Caching Oracle query caches
OracleComp.cachingOracle_query_caches
Plain-language statement
After running cachingOracle on a single query at t, the resulting cache maps t to the returned value.
Exact Lean statement
theorem cachingOracle_query_caches (t : spec.Domain)
(cache₀ : QueryCache spec)
(v : spec.Range t) (cache₁ : QueryCache spec)
(hmem : (v, cache₁) ∈ support ((cachingOracle t).run cache₀)) :
cache₁ t = some vFormal artifact
Lean source
theorem cachingOracle_query_caches (t : spec.Domain) (cache₀ : QueryCache spec) (v : spec.Range t) (cache₁ : QueryCache spec) (hmem : (v, cache₁) ∈ support ((cachingOracle t).run cache₀)) : cache₁ t = some v := by simp only [cachingOracle.apply_eq, StateT.run_bind, StateT.run_get, pure_bind] at hmem cases hc : cache₀ t with | some u => simp only [hc, StateT.run_pure, support_pure, Set.mem_singleton_iff] at hmem obtain ⟨rfl, rfl⟩ := hmem exact hc | none => simp only [hc, StateT.run_bind, StateT.run_monadLift, monad_norm] at hmem rw [mem_support_bind_iff] at hmem obtain ⟨u, _, hmem⟩ := hmem simp only [StateT.run_modifyGet, support_pure, Set.mem_singleton_iff] at hmem obtain ⟨rfl, rfl⟩ := hmem exact QueryCache.cacheQuery_self cache₀ t v- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/QueryTracking/CachingOracle.lean:499-516
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