diff --git a/mlir/include/mlir/IR/AffineMap.h b/mlir/include/mlir/IR/AffineMap.h
--- a/mlir/include/mlir/IR/AffineMap.h
+++ b/mlir/include/mlir/IR/AffineMap.h
@@ -90,7 +90,7 @@
 
   MLIRContext *getContext() const;
 
-  explicit operator bool() { return map != nullptr; }
+  explicit operator bool() const { return map != nullptr; }
   bool operator==(AffineMap other) const { return other.map == map; }
   bool operator!=(AffineMap other) const { return !(other.map == map); }
 
@@ -220,31 +220,31 @@
   ///   map2: `(d0)[s0] -> (d0 + s0, d0 - s0)`
   ///   map1.compose(map2):
   ///     `(d0)[s0, s1, s2] -> (d0 + s1 + s2 + 1, d0 - s0 - s2 - 1)`
-  AffineMap compose(AffineMap map);
+  AffineMap compose(AffineMap map) const;
 
   /// Applies composition by the dims of `this` to the integer `values` and
   /// returns the resulting values. `this` must be symbol-less.
-  SmallVector<int64_t, 4> compose(ArrayRef<int64_t> values);
+  SmallVector<int64_t, 4> compose(ArrayRef<int64_t> values) const;
 
   /// Returns true if the AffineMap represents a subset (i.e. a projection) of a
   /// symbol-less permutation map.
-  bool isProjectedPermutation();
+  bool isProjectedPermutation() const;
 
   /// Returns true if the AffineMap represents a symbol-less permutation map.
-  bool isPermutation();
+  bool isPermutation() const;
 
   /// Returns the map consisting of the `resultPos` subset.
-  AffineMap getSubMap(ArrayRef<unsigned> resultPos);
+  AffineMap getSubMap(ArrayRef<unsigned> resultPos) const;
 
   /// Returns the map consisting of the most major `numResults` results.
   /// Returns the null AffineMap if `numResults` == 0.
   /// Returns `*this` if `numResults` >= `this->getNumResults()`.
-  AffineMap getMajorSubMap(unsigned numResults);
+  AffineMap getMajorSubMap(unsigned numResults) const;
 
   /// Returns the map consisting of the most minor `numResults` results.
   /// Returns the null AffineMap if `numResults` == 0.
   /// Returns `*this` if `numResults` >= `this->getNumResults()`.
-  AffineMap getMinorSubMap(unsigned numResults);
+  AffineMap getMinorSubMap(unsigned numResults) const;
 
   friend ::llvm::hash_code hash_value(AffineMap arg);
 
diff --git a/mlir/lib/IR/AffineMap.cpp b/mlir/lib/IR/AffineMap.cpp
--- a/mlir/lib/IR/AffineMap.cpp
+++ b/mlir/lib/IR/AffineMap.cpp
@@ -334,7 +334,7 @@
   return AffineMap::get(numResultDims, numResultSyms, newResults, getContext());
 }
 
-AffineMap AffineMap::compose(AffineMap map) {
+AffineMap AffineMap::compose(AffineMap map) const {
   assert(getNumDims() == map.getNumResults() && "Number of results mismatch");
   // Prepare `map` by concatenating the symbols and rewriting its exprs.
   unsigned numDims = map.getNumDims();
@@ -358,7 +358,7 @@
   return AffineMap::get(numDims, numSymbols, exprs, map.getContext());
 }
 
-SmallVector<int64_t, 4> AffineMap::compose(ArrayRef<int64_t> values) {
+SmallVector<int64_t, 4> AffineMap::compose(ArrayRef<int64_t> values) const {
   assert(getNumSymbols() == 0 && "Expected symbol-less map");
   SmallVector<AffineExpr, 4> exprs;
   exprs.reserve(values.size());
@@ -373,7 +373,7 @@
   return res;
 }
 
-bool AffineMap::isProjectedPermutation() {
+bool AffineMap::isProjectedPermutation() const {
   if (getNumSymbols() > 0)
     return false;
   SmallVector<bool, 8> seen(getNumInputs(), false);
@@ -389,13 +389,13 @@
   return true;
 }
 
-bool AffineMap::isPermutation() {
+bool AffineMap::isPermutation() const {
   if (getNumDims() != getNumResults())
     return false;
   return isProjectedPermutation();
 }
 
-AffineMap AffineMap::getSubMap(ArrayRef<unsigned> resultPos) {
+AffineMap AffineMap::getSubMap(ArrayRef<unsigned> resultPos) const {
   SmallVector<AffineExpr, 4> exprs;
   exprs.reserve(resultPos.size());
   for (auto idx : resultPos)
@@ -403,7 +403,7 @@
   return AffineMap::get(getNumDims(), getNumSymbols(), exprs, getContext());
 }
 
-AffineMap AffineMap::getMajorSubMap(unsigned numResults) {
+AffineMap AffineMap::getMajorSubMap(unsigned numResults) const {
   if (numResults == 0)
     return AffineMap();
   if (numResults > getNumResults())
@@ -411,7 +411,7 @@
   return getSubMap(llvm::to_vector<4>(llvm::seq<unsigned>(0, numResults)));
 }
 
-AffineMap AffineMap::getMinorSubMap(unsigned numResults) {
+AffineMap AffineMap::getMinorSubMap(unsigned numResults) const {
   if (numResults == 0)
     return AffineMap();
   if (numResults > getNumResults())