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id: ADR-0009 title: Adopt D6: the math IR is relations, and DataFusion Expr computes over it status: accepted date: 2026-09-13 deciders: [paul-heyse] level: decision principles: [DM-21, DM-22, DM-10] blueprint: [§D6, §7.1, §7.2] review: not-required: neither review raised a finding against D6 evidence: Proposed supersedes: [] superseded-by: null revisit: A backend requires an operator the IR cannot express without scalarizing earlier than §7.1 allows verification: tests/conformance operator-contract tests; the expression DSL round-trip test at the phase-0 exit

ADR-0009: Adopt D6: the math IR is relations, and DataFusion Expr computes over it

Context

Blueprint D6 keeps expression nodes, arguments and typed operator payloads as relations, and keeps indexed operators (SumOver, Gather, Broadcast, Derivative, Integral, ImplicitSystem, KernelCall) alive until a backend requires scalarization.

Scope

Binds the representation of mathematics. It does not bind the operator catalog’s contents (§7.2) or canonicalization (§7.4).

Drivers

DataFusion Expr has no indexed reduction, no derivative and no kernel call with declared derivative availability; scalarizing early destroys the structure discretization and index expansion need.

Options

Use Expr as the IR — rejected: the seven indexed operators have no representation and the IR would be tied to the engine version. A hand-written Rust enum — rejected by D1.

Outcome

Expression nodes, arguments and typed payloads are relations; DataFusion Expr is used to compute over the IR, never to be it.

Consequences

Every operator needs a contract record (§7.3) and a lowering per backend; adding one is a code change by §22.3’s own table.

Compensating controls

Canonicalization (P10) is hand-written and complete on its own; egglog stays optional and phase 4 (ADR-0037).

Confirmation

Operator-contract conformance tests run per backend; the DSL round-trip is a phase-0 exit criterion (§25).

Pros and cons

Keeping indexed operators alive costs a scalarization pass (P12); folding them early costs the ability to discretize.

More information

Blueprint §D6, §7.1 (design constraints), §7.2 (operator catalog), §14.1 (P12).

Status history

  • 2026-09-13 — accepted with the repository-seeding pull request (backfilled from blueprint revision 3).