diff --git a/src/abstract-solver/check_res.ml b/src/abstract-solver/check_res.ml
index 77522244..2572a29f 100644
--- a/src/abstract-solver/check_res.ml
+++ b/src/abstract-solver/check_res.ml
@@ -1,16 +1,29 @@
 (** Result of solving for the current set of clauses *)
 
-module Model = Sidekick_model
+type value = Term.t
+
+type sat_result = {
+  get_value: Term.t -> value option;  (** Value for this term *)
+  iter_classes: (Term.t Iter.t * value) Iter.t;
+      (** All equivalence classes in the congruence closure *)
+  eval_lit: Lit.t -> bool option;  (** Evaluate literal *)
+  iter_true_lits: Lit.t Iter.t;
+      (** Iterate on literals that are true in the trail *)
+}
+(** Satisfiable *)
+
+type unsat_result = {
+  unsat_core: unit -> Lit.t Iter.t;
+      (** Unsat core (subset of assumptions), or empty *)
+  unsat_proof: unit -> Sidekick_proof.Step.id option;
+      (** Proof step for the empty clause *)
+}
+(** Unsatisfiable *)
 
 (** Result of calling "check" *)
 type t =
-  | Sat of Model.t  (** Satisfiable *)
-  | Unsat of {
-      unsat_core: unit -> Lit.t Iter.t;
-          (** Unsat core (subset of assumptions), or empty *)
-      unsat_proof: unit -> Sidekick_proof.Step.id option;
-          (** Proof step for the empty clause *)
-    }  (** Unsatisfiable *)
+  | Sat of sat_result
+  | Unsat of unsat_result
   | Unknown of Unknown.t
       (** Unknown, obtained after a timeout, memory limit, etc. *)
 
diff --git a/src/abstract-solver/dune b/src/abstract-solver/dune
index 2e32b504..fe436265 100644
--- a/src/abstract-solver/dune
+++ b/src/abstract-solver/dune
@@ -2,4 +2,4 @@
  (name sidekick_abstract_solver)
  (public_name sidekick.abstract-solver)
  (flags :standard -open Sidekick_util -open Sidekick_core)
- (libraries containers iter sidekick.core sidekick.model sidekick.proof))
+ (libraries containers iter sidekick.core sidekick.proof))
diff --git a/src/base/Statement.ml b/src/base/Statement.ml
index 22abe1aa..222facdb 100644
--- a/src/base/Statement.ml
+++ b/src/base/Statement.ml
@@ -5,8 +5,9 @@ type t = statement =
   | Stmt_set_option of string list
   | Stmt_set_info of string * string
   | Stmt_data of data list
-  | Stmt_ty_decl of ID.t * int (* new atomic cstor *)
-  | Stmt_decl of ID.t * ty list * ty
+  | Stmt_ty_decl of { name: ID.t; arity: int; ty_const: ty }
+      (** new atomic cstor *)
+  | Stmt_decl of { name: ID.t; ty_args: ty list; ty_ret: ty; const: term }
   | Stmt_define of definition list
   | Stmt_assert of term
   | Stmt_assert_clause of term list
@@ -30,10 +31,11 @@ let pp out = function
         Fmt.fprintf out "(@[not %a@])" Term.pp_debug t
     in
     Fmt.fprintf out "(@[check-sat-assuming@ (@[%a@])@])" (Fmt.list pp_pair) l
-  | Stmt_ty_decl (s, n) -> Fmt.fprintf out "(@[declare-sort@ %a %d@])" ID.pp s n
-  | Stmt_decl (id, args, ret) ->
-    Fmt.fprintf out "(@[<1>declare-fun@ %a (@[%a@])@ %a@])" ID.pp id
-      (Util.pp_list Ty.pp) args Ty.pp ret
+  | Stmt_ty_decl { name; arity; ty_const = _ } ->
+    Fmt.fprintf out "(@[declare-sort@ %a %d@])" ID.pp name arity
+  | Stmt_decl { name; ty_args; ty_ret; const = _ } ->
+    Fmt.fprintf out "(@[<1>declare-fun@ %a (@[%a@])@ %a@])" ID.pp name
+      (Util.pp_list Ty.pp) ty_args Ty.pp ty_ret
   | Stmt_assert t -> Fmt.fprintf out "(@[assert@ %a@])" Term.pp_debug t
   | Stmt_assert_clause c ->
     Fmt.fprintf out "(@[assert-clause@ %a@])" (Util.pp_list Term.pp_debug) c
diff --git a/src/base/Statement.mli b/src/base/Statement.mli
index eb917451..4ce18caf 100644
--- a/src/base/Statement.mli
+++ b/src/base/Statement.mli
@@ -11,8 +11,9 @@ type t = statement =
   | Stmt_set_option of string list
   | Stmt_set_info of string * string
   | Stmt_data of data list
-  | Stmt_ty_decl of ID.t * int (* new atomic cstor *)
-  | Stmt_decl of ID.t * ty list * ty
+  | Stmt_ty_decl of { name: ID.t; arity: int; ty_const: ty }
+      (** new atomic cstor *)
+  | Stmt_decl of { name: ID.t; ty_args: ty list; ty_ret: ty; const: term }
   | Stmt_define of definition list
   | Stmt_assert of term
   | Stmt_assert_clause of term list
diff --git a/src/base/types_.ml b/src/base/types_.ml
index 31b31f89..58e0e1a1 100644
--- a/src/base/types_.ml
+++ b/src/base/types_.ml
@@ -66,8 +66,9 @@ type statement =
   | Stmt_set_option of string list
   | Stmt_set_info of string * string
   | Stmt_data of data list
-  | Stmt_ty_decl of ID.t * int (* new atomic cstor *)
-  | Stmt_decl of ID.t * ty list * ty
+  | Stmt_ty_decl of { name: ID.t; arity: int; ty_const: ty }
+      (** new atomic cstor *)
+  | Stmt_decl of { name: ID.t; ty_args: ty list; ty_ret: ty; const: term }
   | Stmt_define of definition list
   | Stmt_assert of term
   | Stmt_assert_clause of term list
diff --git a/src/main/main.ml b/src/main/main.ml
index d1466275..58b05399 100644
--- a/src/main/main.ml
+++ b/src/main/main.ml
@@ -25,7 +25,6 @@ let p_model = ref false
 let check = ref false
 let time_limit = ref 300.
 let mem_limit = ref 1_000_000_000.
-let restarts = ref true
 let p_stat = ref false
 let p_gc_stat = ref false
 let p_progress = ref false
@@ -74,8 +73,6 @@ let argspec =
         Arg.Set check,
         " build, check and print the proof (if output is set), if unsat" );
       "--no-check", Arg.Clear check, " inverse of -check";
-      "--restarts", Arg.Set restarts, " enable restarts";
-      "--no-restarts", Arg.Clear restarts, " disable restarts";
       "--stat", Arg.Set p_stat, " print statistics";
       "--proof", Arg.Set p_proof, " print proof";
       "--no-proof", Arg.Clear p_proof, " do not print proof";
@@ -220,9 +217,8 @@ let main_smt ~config () : _ result =
   parse_res >>= fun input ->
   let driver =
     let asolver = Solver.Smt_solver.Solver.as_asolver solver in
-    Driver.create ~restarts:!restarts ~pp_cnf:!p_cnf ~time:!time_limit
-      ~memory:!mem_limit ~pp_model:!p_model ?proof_file ~check:!check
-      ~progress:!p_progress asolver
+    Driver.create ~pp_cnf:!p_cnf ~time:!time_limit ~memory:!mem_limit
+      ~pp_model:!p_model ?proof_file ~check:!check ~progress:!p_progress asolver
   in
 
   (* process statements *)
diff --git a/src/model/dune b/src/model/dune
deleted file mode 100644
index c3ffcaf7..00000000
--- a/src/model/dune
+++ /dev/null
@@ -1,6 +0,0 @@
-(library
- (name sidekick_model)
- (public_name sidekick.model)
- (synopsis "Finite models for Sidekick")
- (libraries sidekick.sigs sidekick.util sidekick.core)
- (flags :standard -w +32 -open Sidekick_util))
diff --git a/src/model/sidekick_model.ml b/src/model/sidekick_model.ml
deleted file mode 100644
index 7a1e90de..00000000
--- a/src/model/sidekick_model.ml
+++ /dev/null
@@ -1,24 +0,0 @@
-open Sidekick_core
-module T = Term
-
-type t = { m: Term.t T.Map.t } [@@unboxed]
-
-let empty : t = { m = T.Map.empty }
-let is_empty self = T.Map.is_empty self.m
-let mem self t = T.Map.mem t self.m
-let find self t = T.Map.find_opt t self.m
-let eval = find
-let add t v self : t = { m = T.Map.add t v self.m }
-let keys self = T.Map.keys self.m
-let to_iter self = T.Map.to_iter self.m
-
-let pp out (self : t) =
-  if is_empty self then
-    Fmt.string out "(model)"
-  else (
-    let pp_pair out (t, v) =
-      Fmt.fprintf out "(@[<1>%a@ := %a@])" Term.pp t Term.pp v
-    in
-    Fmt.fprintf out "(@[<hv>model@ %a@])" (Util.pp_iter pp_pair)
-      (T.Map.to_iter self.m)
-  )
diff --git a/src/model/sidekick_model.mli b/src/model/sidekick_model.mli
deleted file mode 100644
index 3f0574a9..00000000
--- a/src/model/sidekick_model.mli
+++ /dev/null
@@ -1,19 +0,0 @@
-(** Models
-
-    A model can be produced when the solver is found to be in a
-    satisfiable state after a call to {!solve}. *)
-
-open Sidekick_core
-
-type t
-
-val empty : t
-val is_empty : t -> bool
-val mem : t -> Term.t -> bool
-val find : t -> Term.t -> Term.t option
-val eval : t -> Term.t -> Term.t option
-val add : Term.t -> Term.t -> t -> t
-val keys : t -> Term.t Iter.t
-val to_iter : t -> (Term.t * Term.t) Iter.t
-
-include Sidekick_sigs.PRINT with type t := t
diff --git a/src/sat/sigs.ml b/src/sat/sigs.ml
index 5cb71d1e..dcff8d53 100644
--- a/src/sat/sigs.ml
+++ b/src/sat/sigs.ml
@@ -9,6 +9,8 @@ Copyright 2016 Simon Cruanes
 open Sidekick_core
 module Proof = Sidekick_proof
 
+exception UndecidedLit
+
 (** Solver in a "SATISFIABLE" state *)
 module type SAT_STATE = sig
   val eval : Lit.t -> bool
diff --git a/src/sat/solver.ml b/src/sat/solver.ml
index 061eb332..b3fd08e5 100644
--- a/src/sat/solver.ml
+++ b/src/sat/solver.ml
@@ -36,7 +36,7 @@ type unsat_cause =
 
 exception E_sat
 exception E_unsat of unsat_cause
-exception UndecidedLit
+exception UndecidedLit = Sigs.UndecidedLit
 exception Restart
 exception Conflict of clause
 
diff --git a/src/smt/Sidekick_smt_solver.ml b/src/smt/Sidekick_smt_solver.ml
index b1452b9b..61914980 100644
--- a/src/smt/Sidekick_smt_solver.ml
+++ b/src/smt/Sidekick_smt_solver.ml
@@ -7,7 +7,6 @@
 *)
 
 module Sigs = Sigs
-module Model = Sidekick_model
 module Model_builder = Model_builder
 module Registry = Registry
 module Solver_internal = Solver_internal
diff --git a/src/smt/dune b/src/smt/dune
index 3474e024..599e1ae8 100644
--- a/src/smt/dune
+++ b/src/smt/dune
@@ -3,6 +3,6 @@
  (public_name sidekick.smt-solver)
  (synopsis "main SMT solver")
  (libraries containers iter sidekick.core sidekick.util sidekick.cc
-   sidekick.sat sidekick.abstract-solver sidekick.simplify sidekick.model
-   sidekick.proof sidekick.trace)
+   sidekick.sat sidekick.abstract-solver sidekick.simplify sidekick.proof
+   sidekick.trace)
  (flags :standard -w +32 -open Sidekick_util))
diff --git a/src/smt/model_builder.ml b/src/smt/model_builder.ml
index 0c2ec0ce..28a3dfc6 100644
--- a/src/smt/model_builder.ml
+++ b/src/smt/model_builder.ml
@@ -1,24 +1,23 @@
 open Sigs
 module T = Term
+module TM = Term.Map
 
 type t = {
   tst: Term.store;
-  mutable m: Model.t;
+  mutable m: Term.t TM.t;
   required: Term.t Queue.t;
   gensym: Gensym.t;
 }
 
 let create tst : t =
-  {
-    tst;
-    m = Model.empty;
-    required = Queue.create ();
-    gensym = Gensym.create tst;
-  }
+  { tst; m = TM.empty; required = Queue.create (); gensym = Gensym.create tst }
 
 let pp out (self : t) : unit =
-  Fmt.fprintf out "(@[model-builder@ :model %a@ :q (@[%a@])@])" Model.pp self.m
-    (Util.pp_iter T.pp)
+  let pp_kv out (k, v) =
+    Fmt.fprintf out "(@[%a@ := %a@])" Term.pp k Term.pp v
+  in
+  Fmt.fprintf out "(@[model-builder@ :model %a@ :q (@[%a@])@])"
+    (Util.pp_iter pp_kv) (TM.to_iter self.m) (Util.pp_iter T.pp)
     (Iter.of_queue self.required)
 
 let gensym self ~pre ~ty : Term.t = Gensym.fresh_term self.gensym ~pre ty
@@ -26,33 +25,33 @@ let gensym self ~pre ~ty : Term.t = Gensym.fresh_term self.gensym ~pre ty
 let rec pop_required (self : t) : _ option =
   match Queue.take_opt self.required with
   | None -> None
-  | Some t when Model.mem self.m t -> pop_required self
+  | Some t when TM.mem t self.m -> pop_required self
   | Some t -> Some t
 
 let require_eval (self : t) t : unit =
-  if not @@ Model.mem self.m t then Queue.push t self.required
+  if not @@ TM.mem t self.m then Queue.push t self.required
 
-let[@inline] mem self t : bool = Model.mem self.m t
+let[@inline] mem self t : bool = TM.mem t self.m
 
 let add (self : t) ?(subs = []) t v : unit =
   if not @@ mem self t then (
-    self.m <- Model.add t v self.m;
+    self.m <- TM.add t v self.m;
     List.iter (fun u -> require_eval self u) subs
   )
 
 type eval_cache = Term.Internal_.cache
 
 let eval ?(cache = Term.Internal_.create_cache 8) (self : t) (t : Term.t) =
-  let t = Model.find self.m t |> Option.value ~default:t in
+  let t = TM.get t self.m |> Option.value ~default:t in
   T.Internal_.replace_ ~cache self.tst ~recursive:true t ~f:(fun ~recurse:_ u ->
-      Model.find self.m u)
+      TM.get u self.m)
 
-let to_model (self : t) : Model.t =
+let to_map (self : t) : _ TM.t =
   (* ensure we evaluate each term only once *)
   let cache = T.Internal_.create_cache 8 in
   let m =
-    Model.keys self.m
+    TM.keys self.m
     |> Iter.map (fun t -> t, eval ~cache self t)
-    |> Iter.fold (fun m (t, v) -> Model.add t v m) Model.empty
+    |> Iter.fold (fun m (t, v) -> TM.add t v m) TM.empty
   in
   m
diff --git a/src/smt/model_builder.mli b/src/smt/model_builder.mli
index 592a73c9..965ad71f 100644
--- a/src/smt/model_builder.mli
+++ b/src/smt/model_builder.mli
@@ -33,4 +33,4 @@ val eval : ?cache:eval_cache -> t -> Term.t -> value
 val pop_required : t -> Term.t option
 (** gives the next subterm that is required but has no value yet *)
 
-val to_model : t -> Model.t
+val to_map : t -> Term.t Term.Map.t
diff --git a/src/smt/sigs.ml b/src/smt/sigs.ml
index cc4732d3..9dbbdfd3 100644
--- a/src/smt/sigs.ml
+++ b/src/smt/sigs.ml
@@ -13,7 +13,6 @@
 *)
 
 include Sidekick_core
-module Model = Sidekick_model
 module Simplify = Sidekick_simplify
 module CC = Sidekick_cc.CC
 module E_node = Sidekick_cc.E_node
diff --git a/src/smt/solver.ml b/src/smt/solver.ml
index c7fff0d6..5f05640b 100644
--- a/src/smt/solver.ml
+++ b/src/smt/solver.ml
@@ -11,14 +11,30 @@ module Sat_solver = Sidekick_sat
 
 module Unknown = Sidekick_abstract_solver.Unknown [@@ocaml.warning "-37"]
 
+type value = Term.t
+
+type sat_result = Check_res.sat_result = {
+  get_value: Term.t -> value option;  (** Value for this term *)
+  iter_classes: (Term.t Iter.t * value) Iter.t;
+      (** All equivalence classes in the congruence closure *)
+  eval_lit: Lit.t -> bool option;  (** Evaluate literal *)
+  iter_true_lits: Lit.t Iter.t;
+      (** Iterate on literals that are true in the trail *)
+}
+(** Satisfiable *)
+
+type unsat_result = Check_res.unsat_result = {
+  unsat_core: unit -> Lit.t Iter.t;
+      (** Unsat core (subset of assumptions), or empty *)
+  unsat_proof: unit -> Sidekick_proof.Step.id option;
+      (** Proof step for the empty clause *)
+}
+(** Unsatisfiable *)
+
+(** Result of solving for the current set of clauses *)
 type res = Check_res.t =
-  | Sat of Model.t  (** Satisfiable *)
-  | Unsat of {
-      unsat_core: unit -> lit Iter.t;
-          (** Unsat core (subset of assumptions), or empty *)
-      unsat_proof: unit -> step_id option;
-          (** Proof step for the empty clause *)
-    }  (** Unsatisfiable *)
+  | Sat of sat_result
+  | Unsat of unsat_result
   | Unknown of Unknown.t
       (** Unknown, obtained after a timeout, memory limit, etc. *)
 
@@ -188,26 +204,57 @@ let solve ?(on_exit = []) ?(on_progress = fun _ -> ())
             "(@[sidekick.smt-solver: SAT@ actual: UNKNOWN@ :reason \
              incomplete-fragment@])");
       Unknown Unknown.U_incomplete
-    | Sat_solver.Sat _ ->
+    | Sat_solver.Sat (module SAT) ->
       Log.debug 1 "(sidekick.smt-solver: SAT)";
 
-      Log.debugf 5 (fun k ->
-          let ppc out n =
-            Fmt.fprintf out "{@[<hv1>class@ %a@]}"
-              (Util.pp_iter ~sep:";" E_node.pp)
-              (E_node.iter_class n)
-          in
-          k "(@[sidekick.smt-solver.classes@ (@[%a@])@])" (Util.pp_iter ppc)
-            (CC.all_classes @@ Solver_internal.cc self.si));
-
       let m =
         match SI.last_model self.si with
         | Some m -> m
         | None -> assert false
       in
 
+      let iter_classes =
+        CC.all_classes (Solver_internal.cc self.si)
+        |> Iter.filter (fun repr ->
+               not @@ Term.is_pi (Term.ty @@ E_node.term repr))
+        |> Iter.map (fun repr ->
+               let v =
+                 match
+                   (* find value for this class *)
+                   Iter.find_map
+                     (fun en -> Term.Map.get (E_node.term en) m)
+                     (E_node.iter_class repr)
+                 with
+                 | None ->
+                   Error.errorf
+                     "(@[solver.mk-model.no-value-for-repr@ %a@ :ty %a@])"
+                     E_node.pp repr Term.pp
+                     (Term.ty @@ E_node.term repr)
+                 | Some v -> v
+               in
+               let terms = E_node.iter_class repr |> Iter.map E_node.term in
+               terms, v)
+      in
+
+      Log.debugf 5 (fun k ->
+          let ppc out (cls, v) =
+            Fmt.fprintf out "{@[<hv1>class@ :value %a@ %a@]}" Term.pp v
+              (Util.pp_iter ~sep:";" Term.pp)
+              cls
+          in
+          k "(@[sidekick.smt-solver.classes@ (@[%a@])@])" (Util.pp_iter ppc)
+            iter_classes);
+
       do_on_exit ();
-      Sat m
+      Sat
+        {
+          get_value = (fun t -> Term.Map.get t m);
+          iter_classes;
+          eval_lit =
+            (fun l ->
+              try Some (SAT.eval l) with Sat_solver.UndecidedLit -> None);
+          iter_true_lits = SAT.iter_trail;
+        }
     | Sat_solver.Unsat (module UNSAT) ->
       let unsat_core () = UNSAT.unsat_assumptions () in
       let unsat_proof () = Some (UNSAT.unsat_proof ()) in
diff --git a/src/smt/solver.mli b/src/smt/solver.mli
index b4be6b68..b399a077 100644
--- a/src/smt/solver.mli
+++ b/src/smt/solver.mli
@@ -102,15 +102,30 @@ val assert_term : t -> term -> unit
 
 val add_ty : t -> ty -> unit
 
+type value = Term.t
+
+type sat_result = Check_res.sat_result = {
+  get_value: Term.t -> value option;  (** Value for this term *)
+  iter_classes: (Term.t Iter.t * value) Iter.t;
+      (** All equivalence classes in the congruence closure *)
+  eval_lit: Lit.t -> bool option;  (** Evaluate literal *)
+  iter_true_lits: Lit.t Iter.t;
+      (** Iterate on literals that are true in the trail *)
+}
+(** Satisfiable *)
+
+type unsat_result = Check_res.unsat_result = {
+  unsat_core: unit -> Lit.t Iter.t;
+      (** Unsat core (subset of assumptions), or empty *)
+  unsat_proof: unit -> Sidekick_proof.Step.id option;
+      (** Proof step for the empty clause *)
+}
+(** Unsatisfiable *)
+
 (** Result of solving for the current set of clauses *)
 type res = Check_res.t =
-  | Sat of Model.t  (** Satisfiable *)
-  | Unsat of {
-      unsat_core: unit -> lit Iter.t;
-          (** Unsat core (subset of assumptions), or empty *)
-      unsat_proof: unit -> step_id option;
-          (** Proof step for the empty clause *)
-    }  (** Unsatisfiable *)
+  | Sat of sat_result
+  | Unsat of unsat_result
   | Unknown of Unknown.t
       (** Unknown, obtained after a timeout, memory limit, etc. *)
 
diff --git a/src/smt/solver_internal.ml b/src/smt/solver_internal.ml
index a47e1f99..34351ee6 100644
--- a/src/smt/solver_internal.ml
+++ b/src/smt/solver_internal.ml
@@ -53,7 +53,7 @@ type t = {
   mutable model_complete: model_completion_hook list;
   simp: Simplify.t;
   delayed_actions: delayed_action Queue.t;
-  mutable last_model: Model.t option;
+  mutable last_model: Term.t Term.Map.t option;
   mutable th_states: th_states;  (** Set of theories *)
   mutable level: int;
   mutable complete: bool;
@@ -327,7 +327,7 @@ let rec pop_lvls_theories_ n = function
 (** {2 Model construction and theory combination} *)
 
 (* make model from the congruence closure *)
-let mk_model_ (self : t) (lits : lit Iter.t) : Model.t =
+let mk_model_ (self : t) (lits : lit Iter.t) : Term.t Term.Map.t =
   let@ () = Profile.with_ "smt-solver.mk-model" in
   Log.debug 1 "(smt.solver.mk-model)";
   let module MB = Model_builder in
@@ -395,7 +395,7 @@ let mk_model_ (self : t) (lits : lit Iter.t) : Model.t =
   in
 
   compute_fixpoint ();
-  MB.to_model model
+  MB.to_map model
 
 (* call congruence closure, perform the actions it scheduled *)
 let check_cc_with_acts_ (self : t) (acts : theory_actions) =
diff --git a/src/smt/solver_internal.mli b/src/smt/solver_internal.mli
index 479d3b1c..09f0fe74 100644
--- a/src/smt/solver_internal.mli
+++ b/src/smt/solver_internal.mli
@@ -270,7 +270,7 @@ val on_progress : t -> (unit, unit) Event.t
 val is_complete : t -> bool
 (** Are we still in a complete logic fragment? *)
 
-val last_model : t -> Model.t option
+val last_model : t -> Term.t Term.Map.t option
 
 (** {2 Delayed actions} *)
 
diff --git a/src/smtlib/Driver.ml b/src/smtlib/Driver.ml
index b197f0c3..e3c2b673 100644
--- a/src/smtlib/Driver.ml
+++ b/src/smtlib/Driver.ml
@@ -1,4 +1,3 @@
-open Sidekick_core
 module Profile = Sidekick_util.Profile
 module Proof = Sidekick_proof
 module Asolver = Solver.Asolver
@@ -12,52 +11,10 @@ type 'a or_error = ('a, string) CCResult.t
 module E = CCResult
 module Fmt = CCFormat
 
-(* TODO: use external proof checker instead: check-sat(φ + model)
-   (* check SMT model *)
-   let check_smt_model (solver:Solver.Sat_solver.t) (hyps:_ Vec.t) (m:Model.t) : unit =
-     Log.debug 1 "(smt.check-smt-model)";
-     let module S = Solver.Sat_solver in
-     let check_atom (lit:Lit.t) : Msat.lbool =
-       Log.debugf 5 (fun k->k "(@[smt.check-smt-model.atom@ %a@])" Lit.pp lit);
-       let a = S.make_atom solver lit in
-       let sat_value = S.eval_atom solver a in
-       let t, sign = Lit.as_atom lit in
-       begin match Model.eval m t with
-         | Some (V_bool b) ->
-           let b = if sign then b else not b in
-           if (sat_value <> Msat.L_undefined) &&
-              ((b && sat_value=Msat.L_false) || (not b && sat_value=Msat.L_true)) then (
-             Error.errorf "(@[check-model.error@ :atom %a@ :model-val %B@ :sat-val %a@])"
-               S.Atom.pp a b Msat.pp_lbool sat_value
-           ) else (
-             Log.debugf 5
-               (fun k->k "(@[check-model@ :atom %a@ :model-val %B@ :sat-val %a@])"
-                   S.Atom.pp a b Msat.pp_lbool sat_value);
-           )
-         | Some v ->
-           Error.errorf "(@[check-model.error@ :atom %a@ :non-bool-value %a@])"
-             S.Atom.pp a Value.pp v
-         | None ->
-           if sat_value <> Msat.L_undefined then (
-             Error.errorf "(@[check-model.error@ :atom %a@ :no-smt-value@ :sat-val %a@])"
-               S.Atom.pp a Msat.pp_lbool sat_value
-           );
-       end;
-       sat_value
-     in
-     let check_c c =
-       let bs = List.map check_atom c in
-       if List.for_all (function Msat.L_true -> false | _ -> true) bs then (
-         Error.errorf "(@[check-model.error.none-true@ :clause %a@ :vals %a@])"
-           (Fmt.Dump.list Lit.pp) c Fmt.(Dump.list @@ Msat.pp_lbool) bs
-       );
-     in
-     Vec.iter check_c hyps
-*)
-
 type t = {
   progress: Progress_bar.t option;
   solver: Asolver.t;
+  build_model: Build_model.t;
   time_start: float;
   time_limit: float;
   memory_limit: float;
@@ -65,13 +22,11 @@ type t = {
   pp_model: bool;
   pp_cnf: bool;
   check: bool;
-  restarts: bool;
 }
 
 (* call the solver to check-sat *)
-let create ?(restarts = true) ?(pp_cnf = false) ?proof_file ?(pp_model = false)
-    ?(check = false) ?time ?memory ?(progress = false) (solver : Asolver.t) : t
-    =
+let create ?(pp_cnf = false) ?proof_file ?(pp_model = false) ?(check = false)
+    ?time ?memory ?(progress = false) (solver : Asolver.t) : t =
   let time_start = now () in
   let progress =
     if progress then
@@ -86,7 +41,7 @@ let create ?(restarts = true) ?(pp_cnf = false) ?proof_file ?(pp_model = false)
 
   {
     time_start;
-    restarts;
+    build_model = Build_model.create ();
     progress;
     solver;
     proof_file;
@@ -97,15 +52,20 @@ let create ?(restarts = true) ?(pp_cnf = false) ?proof_file ?(pp_model = false)
     memory_limit;
   }
 
-let decl_sort (_self : t) c n : unit =
-  (* TODO: more? pass to abstract solver? *)
-  Log.debugf 1 (fun k -> k "(@[declare-sort %a@ :arity %d@])" ID.pp c n)
-
-let decl_fun (_self : t) id args ret : unit =
-  (* TODO: more? record for model building *)
+let decl_sort (self : t) c n ty_const : unit =
   Log.debugf 1 (fun k ->
-      k "(@[declare-fun %a@ :args (@[%a@])@ :ret %a@])" ID.pp id
-        (Util.pp_list Ty.pp) args Ty.pp ret)
+      k "(@[declare-sort %a@ :arity %d@ :ty-const %a@])" ID.pp c n Term.pp
+        ty_const);
+  Build_model.add_ty self.build_model ty_const
+
+let decl_fun (self : t) f args ret const : unit =
+  Log.debugf 1 (fun k ->
+      k "(@[declare-fun %a@ :args (@[%a@])@ :ret %a@ :const %a@])" ID.pp f
+        (Util.pp_list Ty.pp) args Ty.pp ret Term.pp const);
+  Build_model.add_fun self.build_model const
+
+let build_model (self : t) (sat : Solver.sat_result) : Model.t =
+  Build_model.build self.build_model sat
 
 (* call the solver to check satisfiability *)
 let solve (self : t) ~assumptions () : Solver.res =
@@ -133,10 +93,12 @@ let solve (self : t) ~assumptions () : Solver.res =
   let t2 = now () in
   flush stdout;
   (match res with
-  | Asolver.Check_res.Sat m ->
-    if self.pp_model then
+  | Asolver.Check_res.Sat sat ->
+    if self.pp_model then (
+      let m = build_model self sat in
       (* TODO: use actual {!Model} in the solver? or build it afterwards *)
-      Format.printf "(@[<hv1>model@ %a@])@." Sidekick_smt_solver.Model.pp m;
+      Format.printf "(@[<hv1>model@ %a@])@." Model.pp m
+    );
     (* TODO
        if check then (
          Solver.check_model s;
@@ -194,8 +156,6 @@ let process_stmt (self : t) (stmt : Statement.t) : unit or_error =
   Log.debugf 5 (fun k ->
       k "(@[smtlib.process-statement@ %a@])" Statement.pp stmt);
 
-  let add_step r = Proof.Tracer.add_step (Asolver.proof self.solver) r in
-
   match stmt with
   | Statement.Stmt_set_logic logic ->
     if not @@ List.mem logic known_logics then
@@ -216,17 +176,17 @@ let process_stmt (self : t) (stmt : Statement.t) : unit or_error =
     in
     ignore (solve self ~assumptions () : Solver.res);
     E.return ()
-  | Statement.Stmt_ty_decl (id, n) ->
-    decl_sort self id n;
+  | Statement.Stmt_ty_decl { name; arity; ty_const } ->
+    decl_sort self name arity ty_const;
     E.return ()
-  | Statement.Stmt_decl (f, ty_args, ty_ret) ->
-    decl_fun self f ty_args ty_ret;
+  | Statement.Stmt_decl { name; ty_args; ty_ret; const } ->
+    decl_fun self name ty_args ty_ret const;
     E.return ()
   | Statement.Stmt_assert t ->
     if self.pp_cnf then Format.printf "(@[<hv1>assert@ %a@])@." Term.pp t;
     let lit = Asolver.lit_of_term self.solver t in
-    Asolver.assert_clause self.solver [| lit |]
-      (fun () -> Proof.Sat_rules.sat_input_clause [ lit ]);
+    Asolver.assert_clause self.solver [| lit |] (fun () ->
+        Proof.Sat_rules.sat_input_clause [ lit ]);
     E.return ()
   | Statement.Stmt_assert_clause c_ts ->
     if self.pp_cnf then
@@ -235,8 +195,7 @@ let process_stmt (self : t) (stmt : Statement.t) : unit or_error =
     let c = CCList.map (fun t -> Asolver.lit_of_term self.solver t) c_ts in
 
     (* proof of assert-input + preprocessing *)
-    let pr =
-      fun () ->
+    let pr () =
       let lits = List.map (Asolver.lit_of_term self.solver) c_ts in
       Proof.Sat_rules.sat_input_clause lits
     in
@@ -245,16 +204,19 @@ let process_stmt (self : t) (stmt : Statement.t) : unit or_error =
     E.return ()
   | Statement.Stmt_get_model ->
     (match Asolver.last_res self.solver with
-    | Some (Solver.Sat m) -> Fmt.printf "%a@." Sidekick_smt_solver.Model.pp m
+    | Some (Solver.Sat sat) ->
+      let m = build_model self sat in
+      Fmt.printf "%a@." Model.pp m
     | _ -> Error.errorf "cannot access model");
     E.return ()
   | Statement.Stmt_get_value l ->
     (match Asolver.last_res self.solver with
-    | Some (Solver.Sat m) ->
+    | Some (Solver.Sat sat) ->
+      let m = build_model self sat in
       let l =
         List.map
           (fun t ->
-            match Sidekick_smt_solver.Model.eval m t with
+            match Model.eval t m with
             | None -> Error.errorf "cannot evaluate %a" Term.pp t
             | Some u -> t, u)
           l
diff --git a/src/smtlib/Driver.mli b/src/smtlib/Driver.mli
index c17d061c..8ebe0292 100644
--- a/src/smtlib/Driver.mli
+++ b/src/smtlib/Driver.mli
@@ -21,7 +21,6 @@ type t
 (** The SMTLIB driver *)
 
 val create :
-  ?restarts:bool ->
   ?pp_cnf:bool ->
   ?proof_file:string ->
   ?pp_model:bool ->
diff --git a/src/smtlib/Sidekick_smtlib.ml b/src/smtlib/Sidekick_smtlib.ml
index cd022f0f..6bd9dea2 100644
--- a/src/smtlib/Sidekick_smtlib.ml
+++ b/src/smtlib/Sidekick_smtlib.ml
@@ -5,6 +5,7 @@ module Solver = Solver
 module Term = Sidekick_base.Term
 module Stmt = Sidekick_base.Statement
 module Check_cc = Check_cc
+module Model = Model
 
 type 'a or_error = ('a, string) CCResult.t
 
diff --git a/src/smtlib/Sidekick_smtlib.mli b/src/smtlib/Sidekick_smtlib.mli
index 563d5f45..9ab2b279 100644
--- a/src/smtlib/Sidekick_smtlib.mli
+++ b/src/smtlib/Sidekick_smtlib.mli
@@ -11,6 +11,7 @@ module Stmt = Sidekick_base.Statement
 module Driver = Driver
 module Solver = Solver
 module Check_cc = Check_cc
+module Model = Model
 
 val parse : Term.store -> string -> Stmt.t list or_error
 val parse_stdin : Term.store -> Stmt.t list or_error
diff --git a/src/smtlib/Typecheck.ml b/src/smtlib/Typecheck.ml
index c54a7de6..85b22398 100644
--- a/src/smtlib/Typecheck.ml
+++ b/src/smtlib/Typecheck.ml
@@ -457,13 +457,13 @@ and conv_statement_aux (ctx : Ctx.t) (stmt : PA.statement) : Stmt.t list =
     let id = ID.make s in
     let ty = Ty.uninterpreted tst id in
     Ctx.add_id_ ctx s id (Ctx.K_ty (Ctx.K_atomic ty));
-    [ Stmt.Stmt_ty_decl (id, n) ]
+    [ Stmt.Stmt_ty_decl { name = id; arity = n; ty_const = ty } ]
   | PA.Stmt_decl fr ->
     let f, args, ret = conv_fun_decl ctx fr in
     let id = ID.make f in
     let c_f = Uconst.uconst_of_id' tst id args ret in
     Ctx.add_id_ ctx f id (Ctx.K_fun c_f);
-    [ Stmt.Stmt_decl (id, args, ret) ]
+    [ Stmt.Stmt_decl { name = id; ty_args = args; ty_ret = ret; const = c_f } ]
   | PA.Stmt_data l ->
     (* first, read and declare each datatype (it can occur in the other
        datatypes' constructors) *)
@@ -572,7 +572,10 @@ and conv_statement_aux (ctx : Ctx.t) (stmt : PA.statement) : Stmt.t list =
     let f = Uconst.uconst_of_id tst id ret in
     Ctx.add_id_ ctx fun_name id (Ctx.K_fun f);
     let rhs = conv_term ctx fr_body in
-    [ Stmt.Stmt_decl (id, [], ret); Stmt.Stmt_assert (Form.eq tst f rhs) ]
+    [
+      Stmt.Stmt_decl { name = id; ty_args = []; ty_ret = ret; const = f };
+      Stmt.Stmt_assert (Form.eq tst f rhs);
+    ]
   | PA.Stmt_fun_rec _ | PA.Stmt_fun_def _ ->
     errorf_ctx ctx "unsupported definition: %a" PA.pp_stmt stmt
   | PA.Stmt_assert t ->
diff --git a/src/smtlib/build_model.ml b/src/smtlib/build_model.ml
new file mode 100644
index 00000000..2a5bb1ea
--- /dev/null
+++ b/src/smtlib/build_model.ml
@@ -0,0 +1,46 @@
+open Common_
+open! Sidekick_base
+
+type t = { fun_symbols: unit Term.Tbl.t; ty_symbols: unit Term.Tbl.t }
+
+let create () : t =
+  { fun_symbols = Term.Tbl.create 32; ty_symbols = Term.Tbl.create 32 }
+
+let add_ty (self : t) ty_const : unit = Term.Tbl.add self.ty_symbols ty_const ()
+let add_fun (self : t) const : unit = Term.Tbl.add self.fun_symbols const ()
+
+let build (self : t) (sat : Solver.sat_result) : Model.t =
+  let m = ref Model.empty in
+
+  (* process [t], whose value is [value] in the model *)
+  let examine_term t ~value : unit =
+    let f, args = Term.unfold_app t in
+
+    (* TODO: types *)
+    if Term.Tbl.mem self.fun_symbols f then (
+      (* add entry for [f], to build a if-then-else tree *)
+      match List.map (fun t -> sat.get_value t |> Option.get) args with
+      | exception _ ->
+        Log.debugf 1 (fun k ->
+            k "(@[build-model.warn@ :no-entry-for %a@])" Term.pp t);
+        () (* TODO: warning? *)
+      | v_args ->
+        (* see if [v_args] already maps to a value *)
+        let other_v = Model.get_fun_entry f v_args !m in
+        Option.iter
+          (fun v' ->
+            if not (Term.equal value v') then
+              Error.errorf
+                "Inconsistent model@ for fun `%a`,@ values %a@ map to `%a` and \
+                 `%a`"
+                Term.pp f (Fmt.Dump.list Term.pp) v_args Term.pp value Term.pp
+                v')
+          other_v;
+        (* save mapping *)
+        m := Model.add_fun_entry f v_args value !m
+    )
+  in
+
+  sat.iter_classes (fun (cls, v) -> cls (fun t -> examine_term t ~value:v));
+
+  !m
diff --git a/src/smtlib/build_model.mli b/src/smtlib/build_model.mli
new file mode 100644
index 00000000..448d70e7
--- /dev/null
+++ b/src/smtlib/build_model.mli
@@ -0,0 +1,9 @@
+open Common_
+open! Sidekick_base
+
+type t
+
+val create : unit -> t
+val add_ty : t -> Term.t -> unit
+val add_fun : t -> Term.t -> unit
+val build : t -> Solver.sat_result -> Model.t
diff --git a/src/smtlib/dune b/src/smtlib/dune
index d401450a..c2be7ab2 100644
--- a/src/smtlib/dune
+++ b/src/smtlib/dune
@@ -4,6 +4,5 @@
  (synopsis "SMTLIB 2.6 driver for Sidekick")
  (private_modules Common_)
  (libraries containers zarith sidekick.core sidekick.util sidekick-base
-            sidekick.abstract-solver
-   sidekick.mini-cc smtlib-utils sidekick.tef)
+   sidekick.abstract-solver sidekick.mini-cc smtlib-utils sidekick.tef)
  (flags :standard -warn-error -a+8 -open Sidekick_util))
diff --git a/src/smtlib/model.ml b/src/smtlib/model.ml
new file mode 100644
index 00000000..141a8fa4
--- /dev/null
+++ b/src/smtlib/model.ml
@@ -0,0 +1,77 @@
+open Sidekick_core
+module T = Term
+module TM = Term.Map
+
+type value = Term.t
+type fun_ = Term.t
+
+module TL_map = CCMap.Make (struct
+  type t = value list
+
+  let compare = CCList.compare Term.compare
+end)
+
+type t = { m: value TL_map.t TM.t } [@@unboxed]
+
+let empty : t = { m = T.Map.empty }
+let is_empty self = T.Map.is_empty self.m
+let iter_fun_entries (self : t) = TM.to_iter self.m
+let get_fun_entries f self = TM.get f self.m
+
+let get_fun_entry f vs self =
+  match get_fun_entries f self with
+  | None -> None
+  | Some tm -> TL_map.get vs tm
+
+let add_fun_entry f vs v self =
+  let m = TM.get_or ~default:TL_map.empty f self.m in
+  { m = TM.add f (TL_map.add vs v m) self.m }
+
+let rec eval t (self : t) : value option =
+  let eval_exn t =
+    match eval t self with
+    | Some v -> v
+    | None -> raise Not_found
+  in
+
+  let f, args = Term.unfold_app t in
+  match List.map eval_exn args with
+  | exception Not_found -> None
+  | v_args -> get_fun_entry f v_args self
+
+let pp out (self : t) =
+  if is_empty self then
+    Fmt.string out "(model)"
+  else (
+    let rec pp_entries out = function
+      | [] -> ()
+      | ([], v) :: _ | [ (_, v) ] -> Term.pp out v
+      | ((_ :: _ as vs), v) :: tl ->
+        let pp_guard out () =
+          match vs with
+          | [] -> ()
+          | [ t ] -> Fmt.fprintf out "(@[= x0 %a@])" Term.pp t
+          | _ ->
+            Fmt.fprintf out "(@[and@ ";
+            List.iteri
+              (fun i t -> Fmt.fprintf out "(@[= x%d %a@])" i Term.pp t)
+              vs;
+            Fmt.fprintf out "@])"
+        in
+
+        Fmt.fprintf out "(@[ite %a@ %a@ %a@])" pp_guard () Term.pp v pp_entries
+          tl
+    in
+    let pp_fun out (f, entries) =
+      match TL_map.choose_opt entries with
+      | None -> ()
+      | Some (args, v) ->
+        let pp_arg out (i, ty) = Fmt.fprintf out "(@[x%d %a@])" i Term.pp ty in
+        Fmt.fprintf out "(@[<1>define-fun %a (@[%a@])@ %a@ %a@])" Term.pp f
+          (Util.pp_list ~sep:"" pp_arg)
+          (List.mapi (fun i v -> i, Term.ty v) args)
+          Term.pp (Term.ty v) pp_entries (TL_map.to_list entries)
+    in
+    Fmt.fprintf out "(@[<hv>model@ %a@])" (Util.pp_iter pp_fun)
+      (TM.to_iter self.m)
+  )
diff --git a/src/smtlib/model.mli b/src/smtlib/model.mli
new file mode 100644
index 00000000..39c14653
--- /dev/null
+++ b/src/smtlib/model.mli
@@ -0,0 +1,22 @@
+(** Models
+
+    A model can be produced when the solver is found to be in a
+    satisfiable state after a call to {!solve}. *)
+
+open Sidekick_core
+
+type t
+type value = Term.t
+type fun_ = Term.t
+
+module TL_map : CCMap.S with type key = value list
+
+val empty : t
+val is_empty : t -> bool
+val add_fun_entry : fun_ -> value list -> value -> t -> t
+val get_fun_entry : fun_ -> value list -> t -> value option
+val get_fun_entries : fun_ -> t -> value TL_map.t option
+val iter_fun_entries : t -> (fun_ * value TL_map.t) Iter.t
+val eval : Term.t -> t -> value option
+
+include Sidekick_sigs.PRINT with type t := t