With State Oracle eval Dist map
SPMFSemantics.withStateOracle_evalDist_map
Plain-language statement
withStateOracle commutes with <$>: mapping a function over the surface computation is the same as mapping it over the observed SPMF. This holds because interpret is the bundled monad morphism simulateQ', and the StateT observer fun mx => toSPMF (StateT.run' mx s) preserves <$> even though it is not a full monad morphism: <$> does not thr...
Exact Lean statement
@[simp] lemma withStateOracle_evalDist_map
{ι : Type} {hashSpec : OracleSpec ι} {σ : Type}
(hashImpl : QueryImpl hashSpec (StateT σ ProbComp)) (s : σ)
{α β : Type} (f : α → β) (mx : OracleComp (unifSpec + hashSpec) α) :
(SPMFSemantics.withStateOracle hashImpl s).evalDist (f <$> mx) =
f <$> (SPMFSemantics.withStateOracle hashImpl s).evalDist mxFormal artifact
Lean source
@[simp] lemma withStateOracle_evalDist_map {ι : Type} {hashSpec : OracleSpec ι} {σ : Type} (hashImpl : QueryImpl hashSpec (StateT σ ProbComp)) (s : σ) {α β : Type} (f : α → β) (mx : OracleComp (unifSpec + hashSpec) α) : (SPMFSemantics.withStateOracle hashImpl s).evalDist (f <$> mx) = f <$> (SPMFSemantics.withStateOracle hashImpl s).evalDist mx := by set impl := (QueryImpl.ofLift unifSpec ProbComp).liftTarget (StateT σ ProbComp) + hashImpl change (liftM (StateT.run' (simulateQ impl (f <$> mx)) s) : SPMF _) = f <$> (liftM (StateT.run' (simulateQ impl mx) s) : SPMF _) rw [simulateQ_map, StateT.run'_map', liftM_map]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/SimSemantics/StateT/BundledSemantics.lean:53-62
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