type 'a substitution = (int * 'a foterm) list
-type comparison = Lt | Le | Eq | Ge | Gt | Incomparable
+type comparison = Lt | Eq | Gt | Incomparable | Invertible
-type rule = SuperpositionRight | SuperpositionLeft | Demodulation
+type rule = Superposition | Demodulation
+
+(* A Discrimination tree is a map: foterm |-> (dir, clause) *)
type direction = Left2Right | Right2Left | Nodir
+
type position = int list
type 'a proof =
- | Exact of 'a
+ | Exact of 'a foterm
+ (* for theorems like T : \forall x. C[x] = D[x] the proof is
+ * a foterm like (Node [ Leaf T ; Var i ]), while for the Goal
+ * it is just (Var g), i.e. the identity proof *)
| Step of rule * int * int * direction * position * 'a substitution
(* rule, eq1, eq2, direction of eq2, position, substitution *)
type 'a passive_clause = int * 'a unit_clause (* weight * equation *)
+val is_eq_clause : 'a unit_clause -> bool
+val vars_of_term : 'a foterm -> int list
+
module M : Map.S with type key = int
-type 'a bag = 'a unit_clause M.t
+type 'a bag = int (* max ID *)
+ * (('a unit_clause * bool * int) M.t)
+
+(* also gives a fresh ID to the clause *)
+ val add_to_bag :
+ 'a unit_clause -> 'a bag ->
+ 'a bag * 'a unit_clause
+
+ val replace_in_bag :
+ 'a unit_clause * bool * int -> 'a bag ->
+ 'a bag
+
+ val get_from_bag :
+ int -> 'a bag -> 'a unit_clause * bool * int
+
+ val empty_bag : 'a bag
module type Blob =
sig
+ (* Blob is the type for opaque leaves:
+ * - checking equlity should be efficient
+ * - atoms have to be equipped with a total order relation
+ *)
type t
val eq : t -> t -> bool
val compare : t -> t -> int
+ val eqP : t
+ (* TODO: consider taking in input an imperative buffer for Format
+ * val pp : Format.formatter -> t -> unit
+ * *)
+ val is_eq : t foterm -> (t foterm * t foterm * t foterm) option
val pp : t -> string
- end
-module Utils (B : Blob) :
- sig
- val eq_literal : B.t literal -> B.t literal -> bool
- val compare_literal : B.t literal -> B.t literal -> int
+ type input
+ val embed : input -> t foterm
+ (* saturate [proof] [type] -> [proof] * [type] *)
+ val saturate : input -> input -> t foterm * t foterm
- val eq_unit_clause : B.t unit_clause -> B.t unit_clause -> bool
- val compare_unit_clause : B.t unit_clause -> B.t unit_clause -> int
end
+