Research proof index

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).

Against a constant-state responder the wired run is the memoryless machine run against the selected handler, with the setup carried along unchanged: the machine-run form of OracleStrategy.iterateAgainst_ofHandlerFamily.

Completing an occurrence resamples the focused answer as a fresh query i: any event on that answer marginalizes the resampled suffix away.

Cache preimage bound: if the initial cache contains at most one preimage of a target value v₀, then the probability that simulateQ cachingOracle oa creates a fresh cache entry equal to v₀ is at most n / |C|, where n is the total query bound. Each cache miss is a fresh uniform draw, so a union bound over the at most n misses gives the resul...

Two events have equal probabilities when their predicates agree on the support of the first computation and the two computations share an evaluation distribution.

A fixed guarded fork is the corresponding component of the dynamic semantic fork.