(*
MSAT is free software, using the Apache license, see file LICENSE
Copyright 2014 Guillaume Bury
Copyright 2014 Simon Cruanes
*)

module type S = sig
  (** Signature for a module handling proof by resolution from sat solving traces *)

    (** {3 Type declarations} *)

  exception Insuficient_hyps
  (** Raised when a complete resolution derivation cannot be found using the current hypotheses. *)

  type atom
  type clause
  type lemma
  (** Abstract types for atoms, clauses and theoriy-specific lemmas *)

  type proof_node = {
    conclusion : clause;
    step : step;
  }
  and proof = unit -> proof_node
  and step =
    | Hypothesis
    | Lemma of lemma
    | Resolution of proof * proof * atom
  (** Lazy type for proof trees. *)

  (** {3 Resolution helpers} *)
  val to_list : clause -> atom list
  (** Returns the sorted list of atoms of a clause. *)

  val merge : atom list -> atom list -> atom list
  (** Merge two sorted atom list using a suitable comparison function. *)

  val resolve : atom list -> atom list * atom list
  (** Performs a "resolution step" on a sorted list of atoms.
      [resolve (List.merge l1 l2)] where [l1] and [l2] are sorted atom lists should return the pair
      [\[a\], l'], where [l'] is the result of the resolution of [l1] and [l2] over [a]. *)

  (** {3 Proof building functions} *)

  val is_proven : clause -> bool
  (** Returns [true] if the clause has a derivation in the current proof graph, and [false] otherwise. *)

  val learn : clause Vec.t -> unit
  (** Learn and build proofs for the clause in the vector. Clauses in the vector should be in the order they were learned. *)

  val assert_can_prove_unsat : clause -> unit
  (** [assert_can_prove_unsat c] tries and prove the empty clause from [c]. [c] may be a learnt clause not yet proved.
      @raise Insuficient_hyps if it is impossible. *)

  val prove_unsat : clause -> proof
  (** Given a conflict clause [c], returns a proof of the empty clause. Same as [assert_can_prove_unsat] but returns
      the proof if it succeeds.
      @raise Insuficient_hyps if it does not succeed. *)

  val unsat_core : proof -> clause list
  (** Returns the unsat_core of the given proof, i.e the lists of conclusions of all leafs of the proof. *)

  val print_dot : Format.formatter -> proof -> unit
  (** Print the given proof in dot format on the given formatter. *)

end