diff --git a/ml-proto/host/script.ml b/ml-proto/host/script.ml
index 1fe8bb512b..53804fcfe9 100644
--- a/ml-proto/host/script.ml
+++ b/ml-proto/host/script.ml
@@ -25,7 +25,7 @@ let trace name = if !Flags.trace then print_endline ("-- " ^ name)
 let current_module : Eval.instance option ref = ref None
 
 let eval_args es at =
-  let evs = List.map Eval.eval es in
+  let evs = List.map Eval.host_eval es in
   let reject_none = function
     | Some v -> v
     | None -> Error.error at "unexpected () value" in
@@ -88,7 +88,7 @@ let run_command cmd =
     let m = get_module cmd.at in
     let arg_vs = eval_args arg_es cmd.at in
     let got_v = Eval.invoke m name arg_vs in
-    let expect_v = Eval.eval expect_e in
+    let expect_v = Eval.host_eval expect_e in
     (match got_v, expect_v with
      | Some Int32 got_i32, Some Int32 expect_i32 ->
        if got_i32 <> expect_i32 then begin
diff --git a/ml-proto/spec/check.ml b/ml-proto/spec/check.ml
index d42de9d2fc..921dcb8766 100644
--- a/ml-proto/spec/check.ml
+++ b/ml-proto/spec/check.ml
@@ -22,13 +22,10 @@ type context =
   tables : func_type list;
   locals : value_type list;
   return : expr_type;
-  labels : expr_type list
+  labels : expr_type list;
+  has_memory : bool
 }
 
-let c0 =
-  {funcs = []; imports = []; tables = [];
-   locals = []; return = None; labels = []}
-
 let lookup category list x =
   try List.nth list x.it with Failure _ ->
     error x.at ("unknown " ^ category ^ " " ^ string_of_int x.it)
@@ -215,12 +212,15 @@ let rec check_expr c et e =
     check_type (Some t) et e.at
 
   | PageSize ->
+    check_has_memory c e.at;
     check_type (Some Int32Type) et e.at
 
   | MemorySize ->
+    check_has_memory c e.at;
     check_type (Some Int32Type) et e.at
 
   | ResizeMemory e ->
+    check_has_memory c e.at;
     check_expr c (Some Int32Type) e;
     check_type None et e.at
 
@@ -243,16 +243,21 @@ and check_arm c t et arm =
   check_expr c (if fallthru then None else et) e
 
 and check_load c et memop e1 at =
+  check_has_memory c at;
   check_align memop.align at;
   check_expr c (Some Int32Type) e1;
   check_type (Some memop.ty) et at
 
 and check_store c et memop e1 e2 at =
+  check_has_memory c at;
   check_align memop.align at;
   check_expr c (Some Int32Type) e1;
   check_expr c (Some memop.ty) e2;
   check_type (Some memop.ty) et at
 
+and check_has_memory c at =
+  require c.has_memory at "memory ops require a memory section";
+
 and check_align align at =
   Lib.Option.app (fun a ->
     require (Lib.Int.is_power_of_two a) at "non-power-of-two alignment") align
@@ -281,14 +286,15 @@ let check_func c f =
                    return = Lib.Option.map it result} in
   check_expr c' (Lib.Option.map it result) e
 
-let check_table c tab =
+let check_table funcs tables tab =
   match tab.it with
   | [] ->
     error tab.at "empty table"
   | x::xs ->
-    let s = func c x in
-    List.iter (fun xI -> check_func_type (func c xI) s xI.at) xs;
-    {c with tables = c.tables @ [s]}
+    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]
 
 module NameSet = Set.Make(String)
 
@@ -315,8 +321,13 @@ let check_memory memory =
 let check_module m =
   let {imports; exports; tables; funcs; memory} = m.it in
   Lib.Option.app check_memory memory;
-  let c = {c0 with funcs = List.map type_func funcs;
-                 imports = List.map type_import imports} in
-  let c' = List.fold_left check_table c tables in
-  List.iter (check_func c') funcs;
-  ignore (List.fold_left (check_export c') NameSet.empty exports)
+  let func_types = List.map type_func funcs in
+  let c = {funcs = func_types;
+           imports = List.map type_import imports;
+           tables = List.fold_left (check_table func_types) [] tables;
+           locals = [];
+           return = None;
+           labels = [];
+           has_memory = memory <> None} in
+  List.iter (check_func c) funcs;
+  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 0a074e6c1b..61e011a112 100644
--- a/ml-proto/spec/eval.ml
+++ b/ml-proto/spec/eval.ml
@@ -25,7 +25,7 @@ type instance =
   imports : import list;
   exports : export_map;
   tables : func list list;
-  memory : Memory.t;
+  memory : Memory.t option;
   host : host_params
 }
 
@@ -88,6 +88,11 @@ let numerics_error at = function
       error at "runtime: invalid conversion to integer"
   | exn -> raise exn
 
+let some_memory c at =
+  match c.module_.memory with
+  | Some m -> m
+  | _ -> error at "memory operation but no memory section"
+
 let some v at =
   match v with
   | Some v -> v
@@ -169,31 +174,31 @@ let rec eval_expr (c : config) (e : expr) =
     Some v1
 
   | Load ({ty; align = _}, e1) ->
+    let mem = some_memory c e.at in
     let v1 = some (eval_expr c e1) e1.at in
     let a = Memory.address_of_value v1 in
-    (try Some (Memory.load c.module_.memory a ty)
-    with exn -> memory_error e.at exn)
+    (try Some (Memory.load mem a ty) with exn -> memory_error e.at exn)
 
   | Store ({ty = _; align = _}, e1, e2) ->
+    let mem = some_memory c e.at in
     let v1 = some (eval_expr c e1) e1.at in
     let v2 = some (eval_expr c e2) e2.at in
     let a = Memory.address_of_value v1 in
-    (try Memory.store c.module_.memory a v2
-    with exn -> memory_error e.at exn);
+    (try Memory.store mem a v2 with exn -> memory_error e.at exn);
     Some v2
 
   | LoadExtend ({memop = {ty; align = _}; sz; ext}, e1) ->
+    let mem = some_memory c e.at in
     let v1 = some (eval_expr c e1) e1.at in
     let a = Memory.address_of_value v1 in
-    (try Some (Memory.load_extend c.module_.memory a sz ext ty)
-    with exn -> memory_error e.at exn)
+    (try Some (Memory.load_extend mem a sz ext ty) with exn -> memory_error e.at exn)
 
   | StoreWrap ({memop = {ty; align = _}; sz}, e1, e2) ->
+    let mem = some_memory c e.at in
     let v1 = some (eval_expr c e1) e1.at in
     let v2 = some (eval_expr c e2) e2.at in
     let a = Memory.address_of_value v1 in
-    (try Memory.store_wrap c.module_.memory a sz v2
-    with exn -> memory_error e.at exn);
+    (try Memory.store_wrap mem a sz v2 with exn -> memory_error e.at exn);
     Some v2
 
   | Const v ->
@@ -235,14 +240,16 @@ let rec eval_expr (c : config) (e : expr) =
     Some (Int32 (page_size c))
 
   | MemorySize ->
-    Some (Int32 (I32.of_int32 (Int32.of_int (Memory.size c.module_.memory))))
+    let mem = some_memory c e.at in
+    Some (Int32 (I32.of_int32 (Int32.of_int (Memory.size mem))))
 
   | ResizeMemory e ->
+    let mem = some_memory c e.at in
     let i = int32 (eval_expr c e) e.at in
     if (I32.rem_u i (page_size c)) <> I32.zero then
       error e.at "runtime: resize_memory operand not multiple of page_size";
     (* TODO: The conversion to int could overflow. *)
-    Memory.resize c.module_.memory (Int32.to_int i);
+    Memory.resize mem (Int32.to_int i);
     None
 
 and eval_expr_option c eo =
@@ -272,36 +279,32 @@ and eval_func (m : instance) (f : func) (evs : value list) =
 
 (* Modules *)
 
-let init_memory ast =
-  match ast with
-  | None ->
-    Memory.create 0
-  | Some {it = {initial; segments; _}} ->
-    let mem = Memory.create initial in
-    Memory.init mem (List.map it segments);
-    mem
+let init_memory {it = {initial; segments; _}} =
+  let mem = Memory.create initial in
+  Memory.init mem (List.map it segments);
+  mem
 
 let init m imports host =
   assert (List.length imports = List.length m.it.Ast.imports);
   assert (host.page_size > 0);
   assert (Lib.Int.is_power_of_two host.page_size);
   let {Ast.exports; tables; funcs; memory; _} = m.it in
-  let mem = init_memory memory 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
-  {funcs; imports; exports; tables; memory = mem; host}
+  {funcs; imports; exports; tables; memory = memory'; host}
 
 let invoke m name vs =
   let f = export m (name @@ no_region) in
   assert (List.length vs = List.length f.it.params);
   eval_func m f vs
 
-let eval e =
+(* This function is not part of the spec. *)
+let host_eval e =
   let f = {params = []; result = None; locals = []; body = e} @@ no_region in
-  let memory = Memory.create 0 in
   let exports = ExportMap.singleton "eval" f in
   let host = {page_size = 1} in
-  let m = {imports = []; exports; tables = []; funcs = [f]; memory; host} in
+  let m = {imports = []; exports; tables = []; funcs = [f]; memory = None; host} in
   eval_func m f []
diff --git a/ml-proto/spec/eval.mli b/ml-proto/spec/eval.mli
index 4c737a0103..2442bfe13f 100644
--- a/ml-proto/spec/eval.mli
+++ b/ml-proto/spec/eval.mli
@@ -10,4 +10,6 @@ type host_params = {page_size : Memory.size}
 val init : Ast.module_ -> import list -> host_params -> instance
 val invoke : instance -> string -> value list -> value option
   (* raise Error.Error *)
-val eval : Ast.expr -> value option (* raise Error.Error *)
+
+(* This function is not part of the spec. *)
+val host_eval : Ast.expr -> value option (* raise Error.Error *)
diff --git a/ml-proto/test/memory.wast b/ml-proto/test/memory.wast
index 2ec068f3c0..f27a8b82cb 100644
--- a/ml-proto/test/memory.wast
+++ b/ml-proto/test/memory.wast
@@ -35,29 +35,29 @@
 )
 
 ;; Test alignment annotation rules
-(module (func (i32.load8_u/2 (i32.const 0))))
-(module (func (i32.load16_u/4 (i32.const 0))))
-(module (func (i32.load/8 (i32.const 0))))
-(module (func (f32.load/8 (i32.const 0))))
+(module (memory 0) (func (i32.load8_u/2 (i32.const 0))))
+(module (memory 0) (func (i32.load16_u/4 (i32.const 0))))
+(module (memory 0) (func (i32.load/8 (i32.const 0))))
+(module (memory 0) (func (f32.load/8 (i32.const 0))))
 
 (assert_invalid
-  (module (func (i64.load/0 (i32.const 0))))
+  (module (memory 0) (func (i64.load/0 (i32.const 0))))
   "non-power-of-two alignment"
 )
 (assert_invalid
-  (module (func (i64.load/3 (i32.const 0))))
+  (module (memory 0) (func (i64.load/3 (i32.const 0))))
   "non-power-of-two alignment"
 )
 (assert_invalid
-  (module (func (i64.load/5 (i32.const 0))))
+  (module (memory 0) (func (i64.load/5 (i32.const 0))))
   "non-power-of-two alignment"
 )
 (assert_invalid
-  (module (func (i64.load/6 (i32.const 0))))
+  (module (memory 0) (func (i64.load/6 (i32.const 0))))
   "non-power-of-two alignment"
 )
 (assert_invalid
-  (module (func (i64.load/7 (i32.const 0))))
+  (module (memory 0) (func (i64.load/7 (i32.const 0))))
   "non-power-of-two alignment"
 )