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.

Theorem input_eq_dec : forall x y: input, {x = y} + {x <> y}.