diff --git a/src/smtlib/Typecheck.ml b/src/smtlib/Typecheck.ml
index 51cc5722..9a67a726 100644
--- a/src/smtlib/Typecheck.ml
+++ b/src/smtlib/Typecheck.ml
@@ -29,10 +29,13 @@ module Ctx = struct
   and ty_kind =
     | K_atomic of Ty.def
 
+  type default_num = [`Real | `Int]
+
   type t = {
     tst: T.store;
     names: (ID.t * kind) StrTbl.t;
     lets: T.t StrTbl.t;
+    mutable default_num: default_num;
     mutable loc: Loc.t option; (* current loc *)
   }
 
@@ -40,9 +43,13 @@ module Ctx = struct
     tst;
     names=StrTbl.create 64;
     lets=StrTbl.create 16;
+    default_num=`Real;
     loc=None;
   }
 
+  let set_default_num_int self = self.default_num <- `Int
+  let set_default_num_real self = self.default_num <- `Real
+
   let loc t = t.loc
   let set_loc ?loc t = t.loc <- loc
 
@@ -137,6 +144,8 @@ let cast_to_real (ctx:Ctx.t) (t:T.t) : T.t =
       (* convert the whole structure to reals *)
       let l = LIA_view.to_lra conv l in
       T.lra ctx.tst l
+    | T.Ite (a,b,c) ->
+      T.ite ctx.tst a (conv b) (conv c)
     | _ ->
       errorf_ctx ctx "cannot cast term to real@ :term %a" T.pp t
   in
@@ -227,9 +236,10 @@ let rec conv_term (ctx:Ctx.t) (t:PA.term) : T.t =
   | PA.True -> T.true_ tst
   | PA.False -> T.false_ tst
   | PA.Const s when is_num s ->
-    begin match string_as_z s with
-      | Some n -> T.lia tst (Const n)
-      | None ->
+    begin match string_as_z s, ctx.default_num with
+      | Some n, `Int -> T.lia tst (Const n)
+      | Some n, `Real -> T.lra tst (Const (Q.of_bigint n))
+      | None, _ ->
         begin match string_as_q s with
           | Some n -> T.lra tst (Const n)
           | None -> errorf_ctx ctx "expected a number for %a" PA.pp_term t
@@ -289,7 +299,11 @@ let rec conv_term (ctx:Ctx.t) (t:PA.term) : T.t =
   | PA.Eq (a,b) ->
     let a = conv_term ctx a in
     let b = conv_term ctx b in
-    Form.eq tst a b
+    if is_real a || is_real b then (
+      Form.eq tst (cast_to_real ctx a) (cast_to_real ctx b)
+    ) else (
+      Form.eq tst a b
+    )
   | PA.Imply (a,b) ->
     let a = conv_term ctx a in
     let b = conv_term ctx b in
@@ -427,6 +441,10 @@ let conv_fun_defs ctx decls bodies : A.definition list =
   defs
    *)
 
+let is_lia s =
+  CCString.mem ~sub:"LIA" s ||
+  CCString.mem ~sub:"LIRA" s
+
 let rec conv_statement ctx (s:PA.statement): Stmt.t list =
   Log.debugf 4 (fun k->k "(@[<1>statement_of_ast@ %a@])" PA.pp_stmt s);
   Ctx.set_loc ctx ?loc:(PA.loc s);
@@ -435,7 +453,13 @@ let rec conv_statement ctx (s:PA.statement): Stmt.t list =
 and conv_statement_aux ctx (stmt:PA.statement) : Stmt.t list =
   let tst = ctx.Ctx.tst in
   match PA.view stmt with
-  | PA.Stmt_set_logic s -> [Stmt.Stmt_set_logic s]
+  | PA.Stmt_set_logic logic ->
+    if is_lia logic then (
+      Ctx.set_default_num_int ctx;
+    ) else (
+      Ctx.set_default_num_real ctx;
+    );
+    [Stmt.Stmt_set_logic logic]
   | PA.Stmt_set_option l -> [Stmt.Stmt_set_option l]
   | PA.Stmt_set_info (a,b) -> [Stmt.Stmt_set_info (a,b)]
   | PA.Stmt_exit -> [Stmt.Stmt_exit]
diff --git a/src/smtlib/Typecheck.mli b/src/smtlib/Typecheck.mli
index c526ce3a..ee2cc957 100644
--- a/src/smtlib/Typecheck.mli
+++ b/src/smtlib/Typecheck.mli
@@ -13,6 +13,8 @@ type 'a or_error = ('a, string) CCResult.t
 
 module Ctx : sig
   type t
+  val set_default_num_real : t -> unit
+  val set_default_num_int : t -> unit
   val create: T.store -> t
 end