infer_noexn p ctx t returns [Some(t',a)] where [t'] is a refinement of [t] and [a] is some type for [t'] in the context [ctx], and [None] otherwise, possibly adding new constraints in [p]. The metavariables of [p] are updated when a metavariable is instantiated or created. [ctx] must be well sorted.

check_noexn p ctx t a returns Some t' if t can be refined to t' of type a in context ctx, and None otherwise, possibly adding new constraints in p. The metavariables of p are updated when a metavariable is instantiated or created. The context ctx and the type a must be well sorted.