diff --git a/src/cc/Sidekick_cc.ml b/src/cc/Sidekick_cc.ml
index 91905900..f6ad319a 100644
--- a/src/cc/Sidekick_cc.ml
+++ b/src/cc/Sidekick_cc.ml
@@ -1,3 +1,4 @@
+open Sidekick_core
 module View = Sidekick_core.CC_view
 
 type ('f, 't, 'ts) view = ('f, 't, 'ts) View.t =
@@ -9,21 +10,27 @@ type ('f, 't, 'ts) view = ('f, 't, 'ts) View.t =
   | Not of 't
   | Opaque of 't (* do not enter *)
 
-module type ARG = Sidekick_core.CC_ARG
 module type S = Sidekick_core.CC_S
 
-module Make(CC_A: ARG) = struct
-  module A = CC_A
-  type term = A.A.Term.t
-  type term_state = A.A.Term.state
-  type lit = A.Lit.t
-  type fun_ = A.A.Fun.t
-  type proof = A.A.Proof.t
-  type actions = A.Actions.t
+module Make (A: CC_ARG)
+  : S with module T = A.T 
+       and module Lit = A.Lit
+       and module P = A.P
+       and module Actions = A.Actions
+= struct
+  module T = A.T
+  module P = A.P
+  module Lit = A.Lit
+  module Actions = A.Actions
+  type term = T.Term.t
+  type term_state = T.Term.state
+  type lit = Lit.t
+  type fun_ = T.Fun.t
+  type proof = P.t
+  type actions = Actions.t
 
-  module T = A.A.Term
-  module Fun = A.A.Fun
-  module Lit = CC_A.Lit
+  module Term = T.Term
+  module Fun = T.Fun
 
   module Bits : sig
     type t = private int
@@ -94,9 +101,9 @@ module Make(CC_A: ARG) = struct
     type t = node
 
     let[@inline] equal (n1:t) n2 = n1 == n2
-    let[@inline] hash n = T.hash n.n_term
+    let[@inline] hash n = Term.hash n.n_term
     let[@inline] term n = n.n_term
-    let[@inline] pp out n = T.pp out n.n_term
+    let[@inline] pp out n = Term.pp out n.n_term
     let[@inline] as_lit n = n.n_as_lit
 
     let make (t:term) : t =
@@ -158,7 +165,7 @@ module Make(CC_A: ARG) = struct
       | E_lit lit -> Lit.pp out lit
       | E_congruence (n1,n2) -> Fmt.fprintf out "(@[congruence@ %a@ %a@])" N.pp n1 N.pp n2
       | E_merge (a,b) -> Fmt.fprintf out "(@[merge@ %a@ %a@])" N.pp a N.pp b
-      | E_merge_t (a,b) -> Fmt.fprintf out "(@[merge@ %a@ %a@])" T.pp a T.pp b
+      | E_merge_t (a,b) -> Fmt.fprintf out "(@[merge@ %a@ %a@])" Term.pp a Term.pp b
       | E_and (a,b) ->
         Format.fprintf out "(@[<hv1>and@ %a@ %a@])" pp a pp b
 
@@ -167,7 +174,7 @@ module Make(CC_A: ARG) = struct
     let[@inline] mk_merge a b : t = 
       assert (same_class a b); 
       if N.equal a b then mk_reduction else E_merge (a,b)
-    let[@inline] mk_merge_t a b : t = if T.equal a b then mk_reduction else E_merge_t (a,b)
+    let[@inline] mk_merge_t a b : t = if Term.equal a b then mk_reduction else E_merge_t (a,b)
     let[@inline] mk_lit l : t = E_lit l
 
     let rec mk_list l =
@@ -227,7 +234,7 @@ module Make(CC_A: ARG) = struct
   end
 
   module Sig_tbl = CCHashtbl.Make(Signature)
-  module T_tbl = CCHashtbl.Make(T)
+  module T_tbl = CCHashtbl.Make(Term)
 
   type combine_task =
     | CT_merge of node * node * explanation
@@ -299,7 +306,7 @@ module Make(CC_A: ARG) = struct
         Fmt.fprintf out " (@[:forest %a :expl %a@])" N.pp e.next Expl.pp e.expl
     in
     let pp_n out n =
-      Fmt.fprintf out "(@[%a%a%a%a@])" T.pp n.n_term pp_root n pp_next n pp_expl n
+      Fmt.fprintf out "(@[%a%a%a%a@])" Term.pp n.n_term pp_root n pp_next n pp_expl n
     and pp_sig_e out (s,n) =
       Fmt.fprintf out "(@[<1>%a@ ~~> %a%a@])" Signature.pp s N.pp n pp_root n
     in
@@ -357,7 +364,7 @@ module Make(CC_A: ARG) = struct
     Vec.clear cc.combine;
     List.iter (fun f -> f cc e) cc.on_conflict;
     Stat.incr cc.count_conflict;
-    CC_A.Actions.raise_conflict acts e A.A.Proof.default
+    Actions.raise_conflict acts e P.default
 
   let[@inline] all_classes cc : repr Iter.t =
     T_tbl.values cc.tbl
@@ -440,7 +447,7 @@ module Make(CC_A: ARG) = struct
       begin match T_tbl.find cc.tbl a, T_tbl.find cc.tbl b with
         | a, b -> explain_pair cc acc a b
         | exception Not_found ->
-          Error.errorf "expl: cannot find node(s) for %a, %a" T.pp a T.pp b
+          Error.errorf "expl: cannot find node(s) for %a, %a" Term.pp a Term.pp b
       end
     | E_and (a,b) ->
       let acc = explain_decompose cc acc a in
@@ -477,7 +484,7 @@ module Make(CC_A: ARG) = struct
   (* add [t] to [cc] when not present already *)
   and add_new_term_ cc (t:term) : node =
     assert (not @@ mem cc t);
-    Log.debugf 15 (fun k->k "(@[cc.add-term@ %a@])" T.pp t);
+    Log.debugf 15 (fun k->k "(@[cc.add-term@ %a@])" Term.pp t);
     let n = N.make t in
     (* register sub-terms, add [t] to their parent list, and return the
        corresponding initial signature *)
@@ -486,7 +493,7 @@ module Make(CC_A: ARG) = struct
     (* remove term when we backtrack *)
     on_backtrack cc
       (fun () ->
-         Log.debugf 15 (fun k->k "(@[cc.remove-term@ %a@])" T.pp t);
+         Log.debugf 15 (fun k->k "(@[cc.remove-term@ %a@])" Term.pp t);
          T_tbl.remove cc.tbl t);
     (* add term to the table *)
     T_tbl.add cc.tbl t n;
@@ -514,7 +521,7 @@ module Make(CC_A: ARG) = struct
       sub
     in
     let[@inline] return x = Some x in
-    match CC_A.cc_view n.n_term with
+    match A.cc_view n.n_term with
     | Bool _ | Opaque _ -> None
     | Eq (a,b) ->
       let a = deref_sub a in
@@ -733,7 +740,7 @@ module Make(CC_A: ARG) = struct
            in
            List.iter (fun f -> f cc lit reason) cc.on_propagate;
            Stat.incr cc.count_props;
-           CC_A.Actions.propagate acts lit ~reason CC_A.A.Proof.default
+           Actions.propagate acts lit ~reason P.default
          | _ -> ())
 
   module Debug_ = struct
@@ -766,7 +773,7 @@ module Make(CC_A: ARG) = struct
     let t = Lit.term lit in
     Log.debugf 5 (fun k->k "(@[cc.assert_lit@ %a@])" Lit.pp lit);
     let sign = Lit.sign lit in
-    begin match CC_A.cc_view t with
+    begin match A.cc_view t with
       | Eq (a,b) when sign ->
         let a = add_term cc a in
         let b = add_term cc b in
@@ -837,9 +844,9 @@ module Make(CC_A: ARG) = struct
       count_props=Stat.mk_int stat "cc.propagations";
       count_merge=Stat.mk_int stat "cc.merges";
     } and true_ = lazy (
-        add_term cc (T.bool tst true)
+        add_term cc (Term.bool tst true)
       ) and false_ = lazy (
-        add_term cc (T.bool tst false)
+        add_term cc (Term.bool tst false)
       )
     in
     ignore (Lazy.force true_ : node);
diff --git a/src/cc/Sidekick_cc.mli b/src/cc/Sidekick_cc.mli
index 07259b23..6201f09e 100644
--- a/src/cc/Sidekick_cc.mli
+++ b/src/cc/Sidekick_cc.mli
@@ -1,6 +1,10 @@
 (** {2 Congruence Closure} *)
 
-module type ARG = Sidekick_core.CC_ARG
+open Sidekick_core
 module type S = Sidekick_core.CC_S
 
-module Make(A: ARG) : S with module A = A
+module Make (A: CC_ARG)
+  : S with module T = A.T 
+       and module Lit = A.Lit
+       and module P = A.P
+       and module Actions = A.Actions
diff --git a/src/core/Sidekick_core.ml b/src/core/Sidekick_core.ml
index 1fa1967c..4ceea0b0 100644
--- a/src/core/Sidekick_core.ml
+++ b/src/core/Sidekick_core.ml
@@ -89,48 +89,58 @@ module type TERM = sig
   end
 end
 
-module type TERM_PROOF = sig
-  include TERM
+module type PROOF = sig
+  type t
+  val pp : t Fmt.printer
 
-  module Proof : sig
-    type t
-    val pp : t Fmt.printer
+  val default : t
+end
 
-    val default : t
-  end
+module type LIT = sig
+  module T : TERM
+  type t
+
+  val term : t -> T.Term.t
+  val sign : t -> bool
+  val neg : t -> t
+
+  val equal : t -> t -> bool
+  val hash : t -> int
+  val pp : t Fmt.printer
+end
+
+module type CC_ACTIONS = sig
+  module T : TERM
+  module P : PROOF
+  module Lit : LIT with module T = T
+  type t
+
+  val raise_conflict : t -> Lit.t list -> P.t -> 'a
+
+  val propagate : t -> Lit.t -> reason:(unit -> Lit.t list) -> P.t -> unit
 end
 
 module type CC_ARG = sig
-  module A : TERM_PROOF
+  module T : TERM
+  module P : PROOF
+  module Lit : LIT with module T = T
+  module Actions : CC_ACTIONS with module T=T and module P = P and module Lit = Lit
 
-  val cc_view : A.Term.t -> (A.Fun.t, A.Term.t, A.Term.t Iter.t) CC_view.t
+  val cc_view : T.Term.t -> (T.Fun.t, T.Term.t, T.Term.t Iter.t) CC_view.t
   (** View the term through the lens of the congruence closure *)
-
-  module Lit : sig
-    type t
-    val term : t -> A.Term.t
-    val sign : t -> bool
-    val neg : t -> t
-    val pp : t Fmt.printer
-  end
-
-  module Actions : sig
-    type t
-
-    val raise_conflict : t -> Lit.t list -> A.Proof.t -> 'a
-
-    val propagate : t -> Lit.t -> reason:(unit -> Lit.t list) -> A.Proof.t -> unit
-  end
 end
 
 module type CC_S = sig
-  module A : CC_ARG 
-  type term_state = A.A.Term.state
-  type term = A.A.Term.t
-  type fun_ = A.A.Fun.t
-  type lit = A.Lit.t
-  type proof = A.A.Proof.t
-  type actions = A.Actions.t
+  module T : TERM
+  module P : PROOF
+  module Lit : LIT with module T = T
+  module Actions : CC_ACTIONS with module T = T and module Lit = Lit and module P = P
+  type term_state = T.Term.state
+  type term = T.Term.t
+  type fun_ = T.Fun.t
+  type lit = Lit.t
+  type proof = P.t
+  type actions = Actions.t
 
   type t
   (** Global state of the congruence closure *)
@@ -305,14 +315,13 @@ end
 
 (** A view of the solver from a theory's point of view *)
 module type SOLVER_INTERNAL = sig
-  module A : TERM_PROOF 
-  module CC_A : CC_ARG with module A = A
-  module CC : CC_S with module A = CC_A
+  module T : TERM
+  module P : PROOF
 
-  type ty = A.Ty.t
-  type term = A.Term.t
-  type term_state = A.Term.state
-  type proof = A.Proof.t
+  type ty = T.Ty.t
+  type term = T.Term.t
+  type term_state = T.Term.state
+  type proof = P.t
 
   (** {3 Main type for a solver} *)
   type t
@@ -320,26 +329,25 @@ module type SOLVER_INTERNAL = sig
 
   val tst : t -> term_state
 
-  val cc : t -> CC.t
-  (** Congruence closure for this solver *)
-
   (** {3 Literals}
 
       A literal is a (preprocessed) term along with its sign.
       It is directly manipulated by the SAT solver.
   *)
-  module Lit : sig
-    type t
-    val term : t -> term
-    val sign : t -> bool
-    val neg : t -> t
+  module Lit : LIT with module T = T
 
-    val equal : t -> t -> bool
-    val hash : t -> int
-    val pp : t Fmt.printer
-  end
   type lit = Lit.t
 
+  (** {2 Congruence Closure} *)
+
+  module CC : CC_S
+    with module T = T
+     and module P = P
+     and module Lit = Lit
+
+  val cc : t -> CC.t
+  (** Congruence closure for this solver *)
+
   (** {3 Simplifiers} *)
 
   module Simplify : sig
@@ -368,11 +376,11 @@ module type SOLVER_INTERNAL = sig
 
   (** {3 hooks for the theory} *)
 
-  type actions = CC_A.Actions.t
+  type actions
 
-  val propagate : t -> actions -> lit -> reason:(unit -> lit list) -> A.Proof.t -> unit
+  val propagate : t -> actions -> lit -> reason:(unit -> lit list) -> proof -> unit
 
-  val raise_conflict : t -> actions -> lit list -> A.Proof.t -> 'a
+  val raise_conflict : t -> actions -> lit list -> proof -> 'a
   (** Give a conflict clause to the solver *)
 
   val propagate: t -> actions -> lit -> (unit -> lit list) -> unit
@@ -472,17 +480,22 @@ end
 
 (** Public view of the solver *)
 module type SOLVER = sig
-  module A : TERM_PROOF
-  module CC_A : CC_ARG with module A = A
-  module Solver_internal : SOLVER_INTERNAL with module A = A and module CC_A = CC_A
+  module T : TERM
+  module P : PROOF
+  module Lit : LIT with module T = T
+  module Solver_internal
+    : SOLVER_INTERNAL
+      with module T = T
+       and module P = P
+       and module Lit = Lit
   (** Internal solver, available to theories.  *)
 
   type t
   type solver = t
-  type term = A.Term.t
-  type ty = A.Ty.t
-  type lit = Solver_internal.Lit.t
-  type lemma = A.Proof.t
+  type term = T.Term.t
+  type ty = T.Ty.t
+  type lit = Lit.t
+  type lemma = P.t
 
   (** {3 A theory}
 
@@ -590,7 +603,7 @@ module type SOLVER = sig
   (** {3 Main API} *)
 
   val stats : t -> Stat.t
-  val tst : t -> A.Term.state
+  val tst : t -> T.Term.state
 
   val create :
     ?stat:Stat.t ->
@@ -598,7 +611,7 @@ module type SOLVER = sig
     (* TODO? ?config:Config.t -> *)
     ?store_proof:bool ->
     theories:theory list ->
-    A.Term.state ->
+    T.Term.state ->
     unit ->
     t
   (** Create a new solver.
diff --git a/src/mini-cc/Sidekick_mini_cc.ml b/src/mini-cc/Sidekick_mini_cc.ml
index 18a98ca0..844b84a0 100644
--- a/src/mini-cc/Sidekick_mini_cc.ml
+++ b/src/mini-cc/Sidekick_mini_cc.ml
@@ -1,9 +1,9 @@
 module CC_view = Sidekick_core.CC_view
 
 module type ARG = sig
-  include Sidekick_core.TERM
+  module T : Sidekick_core.TERM
 
-  val cc_view : Term.t -> (Fun.t, Term.t, Term.t Iter.t) CC_view.t
+  val cc_view : T.Term.t -> (T.Fun.t, T.Term.t, T.Term.t Iter.t) CC_view.t
 end
 
 module type S = sig
@@ -26,11 +26,11 @@ end
 module Make(A: ARG) = struct
   open CC_view
 
-  module Fun = A.Fun
-  module T = A.Term
-  type fun_ = A.Fun.t
+  module Fun = A.T.Fun
+  module T = A.T.Term
+  type fun_ = A.T.Fun.t
   type term = T.t
-  type term_state = A.Term.state
+  type term_state = T.state
 
   module T_tbl = CCHashtbl.Make(T)
 
diff --git a/src/mini-cc/Sidekick_mini_cc.mli b/src/mini-cc/Sidekick_mini_cc.mli
index 4da3afd6..8b48fb9a 100644
--- a/src/mini-cc/Sidekick_mini_cc.mli
+++ b/src/mini-cc/Sidekick_mini_cc.mli
@@ -8,9 +8,9 @@
 module CC_view = Sidekick_core.CC_view
 
 module type ARG = sig
-  include Sidekick_core.TERM
+  module T : Sidekick_core.TERM
 
-  val cc_view : Term.t -> (Fun.t, Term.t, Term.t Iter.t) CC_view.t
+  val cc_view : T.Term.t -> (T.Fun.t, T.Term.t, T.Term.t Iter.t) CC_view.t
 end
 
 module type S = sig
@@ -38,6 +38,6 @@ module type S = sig
 end
 
 module Make(A: ARG)
-  : S with type term = A.Term.t
-       and type fun_ = A.Fun.t
-       and type term_state = A.Term.state
+  : S with type term = A.T.Term.t
+       and type fun_ = A.T.Fun.t
+       and type term_state = A.T.Term.state
diff --git a/src/msat-solver/Sidekick_msat_solver.ml b/src/msat-solver/Sidekick_msat_solver.ml
index 325eb8d6..b72aadee 100644
--- a/src/msat-solver/Sidekick_msat_solver.ml
+++ b/src/msat-solver/Sidekick_msat_solver.ml
@@ -5,11 +5,13 @@ module Log = Msat.Log
 module IM = Util.Int_map
 
 module type ARG = sig
-  include Sidekick_core.TERM_PROOF
+  open Sidekick_core
+  module T : TERM
+  module P : PROOF
 
-  val cc_view : Term.t -> (Fun.t, Term.t, Term.t Iter.t) Sidekick_core.CC_view.t
+  val cc_view : T.Term.t -> (T.Fun.t, T.Term.t, T.Term.t Iter.t) CC_view.t
 
-  val is_valid_literal : Term.t -> bool
+  val is_valid_literal : T.Term.t -> bool
   (** Is this a valid boolean literal? (e.g. is it a closed term, not inside
       a quantifier) *)
 end
@@ -17,16 +19,20 @@ end
 module type S = Sidekick_core.SOLVER
 
 module Make(A : ARG)
-  : S with module A = A
+  : S
+    with module T = A.T
+     and module P = A.P
 = struct
-  module A = A
-  module T = A.Term
-  module Ty = A.Ty
-  type term = T.t
+  module T = A.T
+  module P = A.P
+  module Ty = T.Ty
+  module Term = T.Term
+  type term = Term.t
   type ty = Ty.t
-  type lemma = A.Proof.t
+  type lemma = P.t
 
   module Lit_ = struct
+    module T = T
     type t = {
       lit_term: term;
       lit_sign : bool
@@ -39,21 +45,21 @@ module Make(A : ARG)
     let make ~sign t = {lit_sign=sign; lit_term=t}
 
     let atom tst ?(sign=true) (t:term) : t =
-      let t, sign' = T.abs tst t in
+      let t, sign' = Term.abs tst t in
       let sign = if not sign' then not sign else sign in
       make ~sign t
 
     let equal a b =
       a.lit_sign = b.lit_sign &&
-      T.equal a.lit_term b.lit_term
+      Term.equal a.lit_term b.lit_term
 
     let hash a =
       let sign = a.lit_sign in
-      CCHash.combine3 2 (CCHash.bool sign) (T.hash a.lit_term)
+      CCHash.combine3 2 (CCHash.bool sign) (Term.hash a.lit_term)
 
     let pp out l =
-      if l.lit_sign then T.pp out l.lit_term
-      else Format.fprintf out "(@[@<1>¬@ %a@])" T.pp l.lit_term
+      if l.lit_sign then Term.pp out l.lit_term
+      else Format.fprintf out "(@[@<1>¬@ %a@])" Term.pp l.lit_term
 
     let apply_sign t s = if s then t else neg t
     let norm_sign l = if l.lit_sign then l, true else neg l, false
@@ -63,15 +69,19 @@ module Make(A : ARG)
   type lit = Lit_.t
 
   (* actions from msat *)
-  type msat_acts = (Msat.void, lit, Msat.void, A.Proof.t) Msat.acts
+  type msat_acts = (Msat.void, lit, Msat.void, P.t) Msat.acts
 
   (* the full argument to the congruence closure *)
-  module CC_A = struct
-    module A = A
+  module CC_actions = struct
+    module T = T
+    module P = P
     module Lit = Lit_
     let cc_view = A.cc_view
 
     module Actions = struct
+      module T = T
+      module P = P
+      module Lit = Lit
       type t = msat_acts
       let[@inline] raise_conflict a lits pr =
         a.Msat.acts_raise_conflict lits pr
@@ -81,21 +91,21 @@ module Make(A : ARG)
     end
   end
 
-  module CC = Sidekick_cc.Make(CC_A)
+  module CC = Sidekick_cc.Make(CC_actions)
   module Expl = CC.Expl
   module N = CC.N
 
   (** Internal solver, given to theories and to Msat *)
   module Solver_internal = struct
-    module A = A
-    module CC_A = CC_A
+    module T = T
+    module P = P
     module Lit = Lit_
     module CC = CC
     module N = CC.N
-    type term = T.t
+    type term = Term.t
     type ty = Ty.t
     type lit = Lit.t
-    type term_state = T.state
+    type term_state = Term.state
 
     type th_states = 
       | Ths_nil
@@ -112,33 +122,33 @@ module Make(A : ARG)
       type t = {
         tst: term_state;
         mutable hooks: hook list;
-        cache: T.t T.Tbl.t;
+        cache: Term.t Term.Tbl.t;
       }
       and hook = t -> term -> term option
 
-      let create tst : t = {tst; hooks=[]; cache=T.Tbl.create 32;}
+      let create tst : t = {tst; hooks=[]; cache=Term.Tbl.create 32;}
       let[@inline] tst self = self.tst
       let add_hook self f = self.hooks <- f :: self.hooks
-      let clear self = T.Tbl.clear self.cache
+      let clear self = Term.Tbl.clear self.cache
 
-      let normalize (self:t) (t:T.t) : T.t =
+      let normalize (self:t) (t:Term.t) : Term.t =
         (* compute and cache normal form of [t] *)
         let rec aux t =
-          match T.Tbl.find self.cache t with
+          match Term.Tbl.find self.cache t with
           | u -> u
           | exception Not_found ->
             let u = aux_rec t self.hooks in
-            T.Tbl.add self.cache t u;
+            Term.Tbl.add self.cache t u;
             u
         (* try each function in [hooks] successively, and rewrite subterms *)
         and aux_rec t hooks = match hooks with
           | [] ->
-            let u = T.map_shallow self.tst aux t in
-            if T.equal t u then t else aux u
+            let u = Term.map_shallow self.tst aux t in
+            if Term.equal t u then t else aux u
           | h :: hooks_tl ->
             match h self t with
             | None -> aux_rec t hooks_tl
-            | Some u when T.equal t u -> aux_rec t hooks_tl
+            | Some u when Term.equal t u -> aux_rec t hooks_tl
             | Some u -> aux u
         in
         aux t
@@ -146,7 +156,7 @@ module Make(A : ARG)
     type simplify_hook = Simplify.hook
 
     type t = {
-      tst: T.state; (** state for managing terms *)
+      tst: Term.state; (** state for managing terms *)
       cc: CC.t lazy_t; (** congruence closure *)
       stat: Stat.t;
       count_axiom: int Stat.counter;
@@ -156,7 +166,7 @@ module Make(A : ARG)
       mutable on_progress: unit -> unit;
       simp: Simplify.t;
       mutable preprocess: preprocess_hook list;
-      preprocess_cache: T.t T.Tbl.t;
+      preprocess_cache: Term.t Term.Tbl.t;
       mutable th_states : th_states; (** Set of theories *)
       mutable on_partial_check: (t -> actions -> lit Iter.t -> unit) list;
       mutable on_final_check: (t -> actions -> lit Iter.t -> unit) list;
@@ -179,44 +189,44 @@ module Make(A : ARG)
     module Eq_class = CC.N
     module Expl = CC.Expl
 
-    type proof = A.Proof.t
+    type proof = P.t
 
     let[@inline] cc (t:t) = Lazy.force t.cc
     let[@inline] tst t = t.tst
 
     let simplifier self = self.simp
-    let simp_t self (t:T.t) : T.t = Simplify.normalize self.simp t
+    let simp_t self (t:Term.t) : Term.t = Simplify.normalize self.simp t
     let add_simplifier (self:t) f : unit = Simplify.add_hook self.simp f
 
     let add_preprocess self f = self.preprocess <- f :: self.preprocess
 
     let[@inline] raise_conflict self acts c : 'a =
       Stat.incr self.count_conflict;
-      acts.Msat.acts_raise_conflict c A.Proof.default
+      acts.Msat.acts_raise_conflict c P.default
 
     let[@inline] propagate self acts p cs : unit =
       Stat.incr self.count_propagate;
-      acts.Msat.acts_propagate p (Msat.Consequence (fun () -> cs(), A.Proof.default))
+      acts.Msat.acts_propagate p (Msat.Consequence (fun () -> cs(), P.default))
 
     let[@inline] propagate_l self acts p cs : unit =
       propagate self acts p (fun()->cs)
 
     let add_sat_clause_ self acts ~keep lits : unit =
       Stat.incr self.count_axiom;
-      acts.Msat.acts_add_clause ~keep lits A.Proof.default
+      acts.Msat.acts_add_clause ~keep lits P.default
 
     let preprocess_lit_ (self:t) ~add_clause (lit:lit) : lit =
       let mk_lit t = Lit.atom self.tst t in
       (* compute and cache normal form of [t] *)
       let rec aux t =
-        match T.Tbl.find self.preprocess_cache t with
+        match Term.Tbl.find self.preprocess_cache t with
         | u -> u
         | exception Not_found ->
           (* first, map subterms *)
-          let u = T.map_shallow self.tst aux t in
+          let u = Term.map_shallow self.tst aux t in
           (* then rewrite *)
           let u = aux_rec u self.preprocess in
-          T.Tbl.add self.preprocess_cache t u;
+          Term.Tbl.add self.preprocess_cache t u;
           u
       (* try each function in [hooks] successively *)
       and aux_rec t hooks = match hooks with
@@ -227,7 +237,7 @@ module Make(A : ARG)
           | Some u ->
             Log.debugf 30 
               (fun k->k "(@[msat-solver.preprocess.step@ :from %a@ :to %a@])"
-                  T.pp t T.pp u);
+                  Term.pp t Term.pp u);
             aux u
       in
       let t = Lit.term lit |> simp_t self |> aux in
@@ -339,7 +349,7 @@ module Make(A : ARG)
       CC.mk_model (cc self) m
        *)
 
-    let create ~stat (tst:A.Term.state) () : t =
+    let create ~stat (tst:Term.state) () : t =
       let rec self = {
         tst;
         cc = lazy (
@@ -351,7 +361,7 @@ module Make(A : ARG)
         simp=Simplify.create tst;
         on_progress=(fun () -> ());
         preprocess=[];
-        preprocess_cache=T.Tbl.create 32;
+        preprocess_cache=Term.Tbl.create 32;
         count_axiom = Stat.mk_int stat "solver.th-axioms";
         count_preprocess_clause = Stat.mk_int stat "solver.preprocess-clause";
         count_propagate = Stat.mk_int stat "solver.th-propagations";
@@ -439,8 +449,8 @@ module Make(A : ARG)
     begin
       let tst = Solver_internal.tst self.si in
       Sat_solver.assume self.solver [
-        [Lit.atom tst @@ T.bool tst true];
-      ] A.Proof.default;
+        [Lit.atom tst @@ Term.bool tst true];
+      ] P.default;
     end;
     self
 
@@ -456,9 +466,9 @@ module Make(A : ARG)
     mk_atom_lit_ self lit
 
   (* map boolean subterms to literals *)
-  let add_bool_subterms_ (self:t) (t:T.t) : unit =
-    T.iter_dag t
-    |> Iter.filter (fun t -> Ty.is_bool @@ T.ty t)
+  let add_bool_subterms_ (self:t) (t:Term.t) : unit =
+    Term.iter_dag t
+    |> Iter.filter (fun t -> Ty.is_bool @@ Term.ty t)
     |> Iter.filter
       (fun t -> match A.cc_view t with
          | Sidekick_core.CC_view.Not _ -> false (* will process the subterm just later *)
@@ -466,7 +476,7 @@ module Make(A : ARG)
     |> Iter.filter (fun t -> A.is_valid_literal t)
     |> Iter.iter
       (fun sub ->
-         Log.debugf 5 (fun k->k  "(@[solver.map-bool-subterm-to-lit@ :subterm %a@])" T.pp sub);
+         Log.debugf 5 (fun k->k "(@[solver.map-bool-subterm-to-lit@ :subterm %a@])" Term.pp sub);
          (* ensure that msat has a boolean atom for [sub] *)
          let atom = mk_atom_t_ self sub in
          (* also map [sub] to this atom in the congruence closure, for propagation *)
@@ -485,7 +495,7 @@ module Make(A : ARG)
             (* recursively add these sub-literals, so they're also properly processed *)
             Stat.incr self.si.count_preprocess_clause;
             let atoms = List.map (mk_atom_lit self) lits in
-            Sat_solver.add_clause self.solver atoms A.Proof.default)
+            Sat_solver.add_clause self.solver atoms P.default)
         self.si lit
 
   let[@inline] mk_atom_t self ?sign t : Atom.t =
@@ -507,28 +517,28 @@ module Make(A : ARG)
   end [@@ocaml.warning "-37"]
 
   (* just use terms as values *)
-  module Value = A.Term
+  module Value = Term
 
   module Model = struct
     type t =
       | Empty
-      | Map of Value.t A.Term.Tbl.t
+      | Map of Value.t Term.Tbl.t
     let empty = Empty
     let mem = function
       | Empty -> fun _ -> false
-      | Map tbl -> A.Term.Tbl.mem tbl
+      | Map tbl -> Term.Tbl.mem tbl
     let find = function
       | Empty -> fun _ -> None
-      | Map tbl -> A.Term.Tbl.get tbl
+      | Map tbl -> Term.Tbl.get tbl
     let eval = find
     let pp out = function
       | Empty -> Fmt.string out "(model)"
       | Map tbl ->
         let pp_pair out (t,v) =
-          Fmt.fprintf out "(@[<1>%a@ := %a@])" A.Term.pp t Value.pp v
+          Fmt.fprintf out "(@[<1>%a@ := %a@])" Term.pp t Value.pp v
             in
         Fmt.fprintf out "(@[<hv>model@ %a@])"
-          (Util.pp_seq pp_pair) (A.Term.Tbl.to_seq tbl)
+          (Util.pp_seq pp_pair) (Term.Tbl.to_seq tbl)
   end
 
   type res =
@@ -551,7 +561,7 @@ module Make(A : ARG)
 
   let add_clause (self:t) (c:Atom.t IArray.t) : unit =
     Stat.incr self.count_clause;
-    Sat_solver.add_clause_a self.solver (c:> Atom.t array) A.Proof.default
+    Sat_solver.add_clause_a self.solver (c:> Atom.t array) P.default
 
   let add_clause_l self c = add_clause self (IArray.of_list c)
 
@@ -562,13 +572,13 @@ module Make(A : ARG)
 
   let mk_model (self:t) (lits:lit Iter.t) : Model.t =
     Log.debug 1 "(smt.solver.mk-model)";
-    let module M = A.Term.Tbl in
+    let module M = Term.Tbl in
     let m = M.create 128 in
     let tst = self.si.tst in
     (* first, add all boolean *)
     lits
       (fun {Lit.lit_term=t;lit_sign=sign} ->
-         M.replace m t (A.Term.bool tst sign));
+         M.replace m t (Term.bool tst sign));
     (* then add CC classes *)
     Solver_internal.CC.all_classes (Solver_internal.cc self.si)
       (fun repr ->
diff --git a/src/smtlib/Process.ml b/src/smtlib/Process.ml
index 5702ec45..d3846cef 100644
--- a/src/smtlib/Process.ml
+++ b/src/smtlib/Process.ml
@@ -399,11 +399,11 @@ let conv_term = Conv.conv_term
 
 (* instantiate solver here *)
 module Solver_arg = struct
-  include Sidekick_base_term
+  module T = Sidekick_base_term
 
   let cc_view = Term.cc_view
   let is_valid_literal _ = true
-  module Proof = struct
+  module P = struct
     type t = Default
     let default=Default
     let pp out _ = Fmt.string out "default"
@@ -643,7 +643,7 @@ let process_stmt
 
 module Th_bool = Sidekick_th_bool_static.Make(struct
   module S = Solver
-  type term = S.A.Term.t
+  type term = S.T.Term.t
   include Form
 end)
 
diff --git a/src/smtlib/Process.mli b/src/smtlib/Process.mli
index 9eb818f3..abc4dbed 100644
--- a/src/smtlib/Process.mli
+++ b/src/smtlib/Process.mli
@@ -3,9 +3,9 @@
 open Sidekick_base_term
 
 module Solver
-  : Sidekick_msat_solver.S with type A.Term.t = Term.t
-                            and type A.Term.state = Term.state
-                            and type A.Ty.t = Ty.t
+  : Sidekick_msat_solver.S with type T.Term.t = Term.t
+                            and type T.Term.state = Term.state
+                            and type T.Ty.t = Ty.t
 
 val th_bool : Solver.theory
 
diff --git a/src/th-bool-static/Sidekick_th_bool_static.ml b/src/th-bool-static/Sidekick_th_bool_static.ml
index dd189720..0d436ab9 100644
--- a/src/th-bool-static/Sidekick_th_bool_static.ml
+++ b/src/th-bool-static/Sidekick_th_bool_static.ml
@@ -15,12 +15,12 @@ type 'a bool_view =
 module type ARG = sig
   module S : Sidekick_core.SOLVER
 
-  type term = S.A.Term.t
+  type term = S.T.Term.t
 
   val view_as_bool : term -> term bool_view
   (** Project the term into the boolean view *)
 
-  val mk_bool : S.A.Term.state -> term bool_view -> term
+  val mk_bool : S.T.Term.state -> term bool_view -> term
   (** Make a term from the given boolean view *)
 
   val check_congruence_classes : bool
@@ -32,9 +32,9 @@ module type ARG = sig
   module Gensym : sig
     type t
 
-    val create : S.A.Term.state -> t
+    val create : S.T.Term.state -> t
 
-    val fresh_term : t -> pre:string -> S.A.Ty.t -> term
+    val fresh_term : t -> pre:string -> S.T.Ty.t -> term
     (** Make a fresh term of the given type *)
   end
 end
@@ -44,7 +44,7 @@ module type S = sig
 
   type state
 
-  val create : A.S.A.Term.state -> state
+  val create : A.S.T.Term.state -> state
 
   val simplify : state -> A.S.Solver_internal.simplify_hook
   (** Simplify given term *)
@@ -57,8 +57,8 @@ end
 
 module Make(A : ARG) : S with module A = A = struct
   module A = A
-  module Ty = A.S.A.Ty
-  module T = A.S.A.Term
+  module Ty = A.S.T.Ty
+  module T = A.S.T.Term
   module Lit = A.S.Solver_internal.Lit
   module SI = A.S.Solver_internal
 
diff --git a/src/th-cstor/Sidekick_th_cstor.ml b/src/th-cstor/Sidekick_th_cstor.ml
index 6dfe6228..ec70649e 100644
--- a/src/th-cstor/Sidekick_th_cstor.ml
+++ b/src/th-cstor/Sidekick_th_cstor.ml
@@ -8,7 +8,7 @@ let name = "th-cstor"
 
 module type ARG = sig
   module S : Sidekick_core.SOLVER
-  val view_as_cstor : S.A.Term.t -> (S.A.Fun.t, S.A.Term.t) cstor_view
+  val view_as_cstor : S.T.Term.t -> (S.T.Fun.t, S.T.Term.t) cstor_view
 end
 
 module type S = sig
@@ -19,9 +19,9 @@ end
 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 T = A.S.T.Term
   module N = SI.CC.N
-  module Fun = A.S.A.Fun
+  module Fun = A.S.T.Fun
   module Expl = SI.CC.Expl
 
   type cstor_repr = {