diff --git a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
--- a/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
+++ b/mlir/lib/Dialect/StandardOps/IR/Ops.cpp
@@ -426,6 +426,9 @@
   /// and(x, 0) -> 0
   if (matchPattern(rhs(), m_Zero()))
     return rhs();
+  /// and(x, 1) -> x
+  if (matchPattern(rhs(), m_One()))
+    return lhs();
   /// and(x,x) -> x
   if (lhs() == rhs())
     return rhs();
@@ -2245,6 +2248,9 @@
   // subi(x,x) -> 0
   if (getOperand(0) == getOperand(1))
     return Builder(getContext()).getZeroAttr(getType());
+  // subi(x,0) -> x
+  if (matchPattern(rhs(), m_Zero()))
+    return lhs();
 
   return constFoldBinaryOp<IntegerAttr>(operands,
                                         [](APInt a, APInt b) { return a - b; });
diff --git a/mlir/test/Transforms/constant-fold.mlir b/mlir/test/Transforms/constant-fold.mlir
--- a/mlir/test/Transforms/constant-fold.mlir
+++ b/mlir/test/Transforms/constant-fold.mlir
@@ -92,6 +92,16 @@
 
 // -----
 
+// CHECK: func @simple_and([[ARG0:%[a-zA-Z0-9]+]]: i1)
+func @simple_and(%arg0 : i1) -> i1 {
+  %0 = constant 1 : i1
+  %1 = and %arg0, %0 : i1
+  // CHECK: return [[ARG0]]
+  return %1 : i1
+}
+
+// -----
+
 // CHECK-LABEL: func @addi_splat_vector
 func @addi_splat_vector() -> vector<8xi32> {
   %0 = constant dense<1> : vector<8xi32>
@@ -134,16 +144,19 @@
 
 // -----
 
-// CHECK-LABEL: func @simple_subi
-func @simple_subi() -> i32 {
+//      CHECK: func @simple_subi
+// CHECK-SAME:   [[ARG0:%[a-zA-Z0-9]+]]
+func @simple_subi(%arg0 : i32) -> (i32, i32) {
   %0 = constant 4 : i32
   %1 = constant 1 : i32
+  %2 = constant 0 : i32
 
   // CHECK-NEXT:[[C3:%.+]] = constant 3 : i32
-  %2 = subi %0, %1 : i32
+  %3 = subi %0, %1 : i32
+  %4 = subi %arg0, %2 : i32
 
-  // CHECK-NEXT: return [[C3]]
-  return %2 : i32
+  // CHECK-NEXT: return [[C3]], [[ARG0]]
+  return %3, %4 : i32, i32
 }
 
 // -----