diff --git a/src/bitwuzla_mappings.default.ml b/src/bitwuzla_mappings.default.ml
index e36bb975..8ec027b2 100644
--- a/src/bitwuzla_mappings.default.ml
+++ b/src/bitwuzla_mappings.default.ml
@@ -56,6 +56,10 @@ module Fresh_bitwuzla (B : Bitwuzla_cxx.S) : M = struct
 
   let ite cond t1 t2 = mk_term3 Kind.Ite cond t1 t2
 
+  let forall _ = Fmt.failwith "Bitwuzla_mappings: forall not implemented"
+
+  let exists _ = Fmt.failwith "Bitwuzla_mappings: exists not implemented"
+
   module Types = struct
     let int = Obj.magic 0xdeadc0de
 
diff --git a/src/cvc5_mappings.default.ml b/src/cvc5_mappings.default.ml
index 0135bb1c..68ffa2dc 100644
--- a/src/cvc5_mappings.default.ml
+++ b/src/cvc5_mappings.default.ml
@@ -54,6 +54,10 @@ module Fresh_cvc5 () = struct
 
   let ite cond t1 t2 = Term.mk_term tm Kind.Ite [| cond; t1; t2 |]
 
+  let forall _ = Fmt.failwith "Cvc5_mappings: forall not implemented"
+
+  let exists _ = Fmt.failwith "Cvc5_mappings: exists not implemented"
+
   module Types = struct
     let int = Sort.mk_int_sort tm
 
diff --git a/src/expr.ml b/src/expr.ml
index f302b5dc..62df92a5 100644
--- a/src/expr.ml
+++ b/src/expr.ml
@@ -96,11 +96,11 @@ end
 
 module Set = PatriciaTree.MakeHashconsedSet (Key) ()
 
-let make (e : expr) = Hc.hashcons e [@@inline]
+let[@inline] make e = Hc.hashcons e
 
-let view (hte : t) : expr = hte.node [@@inline]
+let[@inline] view (hte : t) = hte.node
 
-let compare (hte1 : t) (hte2 : t) = compare hte1.tag hte2.tag [@@inline]
+let[@inline] compare (hte1 : t) (hte2 : t) = compare hte1.tag hte2.tag
 
 let symbol s = make (Symbol s)
 
@@ -273,7 +273,13 @@ let ptr base offset = make (Ptr { base; offset })
 
 let app symbol args = make (App (symbol, args))
 
-let let_in vars expr = make (Binder (Let_in, vars, expr))
+let[@inline] binder bt vars expr = make (Binder (bt, vars, expr))
+
+let let_in vars body = binder Let_in vars body
+
+let forall vars body = binder Forall vars body
+
+let exists vars body = binder Exists vars body
 
 let unop' ty op hte = make (Unop (ty, op, hte)) [@@inline]
 
diff --git a/src/expr.mli b/src/expr.mli
index 52fe0d1d..7ce0d672 100644
--- a/src/expr.mli
+++ b/src/expr.mli
@@ -61,6 +61,10 @@ val app : Symbol.t -> t list -> t
 
 val let_in : t list -> t -> t
 
+val forall : t list -> t -> t
+
+val exists : t list -> t -> t
+
 (** Smart unop constructor, applies simplifications at constructor level *)
 val unop : Ty.t -> Ty.Unop.t -> t -> t
 
diff --git a/src/mappings.ml b/src/mappings.ml
index a52b012b..edc0b383 100644
--- a/src/mappings.ml
+++ b/src/mappings.ml
@@ -667,9 +667,18 @@ module Make (M_with_make : M_with_make) : S_with_fresh = struct
         let ctx, e1 = encode_expr ctx e1 in
         let ctx, e2 = encode_expr ctx e2 in
         (ctx, M.Bitv.concat e1 e2)
-      | List _ | App _ | Binder _ -> assert false
-
-    let encode_exprs ctx (es : Expr.t list) : symbol_ctx * M.term list =
+      | Binder (Forall, vars, body) ->
+        let ctx, vars = encode_exprs ctx vars in
+        let ctx, body = encode_expr ctx body in
+        (ctx, M.forall vars body)
+      | Binder (Exists, vars, body) ->
+        let ctx, vars = encode_exprs ctx vars in
+        let ctx, body = encode_expr ctx body in
+        (ctx, M.exists vars body)
+      | List _ | App _ | Binder _ ->
+        Fmt.failwith "Cannot encode expression: %a" Expr.pp hte
+
+    and encode_exprs ctx (es : Expr.t list) : symbol_ctx * M.term list =
       List.fold_left
         (fun (ctx, es) e ->
           let ctx, e = encode_expr ctx e in
diff --git a/src/mappings.nop.ml b/src/mappings.nop.ml
index 9b48199d..394ba19a 100644
--- a/src/mappings.nop.ml
+++ b/src/mappings.nop.ml
@@ -50,6 +50,10 @@ module Nop = struct
 
     let ite _ = assert false
 
+    let forall _ _ = assert false
+
+    let exists _ _ = assert false
+
     module Types = struct
       let int = ()
 
diff --git a/src/mappings_intf.ml b/src/mappings_intf.ml
index 13c3daed..1ecd9dac 100644
--- a/src/mappings_intf.ml
+++ b/src/mappings_intf.ml
@@ -49,6 +49,10 @@ module type M = sig
 
   val ite : term -> term -> term -> term
 
+  val forall : term list -> term -> term
+
+  val exists : term list -> term -> term
+
   module Types : sig
     val int : ty
 
diff --git a/src/rewrite.ml b/src/rewrite.ml
index 8de83752..531e9845 100644
--- a/src/rewrite.ml
+++ b/src/rewrite.ml
@@ -101,7 +101,18 @@ let rec rewrite_expr (type_map, expr_map) hte =
         expr_map vars
     in
     rewrite_expr (type_map, expr_map) e
-  | Binder (_, _, _) -> assert false
+  | Binder (((Forall | Exists) as quantifier), vars, e) ->
+    let type_map, vars =
+      List.fold_left
+        (fun (map, vars) e ->
+          match Expr.view e with
+          | App (sym, [ e ]) ->
+            let ty = Expr.ty e in
+            (Symb_map.add sym ty map, Expr.symbol { sym with ty } :: vars)
+          | _ -> assert false )
+        (type_map, []) vars
+    in
+    Expr.make (Binder (quantifier, vars, rewrite_expr (type_map, expr_map) e))
 
 (** Acccumulates types of symbols in [type_map] and calls rewrite_expr *)
 let rewrite_cmd type_map cmd =
diff --git a/src/smtlib.ml b/src/smtlib.ml
index 7c2ef652..86dab0af 100644
--- a/src/smtlib.ml
+++ b/src/smtlib.ml
@@ -5,6 +5,7 @@
 open Dolmen
 module Loc = Std.Loc
 
+(* FIXME: Dangerous global reference *)
 let custom_sorts = Hashtbl.create 10
 
 let pp_loc fmt = function
@@ -296,11 +297,11 @@ module Term = struct
       (* Ids can only be symbols. Any other expr here is super wrong *)
       assert false
 
-  let letand ?loc:_ (vars : t list) (expr : t) : t = Expr.let_in vars expr
+  let letand ?loc:_ (vars : t list) (body : t) : t = Expr.let_in vars body
 
-  let forall ?loc:_ = assert false
+  let forall ?loc:_ (vars : t list) (body : t) : t = Expr.forall vars body
 
-  let exists ?loc:_ = assert false
+  let exists ?loc:_ (vars : t list) (body : t) : t = Expr.exists vars body
 
   let match_ ?loc:_ = assert false
 
diff --git a/src/z3_mappings.default.ml b/src/z3_mappings.default.ml
index 6777e094..d5de8f66 100644
--- a/src/z3_mappings.default.ml
+++ b/src/z3_mappings.default.ml
@@ -54,6 +54,14 @@ module M = struct
 
     let ite cond e1 e2 = Z3.Boolean.mk_ite ctx cond e1 e2
 
+    let forall vars body =
+      Z3.Quantifier.mk_forall_const ctx vars body None [] [] None None
+      |> Z3.Quantifier.expr_of_quantifier
+
+    let exists vars body =
+      Z3.Quantifier.mk_exists_const ctx vars body None [] [] None None
+      |> Z3.Quantifier.expr_of_quantifier
+
     module Types = struct
       let int = Z3.Arithmetic.Integer.mk_sort ctx
 
@@ -72,11 +80,11 @@ module M = struct
       let to_ety sort =
         match Z3.Sort.get_sort_kind sort with
         | Z3enums.INT_SORT -> Ty.Ty_int
-        | Z3enums.REAL_SORT -> Ty.Ty_real
-        | Z3enums.BOOL_SORT -> Ty.Ty_bool
-        | Z3enums.SEQ_SORT -> Ty.Ty_str
-        | Z3enums.BV_SORT -> Ty.Ty_bitv (Z3.BitVector.get_size sort)
-        | Z3enums.FLOATING_POINT_SORT ->
+        | REAL_SORT -> Ty.Ty_real
+        | BOOL_SORT -> Ty.Ty_bool
+        | SEQ_SORT -> Ty.Ty_str
+        | BV_SORT -> Ty.Ty_bitv (Z3.BitVector.get_size sort)
+        | FLOATING_POINT_SORT ->
           let ebits = Z3.FloatingPoint.get_ebits ctx sort in
           let sbits = Z3.FloatingPoint.get_sbits ctx sort in
           Ty.Ty_fp (ebits + sbits)
@@ -91,8 +99,8 @@ module M = struct
       let to_bool interp =
         match Z3.Boolean.get_bool_value interp with
         | Z3enums.L_TRUE -> true
-        | Z3enums.L_FALSE -> false
-        | Z3enums.L_UNDEF ->
+        | L_FALSE -> false
+        | L_UNDEF ->
           Fmt.failwith "Z3_mappings2: to_bool: something went terribly wrong!"
 
       let to_string interp = Z3.Seq.get_string ctx interp
diff --git a/test/smt2/dune b/test/smt2/dune
index 87666283..fa446046 100644
--- a/test/smt2/dune
+++ b/test/smt2/dune
@@ -10,6 +10,8 @@
   test_core_const.smt2
   test_core_true.smt2
   test_empty.smt2
+  test_exists.smt2
+  test_forall.smt2
   test_fp.smt2
   test_lia.smt2
   test_lra.smt2
diff --git a/test/smt2/test_exists.smt2 b/test/smt2/test_exists.smt2
new file mode 100644
index 00000000..f3eef287
--- /dev/null
+++ b/test/smt2/test_exists.smt2
@@ -0,0 +1,2 @@
+(assert (exists ((x Int)) (= (+ x 1) 2)))
+(check-sat)
diff --git a/test/smt2/test_forall.smt2 b/test/smt2/test_forall.smt2
new file mode 100644
index 00000000..0819f01d
--- /dev/null
+++ b/test/smt2/test_forall.smt2
@@ -0,0 +1,2 @@
+(assert (forall ((x Int)) (= x x)))
+(check-sat)
diff --git a/test/smt2/test_smt2.t b/test/smt2/test_smt2.t
index 043dab01..90d86f55 100644
--- a/test/smt2/test_smt2.t
+++ b/test/smt2/test_smt2.t
@@ -82,3 +82,9 @@ Tests smt2 with the --from-file argument:
   (model
     (x str "abcd")
     (y str "a"))
+
+Test Forall and Exists parsing:
+  $ smtml run test_forall.smt2
+  sat
+  $ smtml run test_exists.smt2
+  sat