diff --git a/mlir/lib/Parser/AffineParser.cpp b/mlir/lib/Parser/AffineParser.cpp
--- a/mlir/lib/Parser/AffineParser.cpp
+++ b/mlir/lib/Parser/AffineParser.cpp
@@ -265,17 +265,25 @@
   return (-1) * operand;
 }
 
+/// Returns true if the given token can be represented as an identifier.
+static bool isIdentifier(const Token &token) {
+  // We include only `inttype` and `bare_identifier` here since they are the
+  // only non-keyword tokens that can be used to represent an identifier.
+  return token.isAny(Token::bare_identifier, Token::inttype) ||
+         token.isKeyword();
+}
+
 /// Parse a bare id that may appear in an affine expression.
 ///
 ///   affine-expr ::= bare-id
 AffineExpr AffineParser::parseBareIdExpr() {
-  if (getToken().isNot(Token::bare_identifier))
+  if (!isIdentifier(getToken()))
     return emitWrongTokenError("expected bare identifier"), nullptr;
 
   StringRef sRef = getTokenSpelling();
   for (auto entry : dimsAndSymbols) {
     if (entry.first == sRef) {
-      consumeToken(Token::bare_identifier);
+      consumeToken();
       return entry.second;
     }
   }
@@ -342,8 +350,6 @@
 //  -l are valid operands that will be parsed by this function.
 AffineExpr AffineParser::parseAffineOperandExpr(AffineExpr lhs) {
   switch (getToken().getKind()) {
-  case Token::bare_identifier:
-    return parseBareIdExpr();
   case Token::kw_symbol:
     return parseSymbolSSAIdExpr();
   case Token::percent_identifier:
@@ -357,6 +363,8 @@
   case Token::kw_ceildiv:
   case Token::kw_floordiv:
   case Token::kw_mod:
+    // Try to treat these tokens as identifiers.
+    return parseBareIdExpr();
   case Token::plus:
   case Token::star:
     if (lhs)
@@ -365,6 +373,10 @@
       emitError("missing left operand of binary operator");
     return nullptr;
   default:
+    // If nothing matches, we try to treat this token as an identifier.
+    if (isIdentifier(getToken()))
+      return parseBareIdExpr();
+
     if (lhs)
       emitError("missing right operand of binary operator");
     else
@@ -458,7 +470,7 @@
 /// expressions of the affine map. Update our state to store the
 /// dimensional/symbolic identifier.
 ParseResult AffineParser::parseIdentifierDefinition(AffineExpr idExpr) {
-  if (getToken().isNot(Token::bare_identifier))
+  if (!isIdentifier(getToken()))
     return emitWrongTokenError("expected bare identifier");
 
   auto name = getTokenSpelling();
@@ -466,7 +478,7 @@
     if (entry.first == name)
       return emitError("redefinition of identifier '" + name + "'");
   }
-  consumeToken(Token::bare_identifier);
+  consumeToken();
 
   dimsAndSymbols.push_back({name, idExpr});
   return success();
diff --git a/mlir/test/IR/affine-map.mlir b/mlir/test/IR/affine-map.mlir
--- a/mlir/test/IR/affine-map.mlir
+++ b/mlir/test/IR/affine-map.mlir
@@ -192,6 +192,25 @@
 // CHECK: #map{{[0-9]+}} = affine_map<(d0, d1) -> (d0 mod 5, (d1 mod 35) mod 4)>
 #map59 = affine_map<(d0, d1) -> ((d0 mod 35) mod 5, (d1 mod 35) mod 4)>
 
+// Check if parser can parse affine_map with identifiers that collide with
+// integer types.
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1) -> (d0, d1)>
+#map60 = affine_map<(i0, i1) -> (i0, i1)>
+
+// Check if parser can parse affine_map with identifiers that collide with
+// reserved keywords.
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1)[s0, s1] -> (-d0 + s0, -d1 + s1)>
+#map61 = affine_map<(d0, d1)[step, loc] -> (step - d0, loc - d1)>
+
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1)[s0, s1] -> (-d0 + s0 floordiv 2, -d1 + s1 mod 3)>
+#map62 = affine_map<(d0, d1)[mod, floordiv] -> (mod floordiv 2 - d0, floordiv mod 3 - d1)>
+
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1)[s0, s1] -> (-d0 + s1 floordiv 2, -d1 + s0 mod 3)>
+#map63 = affine_map<(d0, d1)[mod, floordiv] -> (floordiv floordiv 2 - d0, mod mod 3 - d1)>
+
+// CHECK: #map{{[0-9]+}} = affine_map<(d0, d1)[s0] -> (d0 + d1 + s0)>
+#map64 = affine_map<(i0, i1)[mod] -> (i0 + i1 + mod)>
+
 // Single identity maps are removed.
 // CHECK: @f0(memref<2x4xi8, 1>)
 func.func private @f0(memref<2x4xi8, #map0, 1>)
@@ -379,3 +398,18 @@
 
 // CHECK: "f59"() {map = #map{{[0-9]+}}} : () -> ()
 "f59"() {map = #map59} : () -> ()
+
+// CHECK: "f60"() {map = #map{{[0-9]+}}} : () -> ()
+"f60"() {map = #map60} : () -> ()
+
+// CHECK: "f61"() {map = #map{{[0-9]+}}} : () -> ()
+"f61"() {map = #map61} : () -> ()
+
+// CHECK: "f62"() {map = #map{{[0-9]+}}} : () -> ()
+"f62"() {map = #map62} : () -> ()
+
+// CHECK: "f63"() {map = #map{{[0-9]+}}} : () -> ()
+"f63"() {map = #map63} : () -> ()
+
+// CHECK: "f64"() {map = #map{{[0-9]+}}} : () -> ()
+"f64"() {map = #map64} : () -> ()
diff --git a/mlir/test/IR/invalid-affinemap.mlir b/mlir/test/IR/invalid-affinemap.mlir
--- a/mlir/test/IR/invalid-affinemap.mlir
+++ b/mlir/test/IR/invalid-affinemap.mlir
@@ -54,13 +54,13 @@
 #hello_world = affine_map<(i, j) [s0, s1] -> (i, *j)> // expected-error {{missing left operand of binary op}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (floordiv i 2, j)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (floordiv i 2, j)> // expected-error {{use of undeclared identifier}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (ceildiv i 2, j)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (ceildiv i 2, j)> // expected-error {{use of undeclared identifier}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (mod i 2, j)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (mod i 2, j)> // expected-error {{use of undeclared identifier}}
 
 // -----
 #hello_world = affine_map<(i, j) [s0, s1] -> (-(), j)>
@@ -71,13 +71,13 @@
 #hello_world = affine_map<(i, j) [s0, s1] -> (i, *j+5)> // expected-error {{missing left operand of binary op}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (i, floordiv j+5)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (i, floordiv j+5)> // expected-error {{use of undeclared identifier}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (i, ceildiv j+5)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (i, ceildiv j+5)> // expected-error {{use of undeclared identifier}}
 
 // -----
-#hello_world = affine_map<(i, j) [s0, s1] -> (i, mod j+5)> // expected-error {{missing left operand of binary op}}
+#hello_world = affine_map<(i, j) [s0, s1] -> (i, mod j+5)> // expected-error {{use of undeclared identifier}}
 
 // -----
 #hello_world = affine_map<(i, j) [s0, s1] -> (i*j, j)> // expected-error {{non-affine expression: at least one of the multiply operands has to be either a constant or symbolic}}