diff --git a/WDL/CLI.py b/WDL/CLI.py
index 038c8a9d..07ed44dd 100644
--- a/WDL/CLI.py
+++ b/WDL/CLI.py
@@ -496,7 +496,7 @@ def runner_input(doc, inputs, input_file, empty, task=None):
             )
         if not isinstance(decl.type, Type.Array) or decl.type.nonempty:
             die("Cannot set input {} {} to empty array".format(str(decl.type), decl.name))
-        input_env = input_env.bind(empty_name, Value.Array(decl.type, []), decl)
+        input_env = input_env.bind(empty_name, Value.Array(decl.type.item_type, []), decl)
 
     # add in command-line inputs
     for one_input in inputs:
@@ -524,7 +524,7 @@ def runner_input(doc, inputs, input_file, empty, task=None):
             existing = None
         if existing:
             if isinstance(v, Value.Array):
-                assert isinstance(existing, Value.Array) and existing.type == v.type
+                assert isinstance(existing, Value.Array) and v.type.coerces(existing.type)
                 existing.value.extend(v.value)
             else:
                 die(
@@ -618,7 +618,7 @@ def runner_input_value(s_value, ty):
         ty.item_type, (Type.String, Type.File, Type.Int, Type.Float)
     ):
         # just produce a length-1 array, to be combined ex post facto
-        return Value.Array(ty, [runner_input_value(s_value, ty.item_type)])
+        return Value.Array(ty.item_type, [runner_input_value(s_value, ty.item_type)])
     return die(
         "No command-line support yet for inputs of type {}; workaround: specify in JSON file with --input".format(
             str(ty)
diff --git a/WDL/Expr.py b/WDL/Expr.py
index dbfad163..b00e62ee 100644
--- a/WDL/Expr.py
+++ b/WDL/Expr.py
@@ -462,7 +462,8 @@ def _eval(
         ""
         assert isinstance(self.type, Type.Array)
         return Value.Array(
-            self.type, [item.eval(env, stdlib).coerce(self.type.item_type) for item in self.items]
+            self.type.item_type,
+            [item.eval(env, stdlib).coerce(self.type.item_type) for item in self.items],
         )
 
 
@@ -507,7 +508,7 @@ def _eval(
         assert isinstance(self.type, Type.Pair)
         lv = self.left.eval(env, stdlib)
         rv = self.right.eval(env, stdlib)
-        return Value.Pair(self.type, (lv, rv))
+        return Value.Pair(self.left.type, self.right.type, (lv, rv))
 
 
 class Map(Base):
@@ -584,7 +585,7 @@ def _eval(
         for k, v in self.items:
             eitems.append((k.eval(env, stdlib), v.eval(env, stdlib)))
         # TODO: complain of duplicate keys
-        return Value.Map(self.type, eitems)
+        return Value.Map(self.type.item_type, eitems)
 
 
 class Struct(Base):
diff --git a/WDL/StdLib.py b/WDL/StdLib.py
index 6d9fdf2a..a67e3740 100644
--- a/WDL/StdLib.py
+++ b/WDL/StdLib.py
@@ -548,7 +548,9 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
         assert isinstance(arr, Value.Array)
         arrty = arr.type
         assert isinstance(arrty, Type.Array)
-        return Value.Array(arrty, [arg for arg in arr.value if not isinstance(arg, Value.Null)])
+        return Value.Array(
+            arrty.item_type, [arg for arg in arr.value if not isinstance(arg, Value.Null)]
+        )
 
 
 class _ZipOrCross(EagerFunction):
@@ -589,8 +591,13 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
         if len(lhs.value) != len(rhs.value):
             raise Error.EvalError(expr, "zip(): input arrays must have equal length")
         return Value.Array(
-            ty,
-            [Value.Pair(ty.item_type, (lhs.value[i], rhs.value[i])) for i in range(len(lhs.value))],
+            ty.item_type,
+            [
+                Value.Pair(
+                    ty.item_type.left_type, ty.item_type.right_type, (lhs.value[i], rhs.value[i])
+                )
+                for i in range(len(lhs.value))
+            ],
         )
 
 
@@ -599,9 +606,9 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
         ty, lhs, rhs = self._coerce_args(expr, arguments)
         assert isinstance(ty, Type.Array) and isinstance(ty.item_type, Type.Pair)
         return Value.Array(
-            ty,
+            ty.item_type,
             [
-                Value.Pair(ty.item_type, (lhs_item, rhs_item))
+                Value.Pair(ty.item_type.left_type, ty.item_type.right_type, (lhs_item, rhs_item))
                 for lhs_item in lhs.value
                 for rhs_item in rhs.value
             ],
@@ -634,7 +641,7 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
         ans = []
         for row in arguments[0].coerce(Type.Array(ty)).value:
             ans.extend(row.value)
-        return Value.Array(ty, ans)
+        return Value.Array(ty.item_type, ans)
 
 
 class _Transpose(EagerFunction):
@@ -673,7 +680,7 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
                 raise Error.EvalError(expr, "transpose(): ragged input matrix")
             for i in range(len(row.value)):
                 ans[i].value.append(row.value[i])
-        return Value.Array(ty, ans)
+        return Value.Array(ty.item_type, ans)
 
 
 class _Range(EagerFunction):
@@ -700,7 +707,7 @@ def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.
         assert isinstance(arg0, Value.Int)
         if arg0.value < 0:
             raise Error.EvalError(expr, "range() got negative argument")
-        return Value.Array(Type.Array(Type.Int()), [Value.Int(x) for x in range(arg0.value)])
+        return Value.Array(Type.Int(), [Value.Int(x) for x in range(arg0.value)])
 
 
 class _Prefix(EagerFunction):
@@ -720,6 +727,6 @@ def infer_type(self, expr: "Expr.Apply") -> Type.Base:
     def _call_eager(self, expr: "Expr.Apply", arguments: List[Value.Base]) -> Value.Base:
         pfx = arguments[0].coerce(Type.String()).value
         return Value.Array(
-            Type.Array(Type.String()),
+            Type.String(),
             [Value.String(pfx + s.coerce(Type.String()).value) for s in arguments[1].value],
         )
diff --git a/WDL/Value.py b/WDL/Value.py
index 6e9c4128..ca9764af 100644
--- a/WDL/Value.py
+++ b/WDL/Value.py
@@ -131,10 +131,10 @@ class Array(Base):
     value: List[Base]
     type: Type.Array
 
-    def __init__(self, type: Type.Array, value: List[Base]) -> None:
+    def __init__(self, item_type: Type.Base, value: List[Base]) -> None:
         self.value = []
-        self.type = type
-        super().__init__(type, value)
+        self.type = Type.Array(item_type, nonempty=(len(value) > 0))
+        super().__init__(self.type, value)
 
     @property
     def json(self) -> Any:
@@ -165,10 +165,12 @@ class Map(Base):
     value: List[Tuple[Base, Base]]
     type: Type.Map
 
-    def __init__(self, type: Type.Map, value: List[Tuple[Base, Base]]) -> None:
+    def __init__(
+        self, item_type: Tuple[Type.Base, Type.Base], value: List[Tuple[Base, Base]]
+    ) -> None:
         self.value = []
-        self.type = type
-        super().__init__(type, value)
+        self.type = Type.Map(item_type)
+        super().__init__(self.type, value)
 
     @property
     def json(self) -> Any:
@@ -188,7 +190,7 @@ def coerce(self, desired_type: Optional[Type.Base] = None) -> Base:
         ""
         if isinstance(desired_type, Type.Map) and desired_type != self.type:
             return Map(
-                desired_type,
+                desired_type.item_type,
                 [
                     (k.coerce(desired_type.item_type[0]), v.coerce(desired_type.item_type[1]))
                     for (k, v) in self.value
@@ -209,10 +211,12 @@ class Pair(Base):
     value: Tuple[Base, Base]
     type: Type.Pair
 
-    def __init__(self, type: Type.Pair, value: Tuple[Base, Base]) -> None:
+    def __init__(
+        self, left_type: Type.Base, right_type: Type.Base, value: Tuple[Base, Base]
+    ) -> None:
         self.value = value
-        self.type = type
-        super().__init__(type, value)
+        self.type = Type.Pair(left_type, right_type)
+        super().__init__(self.type, value)
 
     def __str__(self) -> str:
         assert isinstance(self.value, tuple)
@@ -231,7 +235,8 @@ def coerce(self, desired_type: Optional[Type.Base] = None) -> Base:
         ""
         if isinstance(desired_type, Type.Pair) and desired_type != self.type:
             return Pair(
-                desired_type,
+                desired_type.left_type,
+                desired_type.right_type,
                 (
                     self.value[0].coerce(desired_type.left_type),
                     self.value[1].coerce(desired_type.right_type),
@@ -328,7 +333,7 @@ def from_json(type: Type.Base, value: Any) -> Base:
         for k, v in value.items():
             assert isinstance(k, str)
             items.append((from_json(type.item_type[0], k), from_json(type.item_type[1], v)))
-        return Map(type, items)
+        return Map(type.item_type, items)
     if (
         isinstance(type, Type.StructInstance)
         and isinstance(value, dict)
diff --git a/WDL/runtime/task.py b/WDL/runtime/task.py
index dd8399e0..4b8dec38 100644
--- a/WDL/runtime/task.py
+++ b/WDL/runtime/task.py
@@ -559,7 +559,7 @@ def parse_lines(s: str) -> Value.Array:
                 ans = [
                     Value.String(line) for line in (s[:-1] if s.endswith("\n") else s).split("\n")
                 ]
-            return Value.Array(Type.Array(Type.String()), ans)
+            return Value.Array(Type.String(), ans)
 
         self._override_static("read_lines", _read_something(parse_lines))
 
@@ -573,7 +573,7 @@ def parse_tsv(s: str) -> Value.Array:
                 for line in parse_lines(s).value
             ]
             # pyre-ignore
-            return Value.Array(Type.Array(Type.Array(Type.String())), ans)
+            return Value.Array(Type.Array(Type.String()), ans)
 
         self._override_static("read_tsv", _read_something(parse_tsv))
 
@@ -588,7 +588,7 @@ def parse_map(s: str) -> Value.Map:
                     raise Error.InputError("read_map(): duplicate key")
                 keys.add(line.value[0].value)
                 ans.append((line.value[0], line.value[1]))
-            return Value.Map(Type.Map((Type.String(), Type.String())), ans)
+            return Value.Map((Type.String(), Type.String()), ans)
 
         self._override_static("read_map", _read_something(parse_map))
 
@@ -599,9 +599,9 @@ def parse_json(s: str) -> Value.Base:
                 ans = []
                 for k in j:
                     ans.append((Value.String(str(k)), Value.String(str(j[k]))))
-                return Value.Map(Type.Map((Type.String(), Type.String())), ans)
+                return Value.Map((Type.String(), Type.String()), ans)
             if isinstance(j, list):
-                return Value.Array(Type.Array(Type.String()), [Value.String(str(v)) for v in j])
+                return Value.Array(Type.String(), [Value.String(str(v)) for v in j])
             if isinstance(j, bool):
                 return Value.Boolean(j)
             if isinstance(j, int):
@@ -653,7 +653,7 @@ def _serialize_lines(array: Value.Array, outfile: BinaryIO) -> None:
             _write_something(
                 lambda v, outfile: _serialize_lines(
                     Value.Array(
-                        Type.Array(Type.String()),
+                        Type.String(),
                         [
                             Value.String(
                                 "\t".join(
@@ -678,7 +678,7 @@ def _serialize_map(map: Value.Map, outfile: BinaryIO) -> None:
                         "write_map(): keys & values must not contain tab or newline characters"
                     )
                 lines.append(Value.String(k + "\t" + v))
-            _serialize_lines(Value.Array(Type.Array(Type.String()), lines), outfile)
+            _serialize_lines(Value.Array(Type.String(), lines), outfile)
 
         self._override_static("write_map", _write_something(_serialize_map))  # pyre-ignore
 
@@ -728,7 +728,7 @@ def _glob(pattern: Value.String, lib: OutputStdLib = self) -> Value.Array:
                 dstrip += "" if dstrip.endswith("/") else "/"
                 assert hf.startswith(dstrip)
                 container_files.append(os.path.join(lib.container.container_dir, hf[len(dstrip) :]))
-            return Value.Array(Type.Array(Type.File()), [Value.File(fn) for fn in container_files])
+            return Value.Array(Type.File(), [Value.File(fn) for fn in container_files])
 
         self._override_static("glob", _glob)
 
@@ -749,5 +749,5 @@ def _call_eager(self, expr: Expr.Apply, arguments: List[Value.Base]) -> Value.Ba
             for fn_c in files.value
         ]
         # pyre-ignore
-        arguments = [Value.Array(files.type, host_files)] + arguments[1:]
+        arguments = [Value.Array(files.type.item_type, host_files)] + arguments[1:]
         return super()._call_eager(expr, arguments)
diff --git a/WDL/runtime/workflow.py b/WDL/runtime/workflow.py
index 1b465d7e..cf3a8cf9 100644
--- a/WDL/runtime/workflow.py
+++ b/WDL/runtime/workflow.py
@@ -508,7 +508,7 @@ def _gather(
         assert v0 is None or isinstance(v0, Value.Base)
         # bind the array, singleton value, or None as appropriate
         if isinstance(gather.section, Tree.Scatter):
-            rhs = Value.Array(Type.Array(v0.type if v0 else Type.Any()), values)
+            rhs = Value.Array((v0.type if v0 else Type.Any()), values)
         else:
             assert isinstance(gather.section, Tree.Conditional)
             assert len(values) <= 1
diff --git a/tests/test_0eval.py b/tests/test_0eval.py
index 4afb9604..7a45aaf0 100644
--- a/tests/test_0eval.py
+++ b/tests/test_0eval.py
@@ -301,11 +301,11 @@ def test_interpolation(self):
         )
 
     def test_pair(self):
-        env = cons_env(("p", WDL.Value.Pair(WDL.Type.Pair(WDL.Type.Float(), WDL.Type.Float()),
+        env = cons_env(("p", WDL.Value.Pair(WDL.Type.Float(), WDL.Type.Float(),
                                             (WDL.Value.Float(3.14159), WDL.Value.Float(2.71828)))),
-                        ("q", WDL.Value.Pair(WDL.Type.Pair(WDL.Type.Pair(WDL.Type.Int(), WDL.Type.Int()),
-                                                           WDL.Type.Float(optional=True)),
-                                             (WDL.Value.Pair(WDL.Type.Pair(WDL.Type.Int(), WDL.Type.Int()),
+                        ("q", WDL.Value.Pair(WDL.Type.Pair(WDL.Type.Int(), WDL.Type.Int()),
+                                                           WDL.Type.Float(optional=True),
+                                             (WDL.Value.Pair(WDL.Type.Int(), WDL.Type.Int(),
                                                              (WDL.Value.Int(4), WDL.Value.Int(2))),
                                               WDL.Value.Null()))))
         self._test_tuples(
diff --git a/tests/test_1doc.py b/tests/test_1doc.py
index 75d0c733..a2f78bf4 100644
--- a/tests/test_1doc.py
+++ b/tests/test_1doc.py
@@ -189,9 +189,9 @@ def test_placeholders(self):
             }
             """)[0]
         task.typecheck()
-        foobar = WDL.Value.Array(WDL.Type.Array(WDL.Type.String()), [WDL.Value.String("foo"), WDL.Value.String("bar")])
+        foobar = WDL.Value.Array(WDL.Type.String(), [WDL.Value.String("foo"), WDL.Value.String("bar")])
         self.assertEqual(task.command.parts[1].eval(WDL.Env.Bindings().bind('s', foobar)).value, 'foo, bar')
-        foobar = WDL.Value.Array(WDL.Type.Array(WDL.Type.String()), [])
+        foobar = WDL.Value.Array(WDL.Type.String(), [])
         self.assertEqual(task.command.parts[1].eval(WDL.Env.Bindings().bind('s', foobar)).value, '')
         with self.assertRaises(WDL.Error.StaticTypeMismatch):
             task = WDL.parse_tasks("""