diff --git a/src/liballoc/boxed.rs b/src/liballoc/boxed.rs
index 6a05ef68088..c1778ef101a 100644
--- a/src/liballoc/boxed.rs
+++ b/src/liballoc/boxed.rs
@@ -66,7 +66,7 @@ use core::marker::{Unpin, Unsize};
 use core::mem::{self, PinMut};
 use core::ops::{CoerceUnsized, Deref, DerefMut, Generator, GeneratorState};
 use core::ptr::{self, NonNull, Unique};
-use core::task::{Context, Poll, UnsafeTask, TaskObj, LocalTaskObj};
+use core::task::{Context, Poll, UnsafeFutureObj, FutureObj, LocalFutureObj};
 use core::convert::From;
 
 use raw_vec::RawVec;
@@ -933,12 +933,12 @@ impl<'a, F: ?Sized + Future> Future for PinBox<F> {
 }
 
 #[unstable(feature = "futures_api", issue = "50547")]
-unsafe impl<F: Future<Output = ()> + 'static> UnsafeTask for PinBox<F> {
+unsafe impl<T, F: Future<Output = T> + 'static> UnsafeFutureObj<T> for PinBox<F> {
     fn into_raw(self) -> *mut () {
         PinBox::into_raw(self) as *mut ()
     }
 
-    unsafe fn poll(task: *mut (), cx: &mut Context) -> Poll<()> {
+    unsafe fn poll(task: *mut (), cx: &mut Context) -> Poll<T> {
         let ptr = task as *mut F;
         let pin: PinMut<F> = PinMut::new_unchecked(&mut *ptr);
         pin.poll(cx)
@@ -950,29 +950,29 @@ unsafe impl<F: Future<Output = ()> + 'static> UnsafeTask for PinBox<F> {
 }
 
 #[unstable(feature = "futures_api", issue = "50547")]
-impl<F: Future<Output = ()> + Send + 'static> From<PinBox<F>> for TaskObj {
-    fn from(boxed: PinBox<F>) -> Self {
-        TaskObj::new(boxed)
+impl<T, F: Future<Output = T> + Send + 'static> Into<FutureObj<T>> for PinBox<F> {
+    fn into(self) -> FutureObj<T> {
+        FutureObj::new(self)
     }
 }
 
 #[unstable(feature = "futures_api", issue = "50547")]
-impl<F: Future<Output = ()> + Send + 'static> From<Box<F>> for TaskObj {
-    fn from(boxed: Box<F>) -> Self {
-        TaskObj::new(PinBox::from(boxed))
+impl<T, F: Future<Output = T> + Send + 'static> Into<FutureObj<T>> for Box<F> {
+    fn into(self) -> FutureObj<T> {
+        FutureObj::new(PinBox::from(self))
     }
 }
 
 #[unstable(feature = "futures_api", issue = "50547")]
-impl<F: Future<Output = ()> + 'static> From<PinBox<F>> for LocalTaskObj {
-    fn from(boxed: PinBox<F>) -> Self {
-        LocalTaskObj::new(boxed)
+impl<T, F: Future<Output = T> + 'static> Into<LocalFutureObj<T>> for PinBox<F> {
+    fn into(self) -> LocalFutureObj<T> {
+        LocalFutureObj::new(self)
     }
 }
 
 #[unstable(feature = "futures_api", issue = "50547")]
-impl<F: Future<Output = ()> + 'static> From<Box<F>> for LocalTaskObj {
-    fn from(boxed: Box<F>) -> Self {
-        LocalTaskObj::new(PinBox::from(boxed))
+impl<T, F: Future<Output = T> + 'static> Into<LocalFutureObj<T>> for Box<F> {
+    fn into(self) -> LocalFutureObj<T> {
+        LocalFutureObj::new(PinBox::from(self))
     }
 }
diff --git a/src/libcore/task/executor.rs b/src/libcore/task/executor.rs
index 73bf80d2f99..55ea5e724c1 100644
--- a/src/libcore/task/executor.rs
+++ b/src/libcore/task/executor.rs
@@ -13,7 +13,7 @@
             issue = "50547")]
 
 use fmt;
-use super::{TaskObj, LocalTaskObj};
+use super::{FutureObj, LocalFutureObj};
 
 /// A task executor.
 ///
@@ -29,7 +29,7 @@ pub trait Executor {
     ///
     /// The executor may be unable to spawn tasks, either because it has
     /// been shut down or is resource-constrained.
-    fn spawn_obj(&mut self, task: TaskObj) -> Result<(), SpawnObjError>;
+    fn spawn_obj(&mut self, task: FutureObj<()>) -> Result<(), SpawnObjError>;
 
     /// Determine whether the executor is able to spawn new tasks.
     ///
@@ -76,7 +76,7 @@ pub struct SpawnObjError {
     pub kind: SpawnErrorKind,
 
     /// The task for which spawning was attempted
-    pub task: TaskObj,
+    pub task: FutureObj<()>,
 }
 
 /// The result of a failed spawn
@@ -86,5 +86,5 @@ pub struct SpawnLocalObjError {
     pub kind: SpawnErrorKind,
 
     /// The task for which spawning was attempted
-    pub task: LocalTaskObj,
+    pub task: LocalFutureObj<()>,
 }
diff --git a/src/libcore/task/task.rs b/src/libcore/task/future_obj.rs
similarity index 50%
rename from src/libcore/task/task.rs
rename to src/libcore/task/future_obj.rs
index c5a41873db4..3ed3bd51cf6 100644
--- a/src/libcore/task/task.rs
+++ b/src/libcore/task/future_obj.rs
@@ -14,63 +14,68 @@
 
 use fmt;
 use future::Future;
+use marker::PhantomData;
 use mem::PinMut;
-use super::{Context, Poll};
+use task::{Context, Poll};
 
-/// A custom trait object for polling tasks, roughly akin to
-/// `Box<Future<Output = ()>>`.
-/// Contrary to `TaskObj`, `LocalTaskObj` does not have a `Send` bound.
-pub struct LocalTaskObj {
+/// A custom trait object for polling futures, roughly akin to
+/// `Box<dyn Future<Output = T>>`.
+/// Contrary to `FutureObj`, `LocalFutureObj` does not have a `Send` bound.
+pub struct LocalFutureObj<T> {
     ptr: *mut (),
-    poll_fn: unsafe fn(*mut (), &mut Context) -> Poll<()>,
+    poll_fn: unsafe fn(*mut (), &mut Context) -> Poll<T>,
     drop_fn: unsafe fn(*mut ()),
+    _marker: PhantomData<T>,
 }
 
-impl LocalTaskObj {
-    /// Create a `LocalTaskObj` from a custom trait object representation.
+impl<T> LocalFutureObj<T> {
+    /// Create a `LocalFutureObj` from a custom trait object representation.
     #[inline]
-    pub fn new<T: UnsafeTask>(t: T) -> LocalTaskObj {
-        LocalTaskObj {
-            ptr: t.into_raw(),
-            poll_fn: T::poll,
-            drop_fn: T::drop,
+    pub fn new<F: UnsafeFutureObj<T>>(f: F) -> LocalFutureObj<T> {
+        LocalFutureObj {
+            ptr: f.into_raw(),
+            poll_fn: F::poll,
+            drop_fn: F::drop,
+            _marker: PhantomData,
         }
     }
 
-    /// Converts the `LocalTaskObj` into a `TaskObj`
-    /// To make this operation safe one has to ensure that the `UnsafeTask`
-    /// instance from which this `LocalTaskObj` was created actually implements
-    /// `Send`.
-    pub unsafe fn as_task_obj(self) -> TaskObj {
-        TaskObj(self)
+    /// Converts the `LocalFutureObj` into a `FutureObj`
+    /// To make this operation safe one has to ensure that the `UnsafeFutureObj`
+    /// instance from which this `LocalFutureObj` was created actually
+    /// implements `Send`.
+    #[inline]
+    pub unsafe fn as_future_obj(self) -> FutureObj<T> {
+        FutureObj(self)
     }
 }
 
-impl fmt::Debug for LocalTaskObj {
+impl<T> fmt::Debug for LocalFutureObj<T> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        f.debug_struct("LocalTaskObj")
+        f.debug_struct("LocalFutureObj")
             .finish()
     }
 }
 
-impl From<TaskObj> for LocalTaskObj {
-    fn from(task: TaskObj) -> LocalTaskObj {
-        task.0
+impl<T> From<FutureObj<T>> for LocalFutureObj<T> {
+    #[inline]
+    fn from(f: FutureObj<T>) -> LocalFutureObj<T> {
+        f.0
     }
 }
 
-impl Future for LocalTaskObj {
-    type Output = ();
+impl<T> Future for LocalFutureObj<T> {
+    type Output = T;
 
     #[inline]
-    fn poll(self: PinMut<Self>, cx: &mut Context) -> Poll<()> {
+    fn poll(self: PinMut<Self>, cx: &mut Context) -> Poll<T> {
         unsafe {
             (self.poll_fn)(self.ptr, cx)
         }
     }
 }
 
-impl Drop for LocalTaskObj {
+impl<T> Drop for LocalFutureObj<T> {
     fn drop(&mut self) {
         unsafe {
             (self.drop_fn)(self.ptr)
@@ -78,38 +83,38 @@ impl Drop for LocalTaskObj {
     }
 }
 
-/// A custom trait object for polling tasks, roughly akin to
-/// `Box<Future<Output = ()> + Send>`.
-pub struct TaskObj(LocalTaskObj);
+/// A custom trait object for polling futures, roughly akin to
+/// `Box<dyn Future<Output = T>> + Send`.
+pub struct FutureObj<T>(LocalFutureObj<T>);
 
-unsafe impl Send for TaskObj {}
+unsafe impl<T> Send for FutureObj<T> {}
 
-impl TaskObj {
-    /// Create a `TaskObj` from a custom trait object representation.
+impl<T> FutureObj<T> {
+    /// Create a `FutureObj` from a custom trait object representation.
     #[inline]
-    pub fn new<T: UnsafeTask + Send>(t: T) -> TaskObj {
-        TaskObj(LocalTaskObj::new(t))
+    pub fn new<F: UnsafeFutureObj<T> + Send>(f: F) -> FutureObj<T> {
+        FutureObj(LocalFutureObj::new(f))
     }
 }
 
-impl fmt::Debug for TaskObj {
+impl<T> fmt::Debug for FutureObj<T> {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
-        f.debug_struct("TaskObj")
+        f.debug_struct("FutureObj")
             .finish()
     }
 }
 
-impl Future for TaskObj {
-    type Output = ();
+impl<T> Future for FutureObj<T> {
+    type Output = T;
 
     #[inline]
-    fn poll(self: PinMut<Self>, cx: &mut Context) -> Poll<()> {
+    fn poll(self: PinMut<Self>, cx: &mut Context) -> Poll<T> {
         let pinned_field = unsafe { PinMut::map_unchecked(self, |x| &mut x.0) };
         pinned_field.poll(cx)
     }
 }
 
-/// A custom implementation of a task trait object for `TaskObj`, providing
+/// A custom implementation of a future trait object for `FutureObj`, providing
 /// a hand-rolled vtable.
 ///
 /// This custom representation is typically used only in `no_std` contexts,
@@ -118,25 +123,25 @@ impl Future for TaskObj {
 /// The implementor must guarantee that it is safe to call `poll` repeatedly (in
 /// a non-concurrent fashion) with the result of `into_raw` until `drop` is
 /// called.
-pub unsafe trait UnsafeTask: 'static {
+pub unsafe trait UnsafeFutureObj<T>: 'static {
     /// Convert a owned instance into a (conceptually owned) void pointer.
     fn into_raw(self) -> *mut ();
 
-    /// Poll the task represented by the given void pointer.
+    /// Poll the future represented by the given void pointer.
     ///
     /// # Safety
     ///
     /// The trait implementor must guarantee that it is safe to repeatedly call
     /// `poll` with the result of `into_raw` until `drop` is called; such calls
     /// are not, however, allowed to race with each other or with calls to `drop`.
-    unsafe fn poll(task: *mut (), cx: &mut Context) -> Poll<()>;
+    unsafe fn poll(future: *mut (), cx: &mut Context) -> Poll<T>;
 
-    /// Drops the task represented by the given void pointer.
+    /// Drops the future represented by the given void pointer.
     ///
     /// # Safety
     ///
     /// The trait implementor must guarantee that it is safe to call this
     /// function once per `into_raw` invocation; that call cannot race with
     /// other calls to `drop` or `poll`.
-    unsafe fn drop(task: *mut ());
+    unsafe fn drop(future: *mut ());
 }
diff --git a/src/libcore/task/mod.rs b/src/libcore/task/mod.rs
index d167a374105..06cd7a9dd77 100644
--- a/src/libcore/task/mod.rs
+++ b/src/libcore/task/mod.rs
@@ -25,8 +25,8 @@ pub use self::executor::{
 mod poll;
 pub use self::poll::Poll;
 
-mod task;
-pub use self::task::{TaskObj, LocalTaskObj, UnsafeTask};
+mod future_obj;
+pub use self::future_obj::{FutureObj, LocalFutureObj, UnsafeFutureObj};
 
 mod wake;
 pub use self::wake::{Waker, LocalWaker, UnsafeWake};
diff --git a/src/test/run-pass/async-await.rs b/src/test/run-pass/async-await.rs
index 8b649f6ef7b..3a67750e77e 100644
--- a/src/test/run-pass/async-await.rs
+++ b/src/test/run-pass/async-await.rs
@@ -21,7 +21,7 @@ use std::sync::{
 };
 use std::task::{
     Context, Poll, Wake,
-    Executor, TaskObj, SpawnObjError,
+    Executor, FutureObj, SpawnObjError,
     local_waker_from_nonlocal,
 };
 
@@ -37,7 +37,7 @@ impl Wake for Counter {
 
 struct NoopExecutor;
 impl Executor for NoopExecutor {
-    fn spawn_obj(&mut self, _: TaskObj) -> Result<(), SpawnObjError> {
+    fn spawn_obj(&mut self, _: FutureObj<T>) -> Result<(), SpawnObjError> {
         Ok(())
     }
 }
diff --git a/src/test/run-pass/futures-api.rs b/src/test/run-pass/futures-api.rs
index 3b5a1725b66..a427b82af6a 100644
--- a/src/test/run-pass/futures-api.rs
+++ b/src/test/run-pass/futures-api.rs
@@ -22,7 +22,7 @@ use std::sync::{
 use std::task::{
     Context, Poll,
     Wake, Waker, LocalWaker,
-    Executor, TaskObj, SpawnObjError,
+    Executor, FutureObj, SpawnObjError,
     local_waker, local_waker_from_nonlocal,
 };
 
@@ -44,7 +44,7 @@ impl Wake for Counter {
 struct NoopExecutor;
 
 impl Executor for NoopExecutor {
-    fn spawn_obj(&mut self, _: TaskObj) -> Result<(), SpawnObjError> {
+    fn spawn_obj(&mut self, _: FutureObj<()>) -> Result<(), SpawnObjError> {
         Ok(())
     }
 }