Lectures onType Theory
ch:intersection-union: ch:intersection-union
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ch:intersection-union: ch:intersection-union

Exercise 20.19.

Normalize each finite type into positive and negative atoms, then make every failed inclusion return a graph checked against both normal forms. Run the four Kappa gates on artifacts/ch20-semantic-subtyping/corpus.kp; require the eight frozen cases and empty audit. Replay three independent controls: remove the Ω guard, replace universal arrow decomposition by an existential choice, and bypass a typecase scope check. A valid control passes check but fails test. The witness table is the acceptance oracle; simulation completeness and safety remain mathematical theorems.

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