diff --git a/thriller-core/src/buffer.rs b/thriller-core/src/buffer.rs
index 27bffd1..d439f4e 100644
--- a/thriller-core/src/buffer.rs
+++ b/thriller-core/src/buffer.rs
@@ -2,7 +2,7 @@ use crate::shape::Ix;
 use crate::{next_id, Dim, Layout, Shape};
 
 /// Buffer type.
-#[derive(Clone, Copy, Debug)]
+#[derive(Clone, Copy, Debug, PartialEq)]
 pub enum BufType {
     /// Global Tile
     GlobalTile,
diff --git a/thriller-core/src/shape.rs b/thriller-core/src/shape.rs
index 23633a1..581c4c6 100644
--- a/thriller-core/src/shape.rs
+++ b/thriller-core/src/shape.rs
@@ -25,7 +25,7 @@ pub trait Dimension {
 }
 
 /// Stride description.
-#[derive(Clone, Copy, Debug)]
+#[derive(Clone, Copy, Debug, PartialEq)]
 pub enum Layout<D> {
     /// Row-major
     RowMajor,
@@ -54,7 +54,7 @@ where
 ///
 /// [`Dim`] describes the number of axes and the length of each axis
 /// in an array. It is also used as an index type.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 pub struct Dim {
     dims: SmallVec<[Ix; 4]>,
     ndim: usize,
@@ -140,7 +140,7 @@ impl Dimension for Dim {
 }
 
 /// Shape description.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, PartialEq)]
 pub struct Shape {
     dims: Dim,
     layout: Layout<Dim>,
diff --git a/thriller-core/src/task/compute/map.rs b/thriller-core/src/task/compute/map.rs
index 1ad75f1..1a0c5da 100644
--- a/thriller-core/src/task/compute/map.rs
+++ b/thriller-core/src/task/compute/map.rs
@@ -21,6 +21,14 @@ impl Convert {
         src_type: DataType,
         dst_type: DataType,
     ) -> Self {
+        // `src_buf` and `dst_buf` must have the same typing.
+        // TODO(KuanjuX): Don't use assert here.
+        assert_eq!(src_buf.get_typing(), dst_buf.get_typing());
+
+        // `src_buf` and `dst_buf` must have the same shape.
+        // TODO(KuanjuX): Don't use assert here.
+        assert_eq!(src_buf.get_shape(), dst_buf.get_shape());
+
         Self {
             src_buf,
             dst_buf,