Tensorium_lang

Tensorium_lang is a domain-specific language and compiler frontend designed to express tensorial equations arising in numerical relativity (Einstein equations, BSSN-like formulations, tensor contractions).

The compiler is implemented in C++20 and built on top of LLVM/MLIR 20. It performs semantic analysis of tensor indices (variance, contractions), followed by a custom MLIR lowering pipeline.

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Build

Tensorium_lang requires a custom installation of LLVM/MLIR 20.

cmake -S . -B build \
  -DLLVM_DIR=/opt/local/libexec/llvm-20/lib/cmake/llvm \
  -DMLIR_DIR=/opt/local/libexec/llvm-20/lib/cmake/mlir \
  -DCMAKE_BUILD_TYPE=Debug \
  -DCMAKE_CXX_FLAGS="-O0 -g"

cmake --build build -j

Driver

The compiler Driver is:

build/tools/driver/Tensorium_cc

Running the compiler

To compile and analyze a Tensorium source file (.tn):

./build/tools/driver/Tensorium_cc \
  --tensorium-stencil-lower \
  --tensorium-dissipation \
  --tensorium-einstein-lower \
  --tensorium-einstein-analyze-einsum \
  --tensorium-einstein-canonicalize \
  --tensorium-einstein-validate \
  --dump-mlir \
  tests/01_scalar_minimal.tn

This pipeline perform:

• This pipeline performs:
• stencil lowering
• artificial dissipation pass
• Einstein index lowering
• einsum analysis
• canonicalization
• Einstein validity checking
• MLIR dump

Test

All test programs are located in tests/.

• Files starting with valid_ or without error must compile successfully
• Files containing error are expected to fail semantic or Einstein validation

./build/tools/driver/Tensorium_cc --dump-mlir tests/22_BSSN_minimal.tn

Internal architecture (high level)

• Frontend: Lexer / Parser / AST / IndexedAST
• Semantic analysis: tensor variance, free and dummy indices
• MLIR dialect: tensorium
• Transformation passes: Einstein lowering, index analysis, stencil lowering
• Target: MLIR (future LLVM / Linalg lowering)

Tensor rules are explicit and must never be inferred implicitly.