diff --git a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
--- a/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
+++ b/mlir/include/mlir/Dialect/Shape/IR/ShapeOps.td
@@ -168,17 +168,30 @@
   let parser = [{ return ::parse$cppClass(parser, result); }];
 }
 
-def Shape_CreateShapeOp : Shape_Op<"create_shape", []> {
-  let summary = "Creates a shape descriptor from a tensor";
+def Shape_FromExtentTensorOp : Shape_Op<"from_extent_tensor", []> {
+  let summary = "Creates a shape from a tensor of extents";
   let description = [{
-    Creates a shape from a 1D integral tensor. The rank equals the number of
-    elements in the tensor, and extent matches the values of the elements.
+    Creates a shape from a 1D integral tensor of extents. The rank of the
+    resulting shape equals the number of elements in the tensor, and the
+    extents match the values of the elements.
   }];
 
   let arguments = (ins I32Tensor:$input);
   let results = (outs Shape_ShapeType:$result);
 }
 
+def Shape_ToExtentTensorOp : Shape_Op<"to_tensor", []> {
+  let summary = "Creates a dimension tensor from a shape";
+  let description = [{
+    Converts a shape to a 1D integral tensor of extents. The number of elements
+    in the tensor equals the rank of the shape, and the elements equal the
+    extents of the shape.
+  }];
+
+  let arguments = (ins Shape_ShapeType:$input);
+  let results = (outs I32Tensor:$result);
+}
+
 def Shape_JoinOp : Shape_Op<"join", []> {
   let summary = "Returns the least general shape.size of its operands";
   let description = [{
@@ -299,4 +312,60 @@
   let results =  (outs Shape_ShapeOrSizeType:$output);
 }
 
+def Shape_DropBackOp : Shape_Op<"drop_back", []> {
+  let summary = "Drops dimensions off the back of a shape.";
+  let description = [{
+    Drops `amount` dimensions off the back of a shape, resulting in a shape
+    with equal or lesser rank.
+
+    Examples:
+    drop_back([4,5,6], amount=1) -> [4,5]
+    drop_back([4,5,6], amount=3) -> []
+    drop_back([4,5,6], amount=4) -> error
+
+
+    Requires (otherwise result is an error shape):
+    - amount >= 0
+    - amount <= rank(operand)
+  }];
+
+  let arguments = (ins Shape_ShapeType:$operand, I32:$amount);
+  let results = (outs Shape_ShapeType:$result);
+}
+def Shape_TakeBackOp : Shape_Op<"take_back", []> {
+  let summary = "Takes dimensions off the back of a shape.";
+  let description = [{
+    Takes the last `amount` dimensions from `operand`, resulting in a shape
+    with equal or lesser rank.
+
+    Examples:
+    take_back([5,6,7], amount=1) -> [7]
+    take_back([5,6,7], amount=3) -> [5,6,7]
+    take_back([5,6,7], amount=6) -> error
+
+    Requires:
+    - amount >= 0
+    - amount <= rank(operand)
+  }];
+
+  let arguments = (ins Shape_ShapeType:$operand, I32:$amount);
+  let results = (outs Shape_ShapeType:$result);
+}
+
+def Shape_ConcatOp : Shape_Op<"concat", []> {
+  let summary = "Concatenates two shapes.";
+  let description = [{
+    Creates a shape whose dimensions consist of first the dimensions from `lhs`
+    followed by the dimensions of `rhs`.
+
+    Example:
+    concat([2,3], [4,5]) -> [2,3,4,5]
+    concat([], []) -> []
+    concat([], [4,5,6]) -> [4,5,6]
+  }];
+
+  let arguments = (ins Shape_ShapeType:$lhs, Shape_ShapeType:$rhs);
+  let results = (outs Shape_ShapeType:$result);
+}
+
 #endif // SHAPE_OPS