diff --git a/docs/spec.md b/docs/spec.md
index 0173673f76c..de009fd7fd0 100644
--- a/docs/spec.md
+++ b/docs/spec.md
@@ -778,13 +778,13 @@ defined as follows:
 
 Afterwards, within each `process_group`:
 
-* `result@process[result_index] = convert_or_quantize_or_dequantize(exec(
-  schedule), type(result))` for some binary tree `schedule` where:
+* `result@process[result_index] = to_destination_type(exec(schedule),
+  type(result))` for some binary tree `schedule` where:
   * `exec(node)` = `computation(exec(node.left), exec(node.right))`.
   * `exec(leaf)` = `leaf.value`.
 * `schedule` is an implementation-defined binary tree whose in-order
-  traversal is `convert_or_quantize_or_dequantize(
-  operands@process_group...[result_index], type(func_inputs(computation)[0]))`.
+  traversal is `to_destination_type(operands@process_group...[result_index],
+  type(func_inputs(computation)[0]))`.
 
 #### Inputs
 
@@ -1092,11 +1092,8 @@ grad_output, type(grad_operand), type(grad_scale), type(feature_index))`.
 #### Constraints
 
 * (C1) `0 <= feature_index < rank(operand)`.
-* (C2) `baseline_element_type(operand) = baseline_element_type(scale) =
-       baseline_element_type(mean) = baseline_element_type(variance) =
-       baseline_element_type(grad_output) = baseline_element_type(grad_operand)
-       = baseline_element_type(grad_scale) =
-       baseline_element_type(grad_offset)`.
+* (C2) `operand`, `scale`, `mean`, `variance`, `grad_output`, `grad_operand`,
+       `grad_scale` and `grad_offset` have the same `baseline_element_type`.
 * (C3) `operand`, `grad_output` and `grad_operand` have the same shape.
 * (C4) `scale`, `mean`, `variance`, `grad_scale` and `grad_offset` have the
        same shape.
@@ -1183,9 +1180,8 @@ feature_index), operand, scale, offset, mean, variance, type(result))`.
 #### Constraints
 
 * (C1) `0 <= feature_index < rank(operand)`.
-* (C2) `baseline_element_type(operand) = baseline_element_type(scale) =
-       baseline_element_type(offset) = baseline_element_type(mean) =
-       baseline_element_type(variance) = baseline_element_type(result)`.
+* (C2) `operand`, `scale`, `offset`, `mean`, `variance` and `result` have the
+       same `baseline_element_type`.
 * (C3) `size(scale) = dim(operand, feature_index)`.
 * (C4) `size(offset) = dim(operand, feature_index)`.
 * (C5) `size(mean) = dim(operand, feature_index)`.
@@ -1275,9 +1271,8 @@ scale, offset, type(output), type(batch_mean), type(batch_var))`.
 #### Constraints
 
 * (C1) `0 <= feature_index < rank(operand)`.
-* (C2) `baseline_element_type(operand) = baseline_element_type(scale) =
-       baseline_element_type(offset) = baseline_element_type(batch_mean) =
-       baseline_element_type(batch_var) = baseline_element_type(output)`.
+* (C2) `operand`, `scale`, `offset`, `batch_mean`, `batch_var` and `output` have
+       the same `baseline_element_type`.
 * (C3) `size(scale) = dim(operand, feature_index)`.
 * (C4) `size(offset) = dim(operand, feature_index)`.
 * (C5) `size(batch_mean) = dim(operand, feature_index)`.
@@ -4017,13 +4012,15 @@ doesn't hold for many popular reductions. E.g. floating-point addition for
 `body` and zero for `init_values` don't actually form a monoid because
 floating-point addition is not associative.
 
-More formally, `results...[j0, ..., jR-1] = convert_or_quantize_or_dequantize(
+More formally, `results...[j0, ..., jR-1] = to_destination_type(
 reduce(input_slices_converted), type(results...)))` where:
 
 * `input_slices = inputs...[j0, ..., :, ..., jR-1]`, where `:` are inserted
   at `dimensions`.
-* `input_slices_converted = convert_or_quantize_or_dequantize(input_slices...,
+* `input_slices_converted = to_destination_type(input_slices...,
   type(func_inputs(body)[:len(func_inputs(body))//2])...)`.
+* `init_values_converted = to_destination_type(init_values...,
+  type(func_inputs(body)[len(func_inputs(body))//2:])...)`.
 * `reduce(input_slices_converted) = exec(schedule)` for some binary tree
   `schedule` where:
   * `exec(node) = body(exec(node.left), exec(node.right))`.
@@ -4034,9 +4031,7 @@ reduce(input_slices_converted), type(results...)))` where:
     `index_space(input_slices_converted)` in the ascending lexicographic order
     of `index`.
   * Interspersed with an implementation-defined amount of
-    `convert_or_quantize_or_dequantize(init_values...,
-    type(func_inputs(body)[len(func_inputs(body))//2:])...)` at
-    implementation-defined positions.
+    `init_values_converted` at implementation-defined positions.
 
 #### Inputs
 
@@ -4759,14 +4754,14 @@ Given that, `results = exec(schedule, inputs)`, where:
   `index_space(updates[0])`.
 * `exec([update_index, ...], results) = exec([...], updated_results)` where:
   * If `result_index` is in bounds for `shape(results...)`
-    * `updated_values = update_computation(
-      convert_or_quantize_or_dequantize(results...[result_index], type(
-      func_inputs(update_computation)[:len(func_inputs(update_computation))//2])
-      ... ),
-      convert_or_quantize_or_dequantize(updates...[update_index], type(
-      func_inputs(update_computation)[len(func_inputs(update_computation))//2:])
-      ... ))`
-    * `updated_values_converted = convert_or_quantize_or_dequantize(
+    * `results_converted = to_destination_type(
+      results...[result_index], type(func_inputs(update_computation)
+      [:len(func_inputs(update_computation))//2])... )`
+    * `updates_converted = to_destination_type(
+      updates...[update_index], type(func_inputs(update_computation)
+      [len(func_inputs(update_computation))//2:])... )`
+    * `updated_values = update_computation(result_converted, updates_converted)`
+    * `updated_values_converted = to_destination_type(
            updated_values, type(results...))`
     * `updated_results` is a copy of `results` with `results...[result_index]`
       set to `updated_values_converted...`.
@@ -6336,12 +6331,12 @@ and [slicing](https://docs.python.org/3/reference/expressions.html#slicings)
 notations from Python are available to index into tensors, quantized tensors
 and tuples.
 
-* `convert_or_quantize_or_dequantize(x: Value, destination_type: Type) -> Value`
-is defined on tensors and returns the converted value of `x` based on the
-`type(x)` and `destination_type` as follows:
+* `to_destination_type(x: Value, destination_type: Type) -> Value` is defined on
+tensors and returns the converted value of `x` based on the `type(x)` and
+`destination_type` as follows:
 
 ```python
-def convert_or_quantize_or_dequantize(x: Value, destination_type: Type) -> Value:
+def to_destination_type(x: Value, destination_type: Type) -> Value:
   if type(x) == destination_type:
     return x
 
@@ -6358,10 +6353,10 @@ def convert_or_quantize_or_dequantize(x: Value, destination_type: Type) -> Value
   return convert(x, destination_type)
 ```
 
-There is plan to merge `convert`, `uniform_quantize` and `uniform_dequantize`
-operations ([#1576](https://github.com/openxla/stablehlo/issues/1576)). After
-the merge we do not need the above function and can use the operation name for
-`convert` instead.
+There is early discussion on merging `convert`, `uniform_quantize` and
+`uniform_dequantize` operations ([#1576](https://github.com/openxla/stablehlo/issues/1576)).
+After the merge we do not need the above function and can use the operation name
+for `convert` instead.
 
 * `is_nan(x: Value) -> Value` is defined on tensors and returns `true` if
 all elements of `x` are `NaN` or `false` otherwise. If `x` is not a tensor,