Project-declaredLean 4.32.0 · mathlib@81a5d257

Wp simulate Q eq

OracleComp.ProgramLogic.wp_simulateQ_eq

program verification separation logic cryptography simulate q

Plain-language statement

If every oracle query in impl has the same evaluation distribution as the original query, then wp of the simulated computation equals wp of the original.

Exact Lean statement

@[game_rule] theorem wp_simulateQ_eq
    (impl : QueryImpl spec (OracleComp spec))
    (hImpl : ∀ (t : spec.Domain),
      𝒟[impl t] = 𝒟[(liftM (query t) : OracleComp spec (spec.Range t))])
    (oa : OracleComp spec α) (post : α → ℝ≥0∞) :
    wp (simulateQ impl oa) post =
      wp oa post

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

@[game_rule] theorem wp_simulateQ_eq    (impl : QueryImpl spec (OracleComp spec))    (hImpl : ∀ (t : spec.Domain),      𝒟[impl t] = 𝒟[(liftM (query t) : OracleComp spec (spec.Range t))])    (oa : OracleComp spec α) (post : α → ℝ≥0∞) :    wp (simulateQ impl oa) post =      wp oa post := by  induction oa using OracleComp.inductionOn with  | pure x => simp  | query_bind t oa ih =>    simp only [simulateQ_bind, simulateQ_query, OracleQuery.cont_query, id_map,      OracleQuery.input_query]    rw [wp_bind, wp_bind]    simp_rw [ih]    exact wp_congr_evalDist (hImpl t) _

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/ProgramLogic/Unary/SimulateQ.lean:38-52

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