Dedekind

A programming language for scientific computing. Write your simulator once in readable code with units — and get inverse problems, topology optimization, parameter estimation, and Bayesian inference on it for free, without hand-rolled adjoint code.

use atomic

m = 1.0[kg]                                        // compile-time units
k = 4.0[N/m]

fn L(q, v) { return 0.5*m*v[0]*v[0] - 0.5*k*q[0]*q[0] }

traj = ode_solve(lagrange_ode_rhs(L), [1.0, 0.0], linspace(0, 2*pi, 51))

The same AST that runs this simulation generates the LaTeX for your paper (dedekind file.ddk --latex) and a reproducibility report bundling the git commit, package versions, RNG seeds and methods section (dedekind file.ddk --reproducibility-report appendix.md).

Install

pip install dedekind                  # core: torch + numpy + sympy
pip install "dedekind[jupyter,plot]"  # + Jupyter kernel + matplotlib
pip install "dedekind[all]"           # + sci, geo, bio, md, ml, plot, jupyter

Extras: jupyter, plot, sci (scipy), geo (xarray), bio (rdkit), md (openmm), ml (torch_geometric).

Jupyter / JupyterLab / Spyder

pip install "dedekind[jupyter]"
python -m dedekind.install_kernel

Then jupyter lab and pick Dedekind from the kernel list. Variables persist across cells; print_latex(...) renders inline; errors are mapped back to .ddk line numbers.

Hello, Dedekind

hello.ddk:

print("Hello from Dedekind!")
vec = [1, 2, 3]
print(vec.sum())

Run it:

dedekind hello.ddk

What makes Dedekind different

• Native physical units, checked at compile time. 1[m] + 1[s] is a compiler error with line number; 1[m] + 100[cm] auto-converts to 2[m]. Cross-argument unit polymorphism via generics: fn add<U>(a: [U], b: [U]) -> [U].
• Differentiable everything. PDE/ODE solvers, LBM/FEM simulators, N-body integrators, control blocks, IIR filters — all are first-class AST nodes that autograd flows through. minimize(...) and fit(...) optimize through full simulations without writing adjoint code.
• Blackboard notation as syntax. Einstein indices (A^ij * v^j), Ricci contraction, Lagrangians (lagrange_ode_rhs(L)), partial derivatives (partial(u, x, order=2)) are language primitives, not library calls.
• Shape and semantic types. Vector[N], Matrix[M, N], LabeledTensor[lat, lon, time], Sequence[DNA|RNA|Protein] — validated at function boundaries. The classic data.mean(axis=2)-instead-of-dim="time" bug becomes structurally impossible.
• LaTeX is generated from the AST, not typed by hand. Methods sections in papers and the code that runs the simulation share one source of truth. Paper-code drift is structurally eliminated.
• Python interop. pyimport scipy.special as sp; sp.gamma(5.0) — every PyPI package is one line away.

Full feature catalogue: docs/language.md. Why it matters in detail: docs/language.md#core-features.

Showcase examples

If you installed Dedekind via pip, you can initialize the showcase examples in your current directory by running:

dedekind --init-examples

This will automatically download and extract the ./examples/ directory.

A curated entry-point selection (full list: examples/dedekind/):

• physics_astronomy/scientific_ricci_plot.ddk — Einstein notation
• physics_astronomy/lagrange_hamilton.ddk — Lagrangian → ODE in one call
• machine_learning/pinn_oscillator_demo.ddk — physics-informed neural net
• engineering/lbm_shape_optimization.ddk — differentiable CFD shape opt
• engineering/lbm3d_sphere_drag.ddk — D3Q19 + autograd
• engineering/lbm_les_smagorinsky_tuning.ddk — Smagorinsky LES calibration
• engineering/heat_sink_topology_optimization.ddk — SIMP topology opt
• physics_astronomy/crystallography_structure_refinement.ddk — structure refinement via differentiable SF (using atomic)
• compiler_features/reproducibility_demo.ddk — --reproducibility-report
• compiler_features/latex_demo.ddk — --latex

Compile and run every example at once: python run_examples.py (-q for summary, --filter <name> for one).

Status, roadmap, history

• Current release: v3.0.8 (May 2026)
• Roadmap: docs/roadmap.md
• Full changelog: docs/changelog.md
• Formal spec: docs/Dedekind_Language_Specification.md

License

Apache 2.0. See LICENSE.