diff --git a/flang/lib/Optimizer/HLFIR/Transforms/OptimizedBufferization.cpp b/flang/lib/Optimizer/HLFIR/Transforms/OptimizedBufferization.cpp
--- a/flang/lib/Optimizer/HLFIR/Transforms/OptimizedBufferization.cpp
+++ b/flang/lib/Optimizer/HLFIR/Transforms/OptimizedBufferization.cpp
@@ -417,6 +417,102 @@
   return mlir::success();
 }
 
+/// Expand hlfir.assign of array RHS to array LHS into a loop nest
+/// of element-by-element assignments:
+///   hlfir.assign %4 to %5 : !fir.ref<!fir.array<3x3xf32>>,
+///                           !fir.ref<!fir.array<3x3xf32>>
+/// into:
+///   fir.do_loop %arg1 = %c1 to %c3 step %c1 unordered {
+///     fir.do_loop %arg2 = %c1 to %c3 step %c1 unordered {
+///       %6 = hlfir.designate %4 (%arg2, %arg1)  :
+///           (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+///       %7 = fir.load %6 : !fir.ref<f32>
+///       %8 = hlfir.designate %5 (%arg2, %arg1)  :
+///           (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+///       hlfir.assign %7 to %8 : f32, !fir.ref<f32>
+///     }
+///   }
+///
+/// The transformation is correct only when LHS and RHS do not alias.
+/// This transformation does not support runtime checking for
+/// non-conforming LHS/RHS arrays' shapes currently.
+class VariableAssignBufferization
+    : public mlir::OpRewritePattern<hlfir::AssignOp> {
+private:
+public:
+  using mlir::OpRewritePattern<hlfir::AssignOp>::OpRewritePattern;
+
+  mlir::LogicalResult
+  matchAndRewrite(hlfir::AssignOp assign,
+                  mlir::PatternRewriter &rewriter) const override;
+};
+
+mlir::LogicalResult VariableAssignBufferization::matchAndRewrite(
+    hlfir::AssignOp assign, mlir::PatternRewriter &rewriter) const {
+  if (assign.isAllocatableAssignment())
+    return rewriter.notifyMatchFailure(assign, "AssignOp may imply allocation");
+
+  hlfir::Entity rhs{assign.getRhs()};
+  // TODO: ExprType check is here to avoid conflicts with
+  // ElementalAssignBufferization pattern. We need to combine
+  // these matchers into a single one that applies to AssignOp.
+  if (rhs.getType().isa<hlfir::ExprType>())
+    return rewriter.notifyMatchFailure(assign, "RHS is not in memory");
+
+  if (!rhs.isArray())
+    return rewriter.notifyMatchFailure(assign,
+                                       "AssignOp's RHS is not an array");
+
+  mlir::Type rhsEleTy = rhs.getFortranElementType();
+  if (!fir::isa_trivial(rhsEleTy))
+    return rewriter.notifyMatchFailure(
+        assign, "AssignOp's RHS data type is not trivial");
+
+  hlfir::Entity lhs{assign.getLhs()};
+  if (!lhs.isArray())
+    return rewriter.notifyMatchFailure(assign,
+                                       "AssignOp's LHS is not an array");
+
+  mlir::Type lhsEleTy = lhs.getFortranElementType();
+  if (!fir::isa_trivial(lhsEleTy))
+    return rewriter.notifyMatchFailure(
+        assign, "AssignOp's LHS data type is not trivial");
+
+  if (lhsEleTy != rhsEleTy)
+    return rewriter.notifyMatchFailure(assign,
+                                       "RHS/LHS element types mismatch");
+
+  fir::AliasAnalysis aliasAnalysis;
+  mlir::AliasResult aliasRes = aliasAnalysis.alias(lhs, rhs);
+  if (!aliasRes.isNo()) {
+    LLVM_DEBUG(llvm::dbgs() << "VariableAssignBufferization:\n"
+                            << "\tLHS: " << lhs << "\n"
+                            << "\tRHS: " << rhs << "\n"
+                            << "\tALIAS: " << aliasRes << "\n");
+    return rewriter.notifyMatchFailure(assign, "RHS/LHS may alias");
+  }
+
+  mlir::Location loc = assign->getLoc();
+  fir::FirOpBuilder builder(rewriter, assign.getOperation());
+  builder.setInsertionPoint(assign);
+  rhs = hlfir::derefPointersAndAllocatables(loc, builder, rhs);
+  lhs = hlfir::derefPointersAndAllocatables(loc, builder, lhs);
+  mlir::Value shape = hlfir::genShape(loc, builder, lhs);
+  llvm::SmallVector<mlir::Value> extents =
+      hlfir::getIndexExtents(loc, builder, shape);
+  hlfir::LoopNest loopNest =
+      hlfir::genLoopNest(loc, builder, extents, /*isUnordered=*/true);
+  builder.setInsertionPointToStart(loopNest.innerLoop.getBody());
+  auto rhsArrayElement =
+      hlfir::getElementAt(loc, builder, rhs, loopNest.oneBasedIndices);
+  rhsArrayElement = hlfir::loadTrivialScalar(loc, builder, rhsArrayElement);
+  auto lhsArrayElement =
+      hlfir::getElementAt(loc, builder, lhs, loopNest.oneBasedIndices);
+  builder.create<hlfir::AssignOp>(loc, rhsArrayElement, lhsArrayElement);
+  rewriter.eraseOp(assign);
+  return mlir::success();
+}
+
 class OptimizedBufferizationPass
     : public hlfir::impl::OptimizedBufferizationBase<
           OptimizedBufferizationPass> {
@@ -438,6 +534,7 @@
     // This requires small code reordering in ElementalAssignBufferization.
     patterns.insert<ElementalAssignBufferization>(context);
     patterns.insert<BroadcastAssignBufferization>(context);
+    patterns.insert<VariableAssignBufferization>(context);
 
     if (mlir::failed(mlir::applyPatternsAndFoldGreedily(
             func, std::move(patterns), config))) {
diff --git a/flang/test/HLFIR/opt-bufferization.fir b/flang/test/HLFIR/opt-bufferization.fir
--- a/flang/test/HLFIR/opt-bufferization.fir
+++ b/flang/test/HLFIR/opt-bufferization.fir
@@ -251,7 +251,7 @@
 // CHECK:           %[[VAL_5B:.*]]:2 = hlfir.declare %[[ARG_1]](%[[VAL_4]]) {uniq_name = "array2"} : (!fir.ref<!fir.array<42xi32>>, !fir.shape<1>) -> (!fir.ref<!fir.array<42xi32>>, !fir.ref<!fir.array<42xi32>>)
 // CHECK:           %[[VAL_6:.*]] = hlfir.elemental %[[VAL_4]] unordered : (!fir.shape<1>) -> !hlfir.expr<42xi32> {
 // CHECK:           ^bb0(%[[VAL_7:.*]]: index):
-// CHECK:             hlfir.assign %[[VAL_5B]]#0 to %[[VAL_5]]#0 : !fir.ref<!fir.array<42xi32>>, !fir.ref<!fir.array<42xi32>>
+// CHECK:             hlfir.assign
 // CHECK:             %[[VAL_8:.*]] = hlfir.designate %[[VAL_5]]#0 (%[[VAL_7]])  : (!fir.ref<!fir.array<42xi32>>, index) -> !fir.ref<i32>
 // CHECK:             %[[VAL_9:.*]] = fir.load %[[VAL_8]] : !fir.ref<i32>
 // CHECK:             %[[VAL_10:.*]] = arith.subi %[[VAL_9]], %[[VAL_1]] : i32
diff --git a/flang/test/HLFIR/opt-variable-assign.fir b/flang/test/HLFIR/opt-variable-assign.fir
new file mode 100644
--- /dev/null
+++ b/flang/test/HLFIR/opt-variable-assign.fir
@@ -0,0 +1,308 @@
+// Test optimized bufferization for hlfir.assign of arrays
+// variables:
+// RUN: fir-opt --opt-bufferization %s | FileCheck %s
+
+// The two assigns come from the following source forms:
+//   y(:,:) = x(:,:)
+//   y = x
+func.func @_QPtest1(%arg0: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "x"}) {
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %0 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %1:2 = hlfir.declare %arg0(%0) {uniq_name = "_QFtest1Ex"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %2 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest1Ey"}
+  %3:2 = hlfir.declare %2(%0) {uniq_name = "_QFtest1Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4 = hlfir.designate %1#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %0 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  %5 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %0 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  hlfir.assign %4 to %5 : !fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>
+  hlfir.assign %1#0 to %3#0 : !fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest1(
+// CHECK-SAME:                        %[[VAL_0:.*]]: !fir.ref<!fir.array<3x3xf32>> {fir.bindc_name = "x"}) {
+// CHECK:           %[[VAL_1:.*]] = arith.constant 1 : index
+// CHECK:           %[[VAL_2:.*]] = arith.constant 3 : index
+// CHECK:           %[[VAL_3:.*]] = fir.shape %[[VAL_2]], %[[VAL_2]] : (index, index) -> !fir.shape<2>
+// CHECK:           %[[VAL_4:.*]]:2 = hlfir.declare %[[VAL_0]](%[[VAL_3]]) {uniq_name = "_QFtest1Ex"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+// CHECK:           %[[VAL_5:.*]] = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest1Ey"}
+// CHECK:           %[[VAL_6:.*]]:2 = hlfir.declare %[[VAL_5]](%[[VAL_3]]) {uniq_name = "_QFtest1Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+// CHECK:           %[[VAL_7:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_1]]:%[[VAL_2]]:%[[VAL_1]], %[[VAL_1]]:%[[VAL_2]]:%[[VAL_1]])  shape %[[VAL_3]] : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+// CHECK:           %[[VAL_8:.*]] = hlfir.designate %[[VAL_6]]#0 (%[[VAL_1]]:%[[VAL_2]]:%[[VAL_1]], %[[VAL_1]]:%[[VAL_2]]:%[[VAL_1]])  shape %[[VAL_3]] : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+// CHECK:           fir.do_loop %[[VAL_9:.*]] = %[[VAL_1]] to %[[VAL_2]] step %[[VAL_1]] unordered {
+// CHECK:             fir.do_loop %[[VAL_10:.*]] = %[[VAL_1]] to %[[VAL_2]] step %[[VAL_1]] unordered {
+// CHECK:               %[[VAL_11:.*]] = hlfir.designate %[[VAL_7]] (%[[VAL_10]], %[[VAL_9]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_12:.*]] = fir.load %[[VAL_11]] : !fir.ref<f32>
+// CHECK:               %[[VAL_13:.*]] = hlfir.designate %[[VAL_8]] (%[[VAL_10]], %[[VAL_9]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_12]] to %[[VAL_13]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           fir.do_loop %[[VAL_14:.*]] = %[[VAL_1]] to %[[VAL_2]] step %[[VAL_1]] unordered {
+// CHECK:             fir.do_loop %[[VAL_15:.*]] = %[[VAL_1]] to %[[VAL_2]] step %[[VAL_1]] unordered {
+// CHECK:               %[[VAL_16:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_15]], %[[VAL_14]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_17:.*]] = fir.load %[[VAL_16]] : !fir.ref<f32>
+// CHECK:               %[[VAL_18:.*]] = hlfir.designate %[[VAL_6]]#0 (%[[VAL_15]], %[[VAL_14]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_17]] to %[[VAL_18]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           return
+// CHECK:         }
+
+
+func.func @_QPtest2(%arg0: !fir.box<!fir.array<?x?xf32>> {fir.bindc_name = "x"}) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {uniq_name = "_QFtest2Ex"} : (!fir.box<!fir.array<?x?xf32>>) -> (!fir.box<!fir.array<?x?xf32>>, !fir.box<!fir.array<?x?xf32>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest2Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest2Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4:3 = fir.box_dims %0#1, %c0 : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+  %5:3 = fir.box_dims %0#1, %c1 : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+  %6 = arith.cmpi sgt, %4#1, %c0 : index
+  %7 = arith.select %6, %4#1, %c0 : index
+  %8 = arith.cmpi sgt, %5#1, %c0 : index
+  %9 = arith.select %8, %5#1, %c0 : index
+  %10 = fir.shape %7, %9 : (index, index) -> !fir.shape<2>
+  %11 = hlfir.designate %0#0 (%c1:%4#1:%c1, %c1:%5#1:%c1)  shape %10 : (!fir.box<!fir.array<?x?xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+  %12 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %2 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  hlfir.assign %11 to %12 : !fir.box<!fir.array<?x?xf32>>, !fir.ref<!fir.array<3x3xf32>>
+  hlfir.assign %0#0 to %3#0 : !fir.box<!fir.array<?x?xf32>>, !fir.ref<!fir.array<3x3xf32>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest2(
+// CHECK-SAME:                        %[[VAL_0:.*]]: !fir.box<!fir.array<?x?xf32>> {fir.bindc_name = "x"}) {
+// CHECK:           %[[VAL_1:.*]] = arith.constant 0 : index
+// CHECK:           %[[VAL_2:.*]] = arith.constant 1 : index
+// CHECK:           %[[VAL_3:.*]] = arith.constant 3 : index
+// CHECK:           %[[VAL_4:.*]]:2 = hlfir.declare %[[VAL_0]] {uniq_name = "_QFtest2Ex"} : (!fir.box<!fir.array<?x?xf32>>) -> (!fir.box<!fir.array<?x?xf32>>, !fir.box<!fir.array<?x?xf32>>)
+// CHECK:           %[[VAL_5:.*]] = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest2Ey"}
+// CHECK:           %[[VAL_6:.*]] = fir.shape %[[VAL_3]], %[[VAL_3]] : (index, index) -> !fir.shape<2>
+// CHECK:           %[[VAL_7:.*]]:2 = hlfir.declare %[[VAL_5]](%[[VAL_6]]) {uniq_name = "_QFtest2Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+// CHECK:           %[[VAL_8:.*]]:3 = fir.box_dims %[[VAL_4]]#1, %[[VAL_1]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           %[[VAL_9:.*]]:3 = fir.box_dims %[[VAL_4]]#1, %[[VAL_2]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           %[[VAL_10:.*]] = arith.cmpi sgt, %[[VAL_8]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_11:.*]] = arith.select %[[VAL_10]], %[[VAL_8]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_12:.*]] = arith.cmpi sgt, %[[VAL_9]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_13:.*]] = arith.select %[[VAL_12]], %[[VAL_9]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_14:.*]] = fir.shape %[[VAL_11]], %[[VAL_13]] : (index, index) -> !fir.shape<2>
+// CHECK:           %[[VAL_15:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_2]]:%[[VAL_8]]#1:%[[VAL_2]], %[[VAL_2]]:%[[VAL_9]]#1:%[[VAL_2]])  shape %[[VAL_14]] : (!fir.box<!fir.array<?x?xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+// CHECK:           %[[VAL_16:.*]] = hlfir.designate %[[VAL_7]]#0 (%[[VAL_2]]:%[[VAL_3]]:%[[VAL_2]], %[[VAL_2]]:%[[VAL_3]]:%[[VAL_2]])  shape %[[VAL_6]] : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+// CHECK:           fir.do_loop %[[VAL_17:.*]] = %[[VAL_2]] to %[[VAL_3]] step %[[VAL_2]] unordered {
+// CHECK:             fir.do_loop %[[VAL_18:.*]] = %[[VAL_2]] to %[[VAL_3]] step %[[VAL_2]] unordered {
+// CHECK:               %[[VAL_19:.*]] = hlfir.designate %[[VAL_15]] (%[[VAL_18]], %[[VAL_17]])  : (!fir.box<!fir.array<?x?xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_20:.*]] = fir.load %[[VAL_19]] : !fir.ref<f32>
+// CHECK:               %[[VAL_21:.*]] = hlfir.designate %[[VAL_16]] (%[[VAL_18]], %[[VAL_17]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_20]] to %[[VAL_21]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           fir.do_loop %[[VAL_22:.*]] = %[[VAL_2]] to %[[VAL_3]] step %[[VAL_2]] unordered {
+// CHECK:             fir.do_loop %[[VAL_23:.*]] = %[[VAL_2]] to %[[VAL_3]] step %[[VAL_2]] unordered {
+// CHECK:               %[[VAL_24:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_23]], %[[VAL_22]])  : (!fir.box<!fir.array<?x?xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_25:.*]] = fir.load %[[VAL_24]] : !fir.ref<f32>
+// CHECK:               %[[VAL_26:.*]] = hlfir.designate %[[VAL_7]]#0 (%[[VAL_23]], %[[VAL_22]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_25]] to %[[VAL_26]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           return
+// CHECK:         }
+
+
+func.func @_QPtest3(%arg0: !fir.box<!fir.array<?x?xf32>> {fir.bindc_name = "x"}) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {uniq_name = "_QFtest3Ex"} : (!fir.box<!fir.array<?x?xf32>>) -> (!fir.box<!fir.array<?x?xf32>>, !fir.box<!fir.array<?x?xf32>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest3Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest3Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %2 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  %5:3 = fir.box_dims %0#1, %c0 : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+  %6:3 = fir.box_dims %0#1, %c1 : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+  %7 = arith.cmpi sgt, %5#1, %c0 : index
+  %8 = arith.select %7, %5#1, %c0 : index
+  %9 = arith.cmpi sgt, %6#1, %c0 : index
+  %10 = arith.select %9, %6#1, %c0 : index
+  %11 = fir.shape %8, %10 : (index, index) -> !fir.shape<2>
+  %12 = hlfir.designate %0#0 (%c1:%5#1:%c1, %c1:%6#1:%c1)  shape %11 : (!fir.box<!fir.array<?x?xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+  hlfir.assign %4 to %12 : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>
+  hlfir.assign %3#0 to %0#0 : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest3(
+// CHECK-SAME:                        %[[VAL_0:.*]]: !fir.box<!fir.array<?x?xf32>> {fir.bindc_name = "x"}) {
+// CHECK:           %[[VAL_1:.*]] = arith.constant 0 : index
+// CHECK:           %[[VAL_2:.*]] = arith.constant 1 : index
+// CHECK:           %[[VAL_3:.*]] = arith.constant 3 : index
+// CHECK:           %[[VAL_4:.*]]:2 = hlfir.declare %[[VAL_0]] {uniq_name = "_QFtest3Ex"} : (!fir.box<!fir.array<?x?xf32>>) -> (!fir.box<!fir.array<?x?xf32>>, !fir.box<!fir.array<?x?xf32>>)
+// CHECK:           %[[VAL_5:.*]] = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest3Ey"}
+// CHECK:           %[[VAL_6:.*]] = fir.shape %[[VAL_3]], %[[VAL_3]] : (index, index) -> !fir.shape<2>
+// CHECK:           %[[VAL_7:.*]]:2 = hlfir.declare %[[VAL_5]](%[[VAL_6]]) {uniq_name = "_QFtest3Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+// CHECK:           %[[VAL_8:.*]] = hlfir.designate %[[VAL_7]]#0 (%[[VAL_2]]:%[[VAL_3]]:%[[VAL_2]], %[[VAL_2]]:%[[VAL_3]]:%[[VAL_2]])  shape %[[VAL_6]] : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+// CHECK:           %[[VAL_9:.*]]:3 = fir.box_dims %[[VAL_4]]#1, %[[VAL_1]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           %[[VAL_10:.*]]:3 = fir.box_dims %[[VAL_4]]#1, %[[VAL_2]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           %[[VAL_11:.*]] = arith.cmpi sgt, %[[VAL_9]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_12:.*]] = arith.select %[[VAL_11]], %[[VAL_9]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_13:.*]] = arith.cmpi sgt, %[[VAL_10]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_14:.*]] = arith.select %[[VAL_13]], %[[VAL_10]]#1, %[[VAL_1]] : index
+// CHECK:           %[[VAL_15:.*]] = fir.shape %[[VAL_12]], %[[VAL_14]] : (index, index) -> !fir.shape<2>
+// CHECK:           %[[VAL_16:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_2]]:%[[VAL_9]]#1:%[[VAL_2]], %[[VAL_2]]:%[[VAL_10]]#1:%[[VAL_2]])  shape %[[VAL_15]] : (!fir.box<!fir.array<?x?xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+// CHECK:           fir.do_loop %[[VAL_17:.*]] = %[[VAL_2]] to %[[VAL_14]] step %[[VAL_2]] unordered {
+// CHECK:             fir.do_loop %[[VAL_18:.*]] = %[[VAL_2]] to %[[VAL_12]] step %[[VAL_2]] unordered {
+// CHECK:               %[[VAL_19:.*]] = hlfir.designate %[[VAL_8]] (%[[VAL_18]], %[[VAL_17]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_20:.*]] = fir.load %[[VAL_19]] : !fir.ref<f32>
+// CHECK:               %[[VAL_21:.*]] = hlfir.designate %[[VAL_16]] (%[[VAL_18]], %[[VAL_17]])  : (!fir.box<!fir.array<?x?xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_20]] to %[[VAL_21]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           %[[VAL_22:.*]]:3 = fir.box_dims %[[VAL_4]]#0, %[[VAL_1]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           %[[VAL_23:.*]]:3 = fir.box_dims %[[VAL_4]]#0, %[[VAL_2]] : (!fir.box<!fir.array<?x?xf32>>, index) -> (index, index, index)
+// CHECK:           fir.do_loop %[[VAL_24:.*]] = %[[VAL_2]] to %[[VAL_23]]#1 step %[[VAL_2]] unordered {
+// CHECK:             fir.do_loop %[[VAL_25:.*]] = %[[VAL_2]] to %[[VAL_22]]#1 step %[[VAL_2]] unordered {
+// CHECK:               %[[VAL_26:.*]] = hlfir.designate %[[VAL_7]]#0 (%[[VAL_25]], %[[VAL_24]])  : (!fir.ref<!fir.array<3x3xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               %[[VAL_27:.*]] = fir.load %[[VAL_26]] : !fir.ref<f32>
+// CHECK:               %[[VAL_28:.*]] = hlfir.designate %[[VAL_4]]#0 (%[[VAL_25]], %[[VAL_24]])  : (!fir.box<!fir.array<?x?xf32>>, index, index) -> !fir.ref<f32>
+// CHECK:               hlfir.assign %[[VAL_27]] to %[[VAL_28]] : f32, !fir.ref<f32>
+// CHECK:             }
+// CHECK:           }
+// CHECK:           return
+// CHECK:         }
+
+
+// The LHS is a whole allocatable, so the assignment may imply
+// allocation. This is not currently supported.
+func.func @_QPtest4(%arg0: !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>> {fir.bindc_name = "x"}) {
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {fortran_attrs = #fir.var_attrs<allocatable>, uniq_name = "_QFtest4Ex"} : (!fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>) -> (!fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>, !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest4Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest4Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  hlfir.assign %3#0 to %0#0 realloc : !fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest4(
+// CHECK-NOT:       hlfir.assign
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} realloc : !fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>
+// CHECK-NOT:       hlfir.assign
+
+
+// TODO: LHS is a pointer, but RHS is a subroutine local,
+// so they cannot alias.
+func.func @_QPtest5(%arg0: !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>> {fir.bindc_name = "x"}) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {fortran_attrs = #fir.var_attrs<pointer>, uniq_name = "_QFtest5Ex"} : (!fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>) -> (!fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>, !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest5Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest5Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %2 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  %5 = fir.load %0#0 : !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>
+  %6:3 = fir.box_dims %5, %c0 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %7:3 = fir.box_dims %5, %c1 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %8 = arith.addi %6#0, %6#1 : index
+  %9 = arith.subi %8, %c1 : index
+  %10 = arith.addi %7#0, %7#1 : index
+  %11 = arith.subi %10, %c1 : index
+  %12 = arith.subi %9, %6#0 : index
+  %13 = arith.addi %12, %c1 : index
+  %14 = arith.cmpi sgt, %13, %c0 : index
+  %15 = arith.select %14, %13, %c0 : index
+  %16 = arith.subi %11, %7#0 : index
+  %17 = arith.addi %16, %c1 : index
+  %18 = arith.cmpi sgt, %17, %c0 : index
+  %19 = arith.select %18, %17, %c0 : index
+  %20 = fir.shape %15, %19 : (index, index) -> !fir.shape<2>
+  %21 = hlfir.designate %5 (%6#0:%9:%c1, %7#0:%11:%c1)  shape %20 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+  hlfir.assign %4 to %21 : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>
+  %22 = fir.load %0#0 : !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>
+  hlfir.assign %3#0 to %22 : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.ptr<!fir.array<?x?xf32>>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest5(
+// CHECK-NOT:       hlfir.assign
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>
+// CHECK-NOT:       hlfir.assign
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.ptr<!fir.array<?x?xf32>>>
+// CHECK-NOT:       hlfir.assign
+
+
+// TODO: RHS is a pointer, but LHS is a subroutine local,
+// so they cannot alias.
+func.func @_QPtest6(%arg0: !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>> {fir.bindc_name = "x"}) {
+  %c1 = arith.constant 1 : index
+  %c0 = arith.constant 0 : index
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {fortran_attrs = #fir.var_attrs<pointer>, uniq_name = "_QFtest6Ex"} : (!fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>) -> (!fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>, !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest6Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest6Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4 = fir.load %0#0 : !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>
+  %5:3 = fir.box_dims %4, %c0 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %6:3 = fir.box_dims %4, %c1 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %7 = arith.addi %5#0, %5#1 : index
+  %8 = arith.subi %7, %c1 : index
+  %9 = arith.addi %6#0, %6#1 : index
+  %10 = arith.subi %9, %c1 : index
+  %11 = arith.subi %8, %5#0 : index
+  %12 = arith.addi %11, %c1 : index
+  %13 = arith.cmpi sgt, %12, %c0 : index
+  %14 = arith.select %13, %12, %c0 : index
+  %15 = arith.subi %10, %6#0 : index
+  %16 = arith.addi %15, %c1 : index
+  %17 = arith.cmpi sgt, %16, %c0 : index
+  %18 = arith.select %17, %16, %c0 : index
+  %19 = fir.shape %14, %18 : (index, index) -> !fir.shape<2>
+  %20 = hlfir.designate %4 (%5#0:%8:%c1, %6#0:%10:%c1)  shape %19 : (!fir.box<!fir.ptr<!fir.array<?x?xf32>>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+  %21 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %2 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  hlfir.assign %20 to %21 : !fir.box<!fir.array<?x?xf32>>, !fir.ref<!fir.array<3x3xf32>>
+  %22 = fir.load %0#0 : !fir.ref<!fir.box<!fir.ptr<!fir.array<?x?xf32>>>>
+  hlfir.assign %22 to %3#0 : !fir.box<!fir.ptr<!fir.array<?x?xf32>>>, !fir.ref<!fir.array<3x3xf32>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest6(
+// CHECK-NOT:       hlfir.assign
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} : !fir.box<!fir.array<?x?xf32>>, !fir.ref<!fir.array<3x3xf32>>
+// CHECK-NOT:       hlfir.assign
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} : !fir.box<!fir.ptr<!fir.array<?x?xf32>>>, !fir.ref<!fir.array<3x3xf32>>
+// CHECK-NOT:       hlfir.assign
+
+
+// TODO: LHS and RHS do not alias, and the assignment cannot
+// allocate/reallocate LHS, so we should be able to optimize.
+// The box load blocks alias analysis.
+// subroutine test7(x)
+//   real, allocatable :: x(:,:)
+//   real :: y(3,3)
+//   x(:,:) = y(:,:)
+// end subroutine test7
+func.func @_QPtest7(%arg0: !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>> {fir.bindc_name = "x"}) {
+  %c0 = arith.constant 0 : index
+  %c1 = arith.constant 1 : index
+  %c3 = arith.constant 3 : index
+  %0:2 = hlfir.declare %arg0 {fortran_attrs = #fir.var_attrs<allocatable>, uniq_name = "_QFtest7Ex"} : (!fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>) -> (!fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>, !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>)
+  %1 = fir.alloca !fir.array<3x3xf32> {bindc_name = "y", uniq_name = "_QFtest7Ey"}
+  %2 = fir.shape %c3, %c3 : (index, index) -> !fir.shape<2>
+  %3:2 = hlfir.declare %1(%2) {uniq_name = "_QFtest7Ey"} : (!fir.ref<!fir.array<3x3xf32>>, !fir.shape<2>) -> (!fir.ref<!fir.array<3x3xf32>>, !fir.ref<!fir.array<3x3xf32>>)
+  %4 = hlfir.designate %3#0 (%c1:%c3:%c1, %c1:%c3:%c1)  shape %2 : (!fir.ref<!fir.array<3x3xf32>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.ref<!fir.array<3x3xf32>>
+  %5 = fir.load %0#0 : !fir.ref<!fir.box<!fir.heap<!fir.array<?x?xf32>>>>
+  %6:3 = fir.box_dims %5, %c0 : (!fir.box<!fir.heap<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %7:3 = fir.box_dims %5, %c1 : (!fir.box<!fir.heap<!fir.array<?x?xf32>>>, index) -> (index, index, index)
+  %8 = arith.addi %6#0, %6#1 : index
+  %9 = arith.subi %8, %c1 : index
+  %10 = arith.addi %7#0, %7#1 : index
+  %11 = arith.subi %10, %c1 : index
+  %12 = arith.subi %9, %6#0 : index
+  %13 = arith.addi %12, %c1 : index
+  %14 = arith.cmpi sgt, %13, %c0 : index
+  %15 = arith.select %14, %13, %c0 : index
+  %16 = arith.subi %11, %7#0 : index
+  %17 = arith.addi %16, %c1 : index
+  %18 = arith.cmpi sgt, %17, %c0 : index
+  %19 = arith.select %18, %17, %c0 : index
+  %20 = fir.shape %15, %19 : (index, index) -> !fir.shape<2>
+  %21 = hlfir.designate %5 (%6#0:%9:%c1, %7#0:%11:%c1)  shape %20 : (!fir.box<!fir.heap<!fir.array<?x?xf32>>>, index, index, index, index, index, index, !fir.shape<2>) -> !fir.box<!fir.array<?x?xf32>>
+  hlfir.assign %4 to %21 : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>
+  return
+}
+// CHECK-LABEL:   func.func @_QPtest7(
+// CHECK:           hlfir.assign %{{.*}} to %{{.*}} : !fir.ref<!fir.array<3x3xf32>>, !fir.box<!fir.array<?x?xf32>>