Eval Dist simulate Q random Oracle run' eq table Extending
OracleComp.evalDist_simulateQ_randomOracle_run'_eq_tableExtending
Plain-language statement
Lazy random oracle equals eager full-table sampling , cache-parametrized form. Running oa under the lazy random oracle starting from cache c yields the same output distribution as: sample a full table g : D → R uniformly, then evaluate oa deterministically against the table that overlays c on g. This is the induction vehicle: the cache c...
Exact Lean statement
theorem evalDist_simulateQ_randomOracle_run'_eq_tableExtending
{α : Type} (oa : OracleComp (D →ₒ R) α) (c : (D →ₒ R).QueryCache) :
𝒟[(simulateQ randomOracle oa).run' c] =
𝒟[do let g ← $ᵗ (D → R);
pure (evalWithAnswerFn (QueryImpl.ofFn (tableExtending c g)) oa)]Formal artifact
Lean source
theorem evalDist_simulateQ_randomOracle_run'_eq_tableExtending {α : Type} (oa : OracleComp (D →ₒ R) α) (c : (D →ₒ R).QueryCache) : 𝒟[(simulateQ randomOracle oa).run' c] = 𝒟[do let g ← $ᵗ (D → R); pure (evalWithAnswerFn (QueryImpl.ofFn (tableExtending c g)) oa)] := by induction oa using OracleComp.inductionOn generalizing c with | pure a => exact evalDist_simulateQ_randomOracle_run'_pure_eq_tableExtending a c | query_bind t k ih => exact evalDist_simulateQ_randomOracle_run'_query_bind_eq_tableExtending t k ih c- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/QueryTracking/RandomOracle/EagerTable.lean:175-183
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