Add formal/: machine-checked coverage and compaction arguments in Lean - #776
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Two developments, with a summarizing README. Differential/Coverage.lean: for any function of an accumulated input, output changes are confined to joins of input update times; per round, to the novel-involving joins, which coincide exactly with the seed-and- close enumeration reduce.rs performs. Emitting at those times advances the correctness invariant; deferred (pending) times cover exactly the stored output's staleness and are necessary. Exact times throughout; logically compacted input is the intended next step. Differential/Compaction.lean: soundness and canonicity of Lattice::advance_by, with a note bounding its scope. Doc pointers added at Lattice::advance_by and in the reduce module. The directory is a self-contained lake project; nothing in the Rust workspace depends on it, and no CI gates on it. Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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This adds a
formal/directory: a self-contained Lean 4 + Mathlib project with machine-checked arguments about differential dataflow, and a README summarizing them.Differential/Coverage.leanconcerns which times an incremental computation must revisit.It proves that for any function of an accumulated input, the output is again a difference trace whose updates fall only at joins of input update times; that a round's change is covered by the joins involving at least one novel time; and that this set coincides exactly with the seed-and-close enumeration the reduce operator performs.
It further proves that emitting corrections at those times keeps the output correct up to the frontier, and that joins deferred beyond the frontier — the pending obligations — cover exactly the staleness of the stored output and cannot be dropped.
All statements use exact times; extending them to logically compacted input is the intended next step.
Differential/Compaction.leanproves soundness and canonicity ofLattice::advance_by: at or beyond the frontier the representative compares exactly as the original, and two times share a representative precisely when they are indistinguishable there.A scope note bounds what this does and does not establish.
Doc comments at
Lattice::advance_byand in the reduce module point at the corresponding files.The directory builds with
lake build(instructions informal/README.md); nothing in the Rust workspace depends on it, and no CI gates on it.🤖 Generated with Claude Code