Module VarDFunctor (Map : VWS
with Definition E.t := string
with Definition E.eq := @eq string).
Definition key_eq_dec := string_dec.
Definition value_eq_dec := string_dec.
Definition val_eq_dec : forall v v' : option value, {v = v'} + {v <> v'}.
decide equality.
auto using value_eq_dec.
Defined.
Definition trace_state_correct (trace : list (input * output)) (st : data) (st' : data) :=
forall k,
fst (interpret k (rev (inputs_with_key trace k)) (Map.find k st)) = Map.find k st'.
Ltac vard_unfold :=
unfold runHandler,
getk,
setk,
delk,
resp in *; monad_unfold.

Lemma trace_state_correct_trace_correct :
forall st st' st'' trace t,
trace_state_correct trace st st' ->
trace_correct' st trace ->
step_1 st' st'' t ->
trace_correct' st (trace ++ t).