diff --git a/src/th-bool/Sidekick_th_bool.ml b/src/th-bool/Sidekick_th_bool.ml
index 4e5bfb70..0cf324d4 100644
--- a/src/th-bool/Sidekick_th_bool.ml
+++ b/src/th-bool/Sidekick_th_bool.ml
@@ -35,9 +35,9 @@ module Make_dyn_tseitin(A : ARG)
     --> maybe, cache the clause inside the literal *)
 
   module A = A
-  module Solver = A.S.Internal
-  module T = Solver.A.Term
-  module Lit = Solver.A.Lit
+  module SI = A.S.Solver_internal
+  module T = SI.A.Term
+  module Lit = SI.A.Lit
 
   type term = T.t
 
@@ -47,12 +47,12 @@ module Make_dyn_tseitin(A : ARG)
     expanded: unit T_tbl.t; (* set of literals already expanded *)
   }
 
-  let tseitin ~final (self:t) (solver:Solver.t) (lit:Lit.t) (lit_t:term) (v:term View.t) : unit =
+  let tseitin ~final (self:t) (solver:SI.t) (lit:Lit.t) (lit_t:term) (v:term View.t) : unit =
     Log.debugf 5 (fun k->k "(@[th_bool.tseitin@ %a@])" Lit.pp lit);
     let expanded () = T_tbl.mem self.expanded lit_t in
     let add_axiom c =
       T_tbl.replace self.expanded lit_t ();
-      Solver.add_persistent_axiom solver c
+      SI.add_persistent_axiom solver c
     in
     match v with
     | B_not _ -> assert false (* normalized *)
@@ -62,13 +62,13 @@ module Make_dyn_tseitin(A : ARG)
         (* propagate [lit => subs_i] *)
         IArray.iter
           (fun sub ->
-             let sublit = Solver.mk_lit solver sub in
-             Solver.propagate_l solver sublit [lit])
+             let sublit = SI.mk_lit solver sub in
+             SI.propagate_l solver sublit [lit])
           subs
       ) else if final && not @@ expanded () then (
         (* axiom [¬lit => ∨_i ¬ subs_i] *)
         let subs = IArray.to_list subs in
-        let c = Lit.neg lit :: List.map (Solver.mk_lit solver ~sign:false) subs in
+        let c = Lit.neg lit :: List.map (SI.mk_lit solver ~sign:false) subs in
         add_axiom c
       )
     | B_or subs ->
@@ -76,13 +76,13 @@ module Make_dyn_tseitin(A : ARG)
         (* propagate [¬lit => ¬subs_i] *)
         IArray.iter
           (fun sub ->
-             let sublit = Solver.mk_lit solver ~sign:false sub in
-             Solver.add_local_axiom solver [Lit.neg lit; sublit])
+             let sublit = SI.mk_lit solver ~sign:false sub in
+             SI.add_local_axiom solver [Lit.neg lit; sublit])
           subs
       ) else if final && not @@ expanded () then (
         (* axiom [lit => ∨_i subs_i] *)
         let subs = IArray.to_list subs in
-        let c = Lit.neg lit :: List.map (Solver.mk_lit solver ~sign:true) subs in
+        let c = Lit.neg lit :: List.map (SI.mk_lit solver ~sign:true) subs in
         add_axiom c
       )
     | B_imply (guard,concl) ->
@@ -90,17 +90,17 @@ module Make_dyn_tseitin(A : ARG)
         (* axiom [lit => ∨_i ¬guard_i ∨ concl] *)
         let guard = IArray.to_list guard in
         let c =
-          Solver.mk_lit solver concl :: Lit.neg lit ::
-          List.map (Solver.mk_lit solver ~sign:false) guard in
+          SI.mk_lit solver concl :: Lit.neg lit ::
+          List.map (SI.mk_lit solver ~sign:false) guard in
         add_axiom c
       ) else if not @@ Lit.sign lit then (
         (* propagate [¬lit => ¬concl] *)
-        Solver.propagate_l solver (Solver.mk_lit solver ~sign:false concl) [lit];
+        SI.propagate_l solver (SI.mk_lit solver ~sign:false concl) [lit];
         (* propagate [¬lit => ∧_i guard_i] *)
         IArray.iter
           (fun sub ->
-             let sublit = Solver.mk_lit solver ~sign:true sub in
-             Solver.propagate_l solver sublit [lit])
+             let sublit = SI.mk_lit solver ~sign:true sub in
+             SI.propagate_l solver sublit [lit])
           guard
       )
 
@@ -118,10 +118,10 @@ module Make_dyn_tseitin(A : ARG)
   let final_check (self:t) acts (lits:Lit.t Iter.t) =
     check_ ~final:true self acts lits
 
-  let create_and_setup (solver:Solver.t) : t =
+  let create_and_setup (solver:SI.t) : t =
     let self = {expanded=T_tbl.create 24} in
-    Solver.on_final_check solver (final_check self);
-    Solver.on_partial_check solver (partial_check self);
+    SI.on_final_check solver (final_check self);
+    SI.on_partial_check solver (partial_check self);
     self
 
   let theory =
diff --git a/src/th-cstor/Sidekick_th_cstor.ml b/src/th-cstor/Sidekick_th_cstor.ml
index 9e314afb..549a720e 100644
--- a/src/th-cstor/Sidekick_th_cstor.ml
+++ b/src/th-cstor/Sidekick_th_cstor.ml
@@ -19,11 +19,11 @@ end
 
 module Make(A : ARG) : S with module A = A = struct
   module A = A
-  module Solver = A.S.Internal
+  module SI = A.S.Solver_internal
   module T = A.S.A.Term
-  module N = Solver.N
+  module N = SI.N
   module Fun = A.S.A.Fun
-  module Expl = Solver.Expl
+  module Expl = SI.Expl
 
   type data = {
     t: T.t;
@@ -39,10 +39,10 @@ module Make(A : ARG) : S with module A = A = struct
   end
 
   type t = {
-    k: data Solver.Key.t;
+    k: data SI.Key.t;
   }
 
-  let on_merge (solver:Solver.t) n1 tc1 n2 tc2 e_n1_n2 : unit =
+  let on_merge (solver:SI.t) n1 tc1 n2 tc2 e_n1_n2 : unit =
     Log.debugf 5
       (fun k->k "(@[th-cstor.on_merge@ @[:c1 %a@ (term %a)@]@ @[:c2 %a@ (term %a)@]@])"
           N.pp n1 T.pp tc1.t N.pp n2 T.pp tc2.t); 
@@ -54,11 +54,11 @@ module Make(A : ARG) : S with module A = A = struct
         (* same function: injectivity *)
         assert (List.length l1 = List.length l2);
         List.iter2
-          (fun u1 u2 -> Solver.cc_merge_t solver u1 u2 expl)
+          (fun u1 u2 -> SI.cc_merge_t solver u1 u2 expl)
           l1 l2
       ) else (
         (* different function: disjointness *)
-        Solver.raise_conflict solver expl
+        SI.raise_conflict solver expl
       )
     | _ -> assert false
 
@@ -68,10 +68,10 @@ module Make(A : ARG) : S with module A = A = struct
     | T_cstor _ -> Some {t;n}
     | _ -> None
 
-  let create_and_setup (solver:Solver.t) : t =
-    let k = Solver.Key.create solver ~on_merge (module Data) in
-    Solver.on_cc_merge solver ~k on_merge;
-    Solver.on_cc_new_term solver ~k on_new_term;
+  let create_and_setup (solver:SI.t) : t =
+    let k = SI.Key.create solver (module Data) in
+    SI.on_cc_merge solver ~k on_merge;
+    SI.on_cc_new_term solver ~k on_new_term;
     {k}
 
   let theory = A.S.mk_theory ~name ~create_and_setup ()
diff --git a/src/th-distinct/Sidekick_th_distinct.ml b/src/th-distinct/Sidekick_th_distinct.ml
index ca3588d2..a2d413e4 100644
--- a/src/th-distinct/Sidekick_th_distinct.ml
+++ b/src/th-distinct/Sidekick_th_distinct.ml
@@ -1,130 +1,93 @@
 
 module type ARG = sig
-  include Sidekick_core.TERM_LIT
-
-  module Arg_distinct : sig
-    val as_distinct : Term.t -> Term.t Iter.t option
-    val mk_eq : Term.state -> Term.t -> Term.t -> Term.t
-  end
+  module S : Sidekick_core.SOLVER
+  val as_distinct : S.A.Term.t -> S.A.Term.t Iter.t option
+  val mk_eq : S.A.Term.state -> S.A.Term.t -> S.A.Term.t -> S.A.Term.t
 end
   
 module type S = sig
-  type term
-  type term_state
-  type lit
-
-  module Data : sig
-    type t
-    val empty : t
-    val merge : t -> t -> t
-  end
-
-  val th : Sidekick_smt.Theory.t
+  module A : ARG
+  val theory : A.S.theory
 end
 
-module Make(A : ARG with type Lit.t = Sidekick_smt.Lit.t
-                     and type T.t = Sidekick_smt.Term.t
-                     and type T.state = Sidekick_smt.Term.state) = struct
-  module T = A.T
-  module Lit = A.Lit
+module Make(A : ARG) : S with module A = A = struct
+  module A = A
+  module SI = A.S.Solver_internal
+  module T = A.S.A.Term
+  module Lit = A.S.A.Lit
   module IM = CCMap.Make(Lit)
+  module N = SI.N
+  module Expl = SI.Expl
 
   type term = T.t
-  type term_state = T.state
-  type lit = A.Lit.t
-  type data = term IM.t (* "distinct" lit -> term appearing under it*)
 
-  let pp_data out m =
-    Fmt.fprintf out
-      "{@[%a@]}" Fmt.(seq ~sep:(return ",@ ") @@ pair Lit.pp T.pp) (IM.to_seq m)
+  module Data = struct
+    type t = T.t IM.t (* "distinct" lit -> term appearing under it*)
 
-  let key : (term,lit,data) Sidekick_cc.Key.t =
     let merge m1 m2 =
       IM.merge_safe m1 m2
         ~f:(fun _ pair -> match pair with
             | `Left x | `Right x -> Some x
             | `Both (x,_) -> Some x)
-    and eq = IM.equal T.equal in
-    Sidekick_cc.Key.create
-      ~pp:pp_data
-      ~name:"distinct"
-      ~merge ~eq ()
 
-  (* micro theory *)
-  module Micro(CC : Sidekick_cc.Congruence_closure.S
-               with type term = T.t
-                and type lit = Lit.t
-                and module Key = Sidekick_cc.Key) = struct
-    exception E_exit
-
-    let on_merge cc n1 m1 n2 m2 expl12 =
-      Log.debugf 5
-        (fun k->k "(@[th_distinct.on_merge@ @[:n1 %a@ :map2 %a@]@ @[:n2 %a@ :map2 %a@]@])"
-            CC.N.pp n1 pp_data m1 CC.N.pp n2 pp_data m2);
-      try
-        let _i =
-          IM.merge
-            (fun lit o1 o2 ->
-               match o1, o2 with
-               | Some t1, Some t2 ->
-                 (* conflict! two terms under the same "distinct" [lit]
-                    are merged, where [lit = distinct(t1,t2,…)].
-                    The conflict is:
-                    [lit, t1=n1, t2=n2, expl-merge(n1,n2) ==> false]
-                 *)
-                 assert (not @@ T.equal t1 t2);
-                 let expl = CC.Expl.mk_list
-                     [expl12;
-                      CC.Expl.mk_lit lit;
-                      CC.Expl.mk_merge n1 (CC.Theory.add_term cc t1);
-                      CC.Expl.mk_merge n2 (CC.Theory.add_term cc t2);
-                     ] in
-                 CC.Theory.raise_conflict cc expl;
-                 raise_notrace E_exit
-               | _ -> None)
-            m1 m2
-        in
-        ()
-      with E_exit -> ()
-
-    let on_new_term _ _ _ = None
-
-    let th =
-      CC.Theory.make ~key ~on_merge ~on_new_term ()
+    let pp out m =
+      Fmt.fprintf out
+        "{@[%a@]}" Fmt.(seq ~sep:(return ",@ ") @@ pair Lit.pp T.pp) (IM.to_seq m)
   end
 
+  (* called when two classes with "distinct" sets are merged *)
+  let on_merge (solver:SI.t) n1 m1 n2 m2 expl12 =
+    Log.debugf 5
+      (fun k->k "(@[th_distinct.on_merge@ @[:n1 %a@ :map2 %a@]@ @[:n2 %a@ :map2 %a@]@])"
+          N.pp n1 Data.pp m1 N.pp n2 Data.pp m2);
+    let _i: Data.t =
+      IM.merge
+        (fun lit o1 o2 ->
+           match o1, o2 with
+           | Some t1, Some t2 ->
+             (* conflict! two terms under the same "distinct" [lit]
+                are merged, where [lit = distinct(t1,t2,…)].
+                The conflict is:
+                [lit, t1=n1, t2=n2, expl-merge(n1,n2) ==> false]
+             *)
+             assert (not @@ T.equal t1 t2);
+             let expl = Expl.mk_list
+                 [expl12;
+                  Expl.mk_lit lit;
+                  Expl.mk_merge n1 (SI.cc_add_term solver t1);
+                  Expl.mk_merge n2 (SI.cc_add_term solver t2);
+                 ] in
+             SI.raise_conflict solver expl
+           | _ -> None)
+        m1 m2
+    in ()
+
   module T_tbl = CCHashtbl.Make(T)
-  type st = {
-    tst: T.state;
+  type t = {
+    k: Data.t SI.Key.t;
     expanded: unit T_tbl.t; (* negative "distinct" that have been case-split on *)
   }
 
-  let create tst : st = { expanded=T_tbl.create 12; tst; }
-
   let pp_c out c = Fmt.fprintf out "(@[<hv>%a@])" (Util.pp_list Lit.pp) c
 
-  module CC = Sidekick_smt.CC
-
-  let process_lit (st:st) (acts:Theory.actions) (lit:Lit.t) (lit_t:term) (subs:term Iter.t) : unit =
-    let (module A) = acts in
+  (* process one new assertion *)
+  let process_lit (self:t) (solver:SI.t) (lit:Lit.t) (lit_t:term) (subs:term Iter.t) : unit =
     Log.debugf 5 (fun k->k "(@[th_distinct.process@ %a@])" Lit.pp lit);
-    let add_axiom c = A.add_persistent_axiom c in
-    let cc = A.cc in
+    let add_axiom c = SI.add_persistent_axiom solver c in
     if Lit.sign lit then (
-      (* assert [distinct subs], so we update the node of each [t in subs]
-         with [lit] *)
-      (* FIXME: detect if some subs are already equal *)
+      (* assert [distinct subs], so we update the node of each [t in subs] with [lit] *)
       subs
         (fun sub ->
-          let n = CC.Theory.add_term cc sub in
-          CC.Theory.add_data cc n key (IM.singleton lit sub));
-    ) else if not @@ T_tbl.mem st.expanded lit_t then (
+          let n = SI.cc_add_term solver sub in
+          SI.cc_add_data solver n ~k:self.k (IM.singleton lit sub));
+    ) else if not @@ T_tbl.mem self.expanded lit_t then (
       (* add clause [distinct t1…tn ∨ ∨_{i,j>i} t_i=j] *)
-      T_tbl.add st.expanded lit_t ();
+      T_tbl.add self.expanded lit_t ();
       let l = Iter.to_list subs in
       let c =
         Iter.diagonal_l l
-        |> Iter.map (fun (t,u) -> Lit.atom st.tst @@ T.mk_eq st.tst t u)
+        |> Iter.map
+          (fun (t,u) -> SI.mk_lit solver @@ A.mk_eq (SI.tst solver) t u)
         |> Iter.to_rev_list
       in
       let c = Lit.neg lit :: c in
@@ -132,74 +95,21 @@ module Make(A : ARG with type Lit.t = Sidekick_smt.Lit.t
       add_axiom c
     )
 
-  let partial_check st (acts:Theory.actions) lits : unit =
+  let partial_check st (solver: SI.t) lits : unit =
     lits
       (fun lit ->
          let t = Lit.term lit in
-         match T.as_distinct t with
+         match A.as_distinct t with
          | None -> ()
-         | Some subs -> process_lit st acts lit t subs)
+         | Some subs -> process_lit st solver lit t subs)
 
-  let cc_th = let module T = Micro(CC) in T.th
+  let create_and_setup (solver:SI.t) : t =
+    let k = SI.Key.create solver (module Data) in
+    let self = { expanded=T_tbl.create 8; k; } in
+    SI.on_cc_merge solver ~k on_merge;
+    SI.on_final_check solver (partial_check self);
+    self
 
-  let th =
-    Sidekick_smt.Theory.make
-      ~name:"distinct"
-      ~partial_check
-      ~final_check:(fun _ _ _ -> ())
-      ~cc_th:(fun _ -> [cc_th])
-      ~create ()
+  let theory =
+    A.S.mk_theory ~name:"distinct" ~create_and_setup ()
 end
-
-module Arg = struct
-  open Sidekick_smt
-  open Sidekick_smt.Solver_types
-
-  let id_distinct = ID.make "distinct"
-
-  let relevant _id _ _ = true
-  let get_ty _ _ = Ty.prop
-  let abs ~self _a = self, true
-
-  module T = struct
-    include Term
-    let mk_eq = eq
-
-    let as_distinct t : _ option =
-      match view t with
-      | App_cst ({cst_id;_}, args) when ID.equal cst_id id_distinct ->
-        Some (IArray.to_seq args)
-      | _ -> None
-  end
-
-  module Lit = Sidekick_smt.Lit
-
-  let eval args =
-    let module Value = Sidekick_smt.Value in
-    Log.debugf 5
-      (fun k->k "(@[distinct.eval@ %a@])" (Fmt.seq Value.pp) (IArray.to_seq args));
-    if
-      Iter.diagonal (IArray.to_seq args)
-      |> Iter.for_all (fun (x,y) -> not @@ Value.equal x y)
-    then Value.true_
-    else Value.false_
-
-  let c_distinct =
-    {cst_id=id_distinct;
-     cst_view=Cst_def {
-         pp=None; abs; ty=get_ty; relevant; do_cc=true; eval; }; }
-
-  let distinct st a =
-    if IArray.length a <= 1
-    then T.true_ st
-    else T.app_cst st c_distinct a
-
-  let distinct_l st = function
-    | [] | [_] -> T.true_ st
-    | xs -> distinct st (IArray.of_list xs)
-end
-
-let distinct = Arg.distinct
-let distinct_l = Arg.distinct_l
-
-include Make(Arg)
diff --git a/src/th-distinct/Sidekick_th_distinct.mli b/src/th-distinct/Sidekick_th_distinct.mli
index c5578bf4..8e0fdcec 100644
--- a/src/th-distinct/Sidekick_th_distinct.mli
+++ b/src/th-distinct/Sidekick_th_distinct.mli
@@ -5,49 +5,15 @@
     "distinct" efficiently.
   *)
 
-module Term = Sidekick_smt.Term
-
 module type ARG = sig
-  module T : sig
-    type t
-    type state
-    val pp : t Fmt.printer
-    val equal : t -> t -> bool
-    val hash : t -> int
-    val as_distinct : t -> t Iter.t option
-    val mk_eq : state -> t -> t -> t
-  end
-  module Lit : sig
-    type t
-    val term : t -> T.t
-    val neg : t -> t
-    val sign : t -> bool
-    val compare : t -> t -> int
-    val atom : T.state -> ?sign:bool -> T.t -> t
-    val pp : t Fmt.printer
-  end
+  module S : Sidekick_core.SOLVER
+  val as_distinct : S.A.Term.t -> S.A.Term.t Iter.t option
+  val mk_eq : S.A.Term.state -> S.A.Term.t -> S.A.Term.t -> S.A.Term.t
 end
   
 module type S = sig
-  type term
-  type term_state
-  type lit
-
-  type data
-  val key : (term, lit, data) Sidekick_cc.Key.t
-  val th : Sidekick_smt.Theory.t
+  module A : ARG
+  val theory : A.S.theory
 end
 
-(* TODO: generalize theories *)
-module Make(A : ARG with type T.t = Sidekick_smt.Term.t
-              and type T.state = Sidekick_smt.Term.state
-              and type Lit.t = Sidekick_smt.Lit.t) :
-  S with type term = A.T.t
-     and type lit = A.Lit.t
-     and type term_state = A.T.state
-
-val distinct : Term.state -> Term.t IArray.t -> Term.t
-val distinct_l : Term.state -> Term.t list -> Term.t
-
-(** Default instance *)
-include S with type term = Term.t and type lit = Sidekick_smt.Lit.t
+module Make(A : ARG) : S with module A = A
diff --git a/src/th-distinct/dune b/src/th-distinct/dune
index e8237c6c..13e3f26f 100644
--- a/src/th-distinct/dune
+++ b/src/th-distinct/dune
@@ -1,7 +1,7 @@
 
 (library
   (name Sidekick_th_distinct)
-  (public_name sidekick.smt.th-distinct)
+  (public_name sidekick.th-distinct)
   (libraries containers sidekick.core sidekick.util)
   (flags :standard -open Sidekick_util))
 
diff --git a/src/th-ite/Sidekick_th_ite.ml b/src/th-ite/Sidekick_th_ite.ml
index 176b2ea7..a35931fc 100644
--- a/src/th-ite/Sidekick_th_ite.ml
+++ b/src/th-ite/Sidekick_th_ite.ml
@@ -1,79 +1,73 @@
 
 (** {1 Theory for if-then-else} *)
 
-type 't ite_view =
-  | T_ite of 't * 't * 't
-  | T_bool of bool
-  | T_other of 't
-
-
-module type S = sig
-  type lit
-  type term
-
-  val th : Sidekick_smt.Theory.t
+module Ite_view = struct
+  type 't t =
+    | T_ite of 't * 't * 't
+    | T_bool of bool
+    | T_other of 't
 end
 
 module type ARG = sig
-  module T : sig
-    type t
-    type state
-    val pp : t Fmt.printer
-    val equal : t -> t -> bool
-    val view_as_ite : t -> t ite_view
+  module S : Sidekick_core.SOLVER
+  type term = S.A.Term.t
 
-    module Set : CCSet.S with type elt = t
-  end
-  module Lit : sig
-    type t
-    val term : t -> T.t
-    val atom : T.state -> ?sign:bool -> T.t -> t
-    val pp : t Fmt.printer
-  end
+  val view_as_ite : term -> term Ite_view.t
+
+  module T_set : CCSet.S with type elt = term
 end
 
-module Make(Arg : ARG with type T.state = Sidekick_smt.Term.state and type T.t = Sidekick_smt.Term.t)
-  : S with type lit = Arg.Lit.t and type term = Arg.T.t
-= struct
-  module Th = Sidekick_smt.Theory
-  module N = Th.CC_eq_class
-  module Expl = Th.CC_expl
-  module CC = Sidekick_smt.CC
+module type S = sig
+  module A : ARG
+  val theory : A.S.theory
+end
 
-  open Arg
-  type lit = Lit.t
+module Make(A : ARG)
+(*   : S with module A = A *)
+= struct
+  module A = A
+  module Solver = A.S.Solver_internal
+  module N = Solver.N
+  module Expl = Solver.Expl
+  module T = A.S.A.Term
+
+  type lit = A.S.A.Lit.t
   type term = T.t
 
-  type data = T.Set.t
-  (* associate to each class [t] the set of [ite a b c] where [a=t] *)
+  module Data = struct
+    type t = A.T_set.t
+    (* associate to each class [t] the set of [ite a b c] where [a=t] *)
 
-  let pp_data = Fmt.(map T.Set.to_seq @@ seq ~sep:(return ",@ ") T.pp)
+    let pp = Fmt.(map A.T_set.to_seq @@ seq ~sep:(return ",@ ") T.pp)
+    let merge = A.T_set.union
+  end
 
-  let key : (_,_,data) Sidekick_cc.Key.t = Sidekick_cc.Key.create
-      ~pp:pp_data ~name:"ite" ~eq:T.Set.equal ~merge:T.Set.union ()
+  type t = {
+    k: Data.t Solver.Key.t;
+  }
 
-  type t = T.state
-
-  let on_merge (_st:t) (acts:Sidekick_smt.Theory.actions) n1 n2 e_n1_n2 : unit =
-    let (module A) = acts in
+  let on_merge (self:t) (solver:Solver.t) n1 n2 e_n1_n2 : unit =
     Log.debugf 5
       (fun k->k "(@[th-ite.on_merge@ :c1 %a@ :c2 %a@])" N.pp n1 N.pp n2); 
     (* check if [n1] has some [ite] parents, and if [n2] is true/false *)
     let check_ n1 n2 =
-      match CC.Theory.get_data A.cc n1 key, T.view_as_ite (N.term n2) with
+      match Solver.cc_data solver ~k:self.k n1, A.view_as_ite (N.term n2) with
       | Some set, T_bool n2_true ->
-        assert (not @@ T.Set.is_empty set);
-        T.Set.iter
-          (fun parent_1 -> match T.view_as_ite parent_1 with
+        assert (not @@ A.T_set.is_empty set);
+        A.T_set.iter
+          (fun parent_1 -> match A.view_as_ite parent_1 with
              | T_ite (a1,b1,c1) ->
-               let n_parent1 = CC.add_term A.cc parent_1 in
-               let expl = Expl.mk_list [e_n1_n2; Expl.mk_merge n1 (CC.add_term A.cc a1)] in
+               let n_parent1 = Solver.cc_add_term solver parent_1 in
+               let expl =
+                 Expl.mk_list [
+                   e_n1_n2;
+                   Expl.mk_merge n1 (Solver.cc_add_term solver a1)] in
                if n2_true then (
                  (* [a1 = n1 = n2 = true] so [if a1 b1 c1 = b1] *)
-                 CC.Theory.merge A.cc n_parent1 (CC.add_term A.cc b1) expl
+                 Solver.cc_merge solver n_parent1 (Solver.cc_add_term solver b1) expl
                ) else (
                  (* [a1 = n1 = n2 = false] so [if a1 b1 c1 = c1] *)
-                 CC.Theory.merge A.cc n_parent1 (CC.add_term A.cc c1) expl
+                 Solver.cc_merge solver n_parent1 (Solver.cc_add_term solver c1) expl
                )
              | _ -> assert false)
           set
@@ -83,31 +77,22 @@ module Make(Arg : ARG with type T.state = Sidekick_smt.Term.state and type T.t =
     check_ n2 n1;
     ()
 
-  let on_new_term _ (acts:Sidekick_smt.Theory.actions) (t:T.t) =
-    let (module A) = acts in
-    match T.view_as_ite t with
+  let on_new_term (self:t) (solver:Solver.t) _n (t:T.t) =
+    match A.view_as_ite t with
     | T_ite (a,_,_) ->
       (* add [t] to parents of [a] *)
-      let n_a = CC.find A.cc @@ CC.add_term A.cc a in
-      CC.Theory.add_data A.cc n_a key (T.Set.singleton t)
-    | _ -> ()
+      let n_a = Solver.cc_find solver @@ Solver.cc_add_term solver a in
+      Solver.cc_add_data solver n_a ~k:self.k (A.T_set.singleton t);
+      None
+    | _ -> None
 
-  let th =
-    Sidekick_smt.Theory.make ~name:"ite" ~create:(fun st->st)
-      ~on_merge ~final_check:(fun _ _ _ -> ())
-      ~on_new_term
-      ()
+  let create_and_setup (solver:Solver.t) : t =
+    let k = Solver.Key.create solver (module Data) in
+    let self = {k} in
+    Solver.on_cc_merge_all solver (on_merge self);
+    Solver.on_cc_new_term solver ~k (on_new_term self);
+    self
 
+  let theory = A.S.mk_theory ~name:"ite" ~create_and_setup ()
 end
 
-
-include Make(struct
-    module T = struct
-      include Sidekick_smt.Term
-      let[@inline] view_as_ite t = match view t with
-        | If (a,b,c) -> T_ite (a,b,c)
-        | Bool b -> T_bool b
-        | _ -> T_other t
-      end
-    module Lit = Sidekick_smt.Lit
-    end)
diff --git a/src/th-ite/dune b/src/th-ite/dune
index d6cee8a8..a521adf2 100644
--- a/src/th-ite/dune
+++ b/src/th-ite/dune
@@ -2,7 +2,7 @@
 
 (library
   (name Sidekick_th_ite)
-  (public_name sidekick.smt.th-ite)
-  (libraries containers sidekick.smt)
+  (public_name sidekick.th-ite)
+  (libraries containers sidekick.core)
   (flags :standard -open Sidekick_util))