Research proof index

Every counting-oracle support point of the body oa lifts to a counting-oracle support point of replicate n oa whose query count is n times the body's. -/ private lemma countingOracle.support_simulate_replicate_const [DecidableEq ι] {oa : OracleComp spec α} {z : α × QueryCount ι} (hz : z ∈ support (countingOracle.simulate oa 0)) : ∀ n, ∃ ys, (ys, fun...

Key bound of the forking lemma: the probability that both runs succeed with fork point s is at least Pr[cf(main) = s]² - Pr[cf(main) = s] / |Range i|.

Trace noninterference is preserved by sequential composition (bind). The continuations may depend on both the result and the trace, but whenever the traces match, the continuations must themselves be trace noninterfering.

When running loggingOracle inside cachingOracle, every log entry ends up in the cache. We prove two properties simultaneously by induction: 1. Every log entry is in the final cache. 2. The initial cache is a subset of the final cache (monotonicity). The proof works by induction on oa. The pure case is trivial (empty log). For query t >>= mx: the...

Invariant-gated state-projection theorem for a simulated prefix followed by a stateful continuation.

Coherence: lifting an OracleComp to a superspec and then into OptionT via the standard MonadLift equals lifting directly through the transitive MonadLiftT chain (which goes through the simulateQ-based OptionT MonadLift instance).