Module Type DATAFLOW_SOLVER.
Declare Module L: SEMILATTICE.
(** [fixpoint successors transf ep ev] is the solver. It returns either an error or a mapping from program points to values of type [L.t] representing the solution.  [successors] is a finite map returning the list of successors of the given program point. [transf] is the transfer function, [ep] the entry point, and [ev] the minimal abstract value for [ep]. *)
Parameter fixpoint:
forall {A: Type} (code: PTree.t A) (successors: A -> list positive)
(transf: positive -> L.t -> L.t)
(ep: positive) (ev: L.t),
option (PMap.t L.t).
(** The [fixpoint_solution] theorem shows that the returned solution, if any, satisfies the dataflow inequations. *)

Axiom fixpoint_solution:
forall A (code: PTree.t A) successors transf ep ev res n instr s,
fixpoint code successors transf ep ev = Some res ->
code!n = Some instr -> In s (successors instr) ->
(forall n, L.eq (transf n L.bot) L.bot) ->
L.ge res!!s (transf n res!!n).