MANIFEST_FEATURES=test): catch2, nanobench.

Building

Linux

# Bootstrap vcpkg (once)
git clone https://github.com/microsoft/vcpkg "$VCPKG_ROOT"
"$VCPKG_ROOT/bootstrap-vcpkg.sh"

cmake --preset=ci-ubuntu   # release + clang-tidy + cppcheck
cmake --build build -j$(nproc)

Or without presets:

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DCMAKE_CXX_STANDARD=20 \
  -DCMAKE_TOOLCHAIN_FILE="$VCPKG_ROOT/scripts/buildsystems/vcpkg.cmake"
cmake --build build -j$(nproc)

macOS

cmake --preset=release-darwin   # Xcode generator, vcpkg
cmake --build build --config Release

Or without presets:

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DCMAKE_CXX_STANDARD=20 \
  -DCMAKE_TOOLCHAIN_FILE="$VCPKG_ROOT/scripts/buildsystems/vcpkg.cmake"
cmake --build build -j$(sysctl -n hw.logicalcpu)

Windows (MSVC)

Run the commands in a Developer PowerShell for VS 2022 or any shell where cl.exe is on PATH.

cmake --preset=ci-windows   # Visual Studio 17 2022, static vcpkg triplet
cmake --build build --config Release

Or without presets:

cmake -S . -B build `
  -G "Visual Studio 17 2022" -A x64 `
  -DCMAKE_CXX_STANDARD=20 `
  -DCMAKE_TOOLCHAIN_FILE="$env:VCPKG_ROOT\scripts\buildsystems\vcpkg.cmake" `
  -DVCPKG_TARGET_TRIPLET=x64-windows-static-md
cmake --build build --config Release

Nix flake

nix build github:foolnotion/infix-parser

To use as a flake input:

inputs.infix-parser.url = "github:foolnotion/infix-parser";
# Share the foolnotion overlay to avoid duplicate lexy/fast-float in closure:
inputs.infix-parser.inputs.foolnotion.follows = "foolnotion";

Running tests

Tests require the test vcpkg feature and CMake's BUILD_TESTING:

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DCMAKE_TOOLCHAIN_FILE="$VCPKG_ROOT/scripts/buildsystems/vcpkg.cmake" \
  -DVCPKG_MANIFEST_FEATURES=test \
  -DBUILD_TESTING=ON
cmake --build build -j$(nproc)
ctest --test-dir build --output-on-failure

Benchmarks

cmake -S . -B build \
  -DCMAKE_BUILD_TYPE=Release \
  -DCMAKE_TOOLCHAIN_FILE="$VCPKG_ROOT/scripts/buildsystems/vcpkg.cmake" \
  -DVCPKG_MANIFEST_FEATURES=test \
  -DBUILD_BENCHMARKS=ON
cmake --build build -j$(nproc)
./build/benchmark/infix-parser-bench

Consuming the library via CMake

After installation (cmake --install build --prefix /usr/local):

find_package(infix-parser REQUIRED)
target_link_libraries(my_target PRIVATE infix-parser::infix-parser)

All dependencies (lexy, fast-float, fmt) are private implementation details — consumers need no extra find_package calls.

Acknowledgements

The parser is built on lexy by Jonathan Müller — a header-only parser combinator library that made expressing the infix grammar straightforward and type-safe.

License

MIT — see LICENSE. Copyright © 2026 Bogdan Burlacu