Simulate Q option T lift M run eq of query
simulateQ_optionT_liftM_run_eq_of_query
Plain-language statement
OptionT companion to QueryImpl.simulateQ_liftM_eq_of_query: simulating an OracleComp-computation oa lifted into OptionT (OracleComp spec₂') (the shape produced by an OptionT-monadic verifier's let _ ← liftM (queryHelper) binds) agrees, at the run (Option) level, with some-mapping the simulation of oa through a per-query-bridged handler...
Exact Lean statement
lemma simulateQ_optionT_liftM_run_eq_of_query
{ι₁' ι₂' : Type} {spec₁' : OracleSpec ι₁'} {spec₂' : OracleSpec ι₂'}
{α : Type} {m' : Type → Type} [Monad m'] [LawfulMonad m']
[MonadLiftT (OracleComp spec₁') (OracleComp spec₂')]
[LawfulMonadLiftT (OracleComp spec₁') (OracleComp spec₂')]
(impl : QueryImpl spec₂' m') (impl₁ : QueryImpl spec₁' m')
(h : ∀ t, simulateQ impl
(liftM (liftM (spec₁'.query t) : OracleComp spec₁' (spec₁'.Range t)) :
OracleComp spec₂' (spec₁'.Range t)) = impl₁ t)
(oa : OracleComp spec₁' α) :
simulateQ impl ((liftM oa : OptionT (OracleComp spec₂') α) :
OracleComp spec₂' (Option α))
= (some <$> simulateQ impl₁ oa : m' (Option α))Formal artifact
Lean source
lemma simulateQ_optionT_liftM_run_eq_of_query {ι₁' ι₂' : Type} {spec₁' : OracleSpec ι₁'} {spec₂' : OracleSpec ι₂'} {α : Type} {m' : Type → Type} [Monad m'] [LawfulMonad m'] [MonadLiftT (OracleComp spec₁') (OracleComp spec₂')] [LawfulMonadLiftT (OracleComp spec₁') (OracleComp spec₂')] (impl : QueryImpl spec₂' m') (impl₁ : QueryImpl spec₁' m') (h : ∀ t, simulateQ impl (liftM (liftM (spec₁'.query t) : OracleComp spec₁' (spec₁'.Range t)) : OracleComp spec₂' (spec₁'.Range t)) = impl₁ t) (oa : OracleComp spec₁' α) : simulateQ impl ((liftM oa : OptionT (OracleComp spec₂') α) : OracleComp spec₂' (Option α)) = (some <$> simulateQ impl₁ oa : m' (Option α)) := by have hrun : ((liftM oa : OptionT (OracleComp spec₂') α) : OracleComp spec₂' (Option α)) = some <$> (liftM oa : OracleComp spec₂' α) := by change OptionT.run (OptionT.lift (liftM oa : OracleComp spec₂' α)) = _ rw [map_eq_bind_pure_comp] rfl rw [hrun, simulateQ_map, QueryImpl.simulateQ_liftM_eq_of_query impl impl₁ h oa]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/SimSemantics/Append.lean:382-400
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