ddx

JAX-style automatic differentiation in SQL

Write calculus directly in SQL and get derivatives back as ordinary columns, evaluated row by row by the engine alongside everything else:

SELECT i, grad(x * y, x) AS dfdx, grad(x * y, y) AS dfdy FROM g

grad/jvp are compile-time markers: they carry a differentiation request through parsing and are rewritten away — to plain derivative SQL — before the query ever runs. One engine-neutral Rust core, thin per-engine adapters.

status: M0 landed — the scalar core (ddx-core) is implemented. The rest is in progress; see docs/design.md §8 for the milestones.

Layout

crates/
  ddx-core/         # v1 engine — differentiate sqlparser::ast::Expr + rewrite_sql    [M0 ✓]
  ddx-ad/           # v2 engine — query-level reverse-mode AD over Substrait          [M3/M4]
  ddx-datafusion/   # DataFusion adapter: ddx_sql + AnalyzerRule                      [M2]
  ddx-duckdb/       # DuckDB community extension                                      [M5]
python/ddxdb/       # PyO3/maturin wheel: rewrite_sql + Context.sql() shim            [M2]
tests/              # cross-engine numeric-agreement suites (vs JAX)                  [M2/M6]
docs/spikes/        # runnable evidence for every design claim
docs/design.md      # the design

Try the core

use ddx_core::Ddx;
use ddx_core::sqlparser::dialect::GenericDialect;

let out = Ddx::new()
    .rewrite_sql("SELECT grad(sin(x), x) AS d FROM t", &GenericDialect {})
    .unwrap();
assert_eq!(out, "SELECT (cos(x)) AS d FROM t");

cargo test -p ddx-core

See crates/ddx-core/README.md for what the engine supports and the correctness properties worth knowing.

License

Copyright 2026 Alexander Merose

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    https://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.