Reduce#1
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- Move 'Partial Reducers' remark to after Theorem 4 (was prematurely placed) - Add proper definition of algebraic aggregates in Section 3.2 - Remove incoherent 'partial average reducer' paragraph - you cannot maintain average incrementally with only the average value (need count too) - Clarify min reducer as canonical example of non-invertible aggregate - Explain Skip's strategies for handling partial reducers
…ssumptions" This reverts commit a72cc21.
- Rewrite abstract to emphasize first-class combinators vs callbacks - Contrast with Flink, Kafka Streams, FRP, and incremental computation frameworks - Add 'What distinguishes Skip's design' paragraph with 3 key differentiators - Qualify claims about formal correctness to acknowledge DBSP/differential dataflow foundations - Add 'Reactive JS and FRP streams' paragraph to related work
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Summary
This PR adds a formal semantics for Skip's reactive
reducecombinator, including a paper and a Lean formalization.What's Included
reduce.tex): Formal semantics for Skip'sreducecombinator with correctness proofslean-formalisation/): Machine-checked proofs of the main theoremsKey Contributions
reduceas a derived view over collections⊖is the inverse of⊕)Main Results
(fold_⊕(ι, M) ⊕ v) ⊖ v = fold_⊕(ι, M)for all reachable accumulator statesWhat Distinguishes This Work
Unlike related systems (Flink, Kafka Streams, FRP frameworks), Skip exposes reducers as:
⊖operation, not hidden internally)The Lean formalization provides machine-checked verification of the main correctness theorem and supporting lemmas.