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
@@ -106,6 +106,30 @@
   let assemblyFormat = "attr-dict $value";
 }
 
+def Shape_FromIndexOp : Shape_Op<"from_index", []> {
+  let summary = "Creates a shape size from a standard index";
+  let description = [{
+    Converts a standard index to a shape size.
+    This is to convert between types of the standard dialect and types of the
+    shape dialect.
+  }];
+
+  let arguments = (ins Index:$input);
+  let results = (outs Shape_SizeType:$result);
+}
+
+def Shape_ToIndexOp : Shape_Op<"to_index", []> {
+  let summary = "Creates a standard index from a shape size";
+  let description = [{
+    Converts a shape size to a standard index.
+    This is to convert between types of the standard dialect and types of the
+    shape dialect.
+  }];
+
+  let arguments = (ins Shape_SizeType:$input);
+  let results = (outs Index:$result);
+}
+
 def Shape_FromExtentTensorOp : Shape_Op<"from_extent_tensor", []> {
   let summary = "Creates a shape from a tensor of extents";
   let description = [{
@@ -114,7 +138,7 @@
     extents match the values of the elements.
   }];
 
-  let arguments = (ins I32Tensor:$input);
+  let arguments = (ins IndexTensor:$input);
   let results = (outs Shape_ShapeType:$result);
 }
 
@@ -204,14 +228,14 @@
     number of elements
 
     ```mlir
-    func @shape_num_elements(%shape : !shape.type) -> !shape.size {
+    func @shape_num_elements(%shape : !shape.shape) -> !shape.size {
       %0 = "shape.constant_dim"() {value = 1 : i32} : () -> !shape.size
       %1 = "shape.reduce"(%shape, %0) ( {
         ^bb0(%index: i32, %dim: !shape.size, %lci: !shape.size):
           %acc = "shape.mul"(%lci, %dim) :
             (!shape.size, !shape.size) -> !shape.size
           shape.yield %acc : !shape.size
-        }) : (!shape.type, !shape.size) -> (!shape.size)
+        }) : (!shape.shape, !shape.size) -> (!shape.size)
       return %1 : !shape.size
     }
     ```
@@ -225,6 +249,18 @@
   let regions = (region SizedRegion<1>:$body);
 }
 
+def Shape_NumElementsOp : Shape_Op<"num_elements", []> {
+  let summary = "Returns the number of elements for a given shape";
+  let description = [{
+    Returns the number of elements for a given shape which is the product of its
+    dimensions.
+    A tensor of the given shape will hold this many elements.
+  }];
+
+  let arguments = (ins Shape_ShapeType:$shape);
+  let results = (outs Shape_SizeType:$result);
+}
+
 def Shape_ShapeOfOp : Shape_Op<"shape_of",
     [NoSideEffect, DeclareOpInterfaceMethods<InferTypeOpInterface>]> {
   let summary = "Returns shape of a value or shaped type operand";
diff --git a/mlir/include/mlir/IR/Builders.h b/mlir/include/mlir/IR/Builders.h
--- a/mlir/include/mlir/IR/Builders.h
+++ b/mlir/include/mlir/IR/Builders.h
@@ -69,6 +69,8 @@
   IndexType getIndexType();
 
   IntegerType getI1Type();
+  IntegerType getI32Type();
+  IntegerType getI64Type();
   IntegerType getIntegerType(unsigned width);
   IntegerType getIntegerType(unsigned width, bool isSigned);
   FunctionType getFunctionType(ArrayRef<Type> inputs, ArrayRef<Type> results);
diff --git a/mlir/include/mlir/IR/StandardTypes.h b/mlir/include/mlir/IR/StandardTypes.h
--- a/mlir/include/mlir/IR/StandardTypes.h
+++ b/mlir/include/mlir/IR/StandardTypes.h
@@ -396,6 +396,7 @@
 
 //===----------------------------------------------------------------------===//
 // RankedTensorType
+//===----------------------------------------------------------------------===//
 
 /// Ranked tensor types represent multi-dimensional arrays that have a shape
 /// with a fixed number of dimensions. Each shape element can be a non-negative
diff --git a/mlir/lib/IR/Builders.cpp b/mlir/lib/IR/Builders.cpp
--- a/mlir/lib/IR/Builders.cpp
+++ b/mlir/lib/IR/Builders.cpp
@@ -54,6 +54,10 @@
 
 IntegerType Builder::getI1Type() { return IntegerType::get(1, context); }
 
+IntegerType Builder::getI32Type() { return IntegerType::get(32, context); }
+
+IntegerType Builder::getI64Type() { return IntegerType::get(64, context); }
+
 IntegerType Builder::getIntegerType(unsigned width) {
   return IntegerType::get(width, context);
 }