diff --git a/ml-proto/host/parser.mly b/ml-proto/host/parser.mly
index 38b48ba0b3..2c4e15126f 100644
--- a/ml-proto/host/parser.mly
+++ b/ml-proto/host/parser.mly
@@ -67,7 +67,7 @@ let enter_func c =
   assert (VarMap.is_empty c.labels);
   {c with labels = VarMap.add "return" 0 c.labels; locals = empty ()}
 
-let lookup_type c x =
+let type_ c x =
   try VarMap.find x.it c.types.tmap
   with Not_found -> Error.error x.at ("unknown type " ^ x.it)
 
@@ -78,7 +78,6 @@ let lookup category space x =
 let func c x = lookup "function" c.funcs x
 let import c x = lookup "import" c.imports x
 let local c x = lookup "local" c.locals x
-let table c x = lookup "table" (empty ()) x
 let label c x =
   try VarMap.find x.it c.labels
   with Not_found -> Error.error x.at ("unknown label " ^ x.it)
@@ -114,7 +113,7 @@ let anon_label c = {c with labels = VarMap.map ((+) 1) c.labels}
 let empty_type = {ins = []; out = None}
 
 let explicit_decl c name t at =
-  let x = name c lookup_type in
+  let x = name c type_ in
   if x.it < List.length c.types.tlist &&
      t <> empty_type &&
      t <> List.nth c.types.tlist x.it then
@@ -126,7 +125,6 @@ let implicit_decl c t at =
   | None -> let i = List.length c.types.tlist in anon_type c t; i @@ at
   | Some i -> i @@ at
 
-
 %}
 
 %token INT FLOAT TEXT VAR VALUE_TYPE LPAR RPAR
@@ -231,7 +229,7 @@ expr1 :
   | CALL var expr_list { fun c -> call ($2 c func, $3 c) }
   | CALL_IMPORT var expr_list { fun c -> call_import ($2 c import, $3 c) }
   | CALL_INDIRECT var expr expr_list
-    { fun c -> call_indirect ($2 c table, $3 c, $4 c) }
+    { fun c -> call_indirect ($2 c type_, $3 c, $4 c) }
   | GET_LOCAL var { fun c -> get_local ($2 c local) }
   | SET_LOCAL var expr { fun c -> set_local ($2 c local, $3 c) }
   | LOAD expr { fun c -> load ($1, $2 c) }
@@ -354,6 +352,11 @@ type_def :
     { fun c -> bind_type c $3 $6 }
 ;
 
+table :
+  | LPAR TABLE var_list RPAR
+    { fun c -> $3 c func }
+;
+
 import :
   | LPAR IMPORT TEXT TEXT type_use RPAR
     { let at = at () in
@@ -382,7 +385,7 @@ module_fields :
   | /* empty */
     { fun c ->
       {memory = None; types = c.types.tlist; funcs = []; imports = [];
-       exports = []; tables = []} }
+       exports = []; table = []} }
   | func module_fields
     { fun c -> let f = $1 c in let m = $2 c in
       {m with funcs = f () :: m.funcs} }
@@ -392,9 +395,9 @@ module_fields :
   | export module_fields
     { fun c -> let m = $2 c in
       {m with exports = $1 c :: m.exports} }
-  | LPAR TABLE var_list RPAR module_fields
-    { fun c -> let m = $5 c in
-      {m with tables = ($3 c func @@ ati 3) :: m.tables} }
+  | table module_fields
+    { fun c -> let m = $2 c in
+      {m with table = ($1 c) @ m.table} }
   | type_def module_fields
     { fun c -> $1 c; $2 c }
   | memory module_fields
diff --git a/ml-proto/host/print.ml b/ml-proto/host/print.ml
index e718723074..7ba63b784e 100644
--- a/ml-proto/host/print.ml
+++ b/ml-proto/host/print.ml
@@ -28,8 +28,8 @@ let print_func_sig m prefix i f =
 let print_export_sig m prefix n f =
   printf "%s \"%s\" : %s\n" prefix n (string_of_func_type (func_type m f))
 
-let print_table_sig prefix i t_opt =
-  printf "%s %d : %s\n" prefix i (string_of_table_type t_opt)
+let print_table_elem i x =
+  printf "table [%d] = func %d\n" i x.it
 
 
 (* Ast *)
@@ -40,19 +40,11 @@ let print_func m i f =
 let print_export m i ex =
   print_export_sig m "export" ex.it.name (List.nth m.it.funcs ex.it.func.it)
 
-let print_table m i tab =
-  let t_opt =
-    match tab.it with
-    | [] -> None
-    | x::_ -> Some (func_type m (List.nth m.it.funcs x.it))
-  in print_table_sig "table" i t_opt
-
-
 let print_module m =
-  let {funcs; exports; tables} = m.it in
+  let {funcs; exports; table} = m.it in
   List.iteri (print_func m) funcs;
   List.iteri (print_export m) exports;
-  List.iteri (print_table m) tables;
+  List.iteri print_table_elem table;
   flush_all ()
 
 let print_module_sig m =
diff --git a/ml-proto/spec/ast.ml b/ml-proto/spec/ast.ml
index a52fd5056f..7e0cf8e90e 100644
--- a/ml-proto/spec/ast.ml
+++ b/ml-proto/spec/ast.ml
@@ -140,8 +140,6 @@ and import' =
   func_name : string;
 }
 
-type table = var list Source.phrase
-
 type module_ = module_' Source.phrase
 and module_' =
 {
@@ -150,5 +148,5 @@ and module_' =
   funcs : func list;
   imports : import list;
   exports : export list;
-  tables : table list;
+  table : var list;
 }
diff --git a/ml-proto/spec/check.ml b/ml-proto/spec/check.ml
index 0ce2e17fd0..6b7ac6758f 100644
--- a/ml-proto/spec/check.ml
+++ b/ml-proto/spec/check.ml
@@ -20,7 +20,6 @@ type context =
   types : func_type list;
   funcs : func_type list;
   imports : func_type list;
-  tables : func_type list;
   locals : value_type list;
   return : expr_type;
   labels : expr_type list;
@@ -31,10 +30,10 @@ let lookup category list x =
   try List.nth list x.it with Failure _ ->
     error x.at ("unknown " ^ category ^ " " ^ string_of_int x.it)
 
+let type_ types x = lookup "function type" types x
 let func c x = lookup "function" c.funcs x
 let import c x = lookup "import" c.imports x
 let local c x = lookup "local" c.locals x
-let table c x = lookup "table" c.tables x
 let label c x = lookup "label" c.labels x
 
 
@@ -45,9 +44,6 @@ let check_type actual expected at =
     ("type mismatch: expression has type " ^ string_of_expr_type actual ^
      " but the context requires " ^ string_of_expr_type expected)
 
-let check_func_type actual expected at =
-  require (actual = expected) at "inconsistent function type in table"
-
 
 (* Type Synthesis *)
 
@@ -154,7 +150,7 @@ let rec check_expr c et e =
     check_type out et e.at
 
   | CallIndirect (x, e1, es) ->
-    let {ins; out} = table c x in
+    let {ins; out} = type_ c.types x in
     check_expr c (Some Int32Type) e1;
     check_exprs c ins es;
     check_type out et e.at
@@ -268,25 +264,14 @@ and check_mem_type ty sz at =
  *   s : func_type
  *)
 
-let get_type types t =
-  require (t.it < List.length types) t.at "type index out of bounds";
-  List.nth types t.it
-
 let check_func c f =
   let {ftype; locals; body} = f.it in
-  let s = get_type c.types ftype in
+  let s = type_ c.types ftype in
   let c' = {c with locals = s.ins @ locals; return = s.out} in
   check_expr c' s.out body
 
-let check_table funcs tables tab =
-  match tab.it with
-  | [] ->
-    error tab.at "empty table"
-  | x::xs ->
-    let func x = lookup "function" funcs x in
-    let s = func x in
-    List.iter (fun xI -> check_func_type (func xI) s xI.at) xs;
-    tables @ [s]
+let check_elem c x =
+  ignore (func c x)
 
 module NameSet = Set.Make(String)
 
@@ -315,16 +300,15 @@ let check_memory memory =
   ignore (List.fold_left (check_segment mem.initial) Int64.zero mem.segments)
 
 let check_module m =
-  let {memory; types; funcs; imports; exports; tables} = m.it in
+  let {memory; types; funcs; imports; exports; table} = m.it in
   Lib.Option.app check_memory memory;
-  let func_types = List.map (fun f -> get_type types f.it.ftype) funcs in
   let c = {types;
-           funcs = func_types;
-           imports = List.map (fun i -> get_type types i.it.itype) imports;
-           tables = List.fold_left (check_table func_types) [] tables;
+           funcs = List.map (fun f -> type_ types f.it.ftype) funcs;
+           imports = List.map (fun i -> type_ types i.it.itype) imports;
            locals = [];
            return = None;
            labels = [];
            has_memory = memory <> None} in
   List.iter (check_func c) funcs;
+  List.iter (check_elem c) table;
   ignore (List.fold_left (check_export c) NameSet.empty exports)
diff --git a/ml-proto/spec/eval.ml b/ml-proto/spec/eval.ml
index 32d16ba0a9..c8fdec62ac 100644
--- a/ml-proto/spec/eval.ml
+++ b/ml-proto/spec/eval.ml
@@ -24,7 +24,6 @@ type instance =
   module_ : module_;
   imports : import list;
   exports : export_map;
-  tables : func list list;
   memory : Memory.t option;
   host : host_params
 }
@@ -45,12 +44,18 @@ let lookup category list x =
   try List.nth list x.it with Failure _ ->
     error x.at ("runtime: undefined " ^ category ^ " " ^ string_of_int x.it)
 
+let type_ c x = lookup "type" c.instance.module_.it.types x
 let func c x = lookup "function" c.instance.module_.it.funcs x
 let import c x = lookup "import" c.instance.imports x
-let table c x y = lookup "entry" (lookup "table" c.instance.tables x) y
 let local c x = lookup "local" c.locals x
 let label c x = lookup "label" c.labels x
 
+let table_elem c i at =
+  if i < 0l || i <> Int32.of_int (Int32.to_int i) then
+    error at ("runtime: undefined table element " ^ Int32.to_string i);
+  let x = (Int32.to_int i) @@ at in
+  lookup "table element" c.instance.module_.it.table x
+
 let export m x =
   try ExportMap.find x.it m.exports
   with Not_found ->
@@ -114,10 +119,6 @@ let mem_overflow x =
 let callstack_exhaustion at =
   error at ("runtime: callstack exhausted")
 
-let func_type instance f =
-  assert (f.it.ftype.it < List.length instance.module_.it.types);
-  List.nth instance.module_.it.types f.it.ftype.it
-
 
 (* Evaluation *)
 
@@ -171,11 +172,13 @@ let rec eval_expr (c : config) (e : expr) =
     let vs = List.map (fun ev -> some (eval_expr c ev) ev.at) es in
     (import c x) vs
 
-  | CallIndirect (x, e1, es) ->
+  | CallIndirect (ftype, e1, es) ->
     let i = int32 (eval_expr c e1) e1.at in
     let vs = List.map (fun vo -> some (eval_expr c vo) vo.at) es in
-    (* TODO: The conversion to int could overflow. *)
-    eval_func c.instance (table c x (Int32.to_int i @@ e1.at)) vs
+    let f = func c (table_elem c i e1.at) in
+    if ftype.it <> f.it.ftype.it then
+      error e1.at "runtime: indirect call signature mismatch";
+    eval_func c.instance f vs
 
   | GetLocal x ->
     Some !(local c x)
@@ -269,7 +272,7 @@ and eval_func instance f vs =
   let vars = List.map (fun t -> ref (default_value t)) f.it.locals in
   let locals = args @ vars in
   let c = {instance; locals; labels = []} in
-  coerce (func_type instance f).out (eval_expr c f.it.body)
+  coerce (type_ c f.it.ftype).out (eval_expr c f.it.body)
 
 and coerce et vo =
   if et = None then None else vo
@@ -309,22 +312,22 @@ let init_memory {it = {initial; segments; _}} =
   Memory.init mem (List.map it segments);
   mem
 
+let add_export funcs ex =
+  ExportMap.add ex.it.name (List.nth funcs ex.it.func.it)
+
 let init m imports host =
   assert (List.length imports = List.length m.it.Ast.imports);
   assert (host.page_size > 0L);
   assert (Lib.Int64.is_power_of_two host.page_size);
-  let {memory; funcs; exports; tables; _} = m.it in
-  let memory' = Lib.Option.map init_memory memory in
-  let func x = List.nth funcs x.it in
-  let export ex = ExportMap.add ex.it.name (func ex.it.func) in
-  let exports = List.fold_right export exports ExportMap.empty in
-  let tables = List.map (fun tab -> List.map func tab.it) tables in
-  {module_ = m; imports; exports; tables; memory = memory'; host}
+  let {memory; funcs; exports; _} = m.it in
+  {module_ = m;
+   imports;
+   exports = List.fold_right (add_export funcs) exports ExportMap.empty;
+   memory = Lib.Option.map init_memory memory;
+   host}
 
 let invoke instance name vs =
   try
-    let f = export instance (name @@ no_region) in
-    assert (List.length vs = List.length (func_type instance f).ins);
-    eval_func instance f vs
+    eval_func instance (export instance (name @@ no_region)) vs
   with Stack_overflow -> callstack_exhaustion no_region
 
diff --git a/ml-proto/test/func_ptrs.wast b/ml-proto/test/func_ptrs.wast
index c79144f7bb..43d65bd289 100644
--- a/ml-proto/test/func_ptrs.wast
+++ b/ml-proto/test/func_ptrs.wast
@@ -30,5 +30,48 @@
 (assert_return (invoke "three" (i32.const 13)) (i32.const 11))
 (invoke "four" (i32.const 83))
 
-(assert_invalid (module (func (type 42))) "type index out of bounds")
-(assert_invalid (module (import "stdio" "print" (type 43))) "type index out of bounds")
+(assert_invalid (module (func (type 42))) "unknown function type 42")
+(assert_invalid (module (import "stdio" "print" (type 43))) "unknown function type 43")
+
+(module
+    (type $T (func (param) (result i32)))
+    (type $U (func (param) (result i32)))
+    (table $t1 $t2 $t3 $u1 $u2 $t1 $t3)
+
+    (func $t1 (type $T) (i32.const 1))
+    (func $t2 (type $T) (i32.const 2))
+    (func $t3 (type $T) (i32.const 3))
+    (func $u1 (type $U) (i32.const 4))
+    (func $u2 (type $U) (i32.const 5))
+
+    (func $callt (param $i i32) (result i32)
+        (call_indirect $T (get_local $i))
+    )
+    (export "callt" $callt)
+
+    (func $callu (param $i i32) (result i32)
+        (call_indirect $U (get_local $i))
+    )
+    (export "callu" $callu)
+)
+
+(assert_return (invoke "callt" (i32.const 0)) (i32.const 1))
+(assert_return (invoke "callt" (i32.const 1)) (i32.const 2))
+(assert_return (invoke "callt" (i32.const 2)) (i32.const 3))
+(assert_trap   (invoke "callt" (i32.const 3)) "runtime: indirect call signature mismatch")
+(assert_trap   (invoke "callt" (i32.const 4)) "runtime: indirect call signature mismatch")
+(assert_return (invoke "callt" (i32.const 5)) (i32.const 1))
+(assert_return (invoke "callt" (i32.const 6)) (i32.const 3))
+(assert_trap   (invoke "callt" (i32.const 7)) "runtime: undefined table element 7")
+(assert_trap   (invoke "callt" (i32.const 100)) "runtime: undefined table element 100")
+(assert_trap   (invoke "callt" (i32.const -1)) "runtime: undefined table element -1")
+
+(assert_trap   (invoke "callu" (i32.const 0)) "runtime: indirect call signature mismatch")
+(assert_trap   (invoke "callu" (i32.const 1)) "runtime: indirect call signature mismatch")
+(assert_trap   (invoke "callu" (i32.const 2)) "runtime: indirect call signature mismatch")
+(assert_return (invoke "callu" (i32.const 3)) (i32.const 4))
+(assert_return (invoke "callu" (i32.const 4)) (i32.const 5))
+(assert_trap   (invoke "callu" (i32.const 5)) "runtime: indirect call signature mismatch")
+(assert_trap   (invoke "callu" (i32.const 6)) "runtime: indirect call signature mismatch")
+(assert_trap   (invoke "callu" (i32.const 7)) "runtime: undefined table element 7")
+(assert_trap   (invoke "callu" (i32.const -1)) "runtime: undefined table element -1")