diff --git a/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.h b/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.h
--- a/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.h
+++ b/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.h
@@ -105,10 +105,14 @@
   // TODO(wrengr): Most if not all of these don't actually need to be
   // methods, they could be free-functions instead.
   //
+  Var castAnyVar() const;
+  std::optional<Var> dyn_castAnyVar() const;
   SymVar castSymVar() const;
+  std::optional<SymVar> dyn_castSymVar() const;
   Var castDimLvlVar() const;
+  std::optional<Var> dyn_castDimLvlVar() const;
   int64_t castConstantValue() const;
-  std::optional<int64_t> tryGetConstantValue() const;
+  std::optional<int64_t> dyn_castConstantValue() const;
   bool hasConstantValue(int64_t val) const;
   DimLvlExpr getLHS() const;
   DimLvlExpr getRHS() const;
@@ -155,6 +159,12 @@
     return expr->getExprKind() == Kind;
   }
   constexpr explicit DimExpr(AffineExpr expr) : DimLvlExpr(Kind, expr) {}
+
+  LvlVar castLvlVar() const { return castDimLvlVar().cast<LvlVar>(); }
+  std::optional<LvlVar> dyn_castLvlVar() const {
+    const auto var = dyn_castDimLvlVar();
+    return var ? std::make_optional(var->cast<LvlVar>()) : std::nullopt;
+  }
 };
 static_assert(IsZeroCostAbstraction<DimExpr>);
 
@@ -169,6 +179,12 @@
     return expr->getExprKind() == Kind;
   }
   constexpr explicit LvlExpr(AffineExpr expr) : DimLvlExpr(Kind, expr) {}
+
+  DimVar castDimVar() const { return castDimLvlVar().cast<DimVar>(); }
+  std::optional<DimVar> dyn_castDimVar() const {
+    const auto var = dyn_castDimLvlVar();
+    return var ? std::make_optional(var->cast<DimVar>()) : std::nullopt;
+  }
 };
 static_assert(IsZeroCostAbstraction<LvlExpr>);
 
diff --git a/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.cpp b/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.cpp
--- a/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.cpp
+++ b/mlir/lib/Dialect/SparseTensor/IR/Detail/DimLvlMap.cpp
@@ -16,19 +16,46 @@
 // `DimLvlExpr` implementation.
 //===----------------------------------------------------------------------===//
 
+Var DimLvlExpr::castAnyVar() const {
+  assert(expr && "uninitialized DimLvlExpr");
+  const auto var = dyn_castAnyVar();
+  assert(var && "expected DimLvlExpr to be a Var");
+  return *var;
+}
+
+std::optional<Var> DimLvlExpr::dyn_castAnyVar() const {
+  if (const auto s = expr.dyn_cast_or_null<AffineSymbolExpr>())
+    return SymVar(s);
+  if (const auto x = expr.dyn_cast_or_null<AffineDimExpr>())
+    return Var(getAllowedVarKind(), x);
+  return std::nullopt;
+}
+
 SymVar DimLvlExpr::castSymVar() const {
   return SymVar(expr.cast<AffineSymbolExpr>());
 }
 
+std::optional<SymVar> DimLvlExpr::dyn_castSymVar() const {
+  if (const auto s = expr.dyn_cast_or_null<AffineSymbolExpr>())
+    return SymVar(s);
+  return std::nullopt;
+}
+
 Var DimLvlExpr::castDimLvlVar() const {
   return Var(getAllowedVarKind(), expr.cast<AffineDimExpr>());
 }
 
+std::optional<Var> DimLvlExpr::dyn_castDimLvlVar() const {
+  if (const auto x = expr.dyn_cast_or_null<AffineDimExpr>())
+    return Var(getAllowedVarKind(), x);
+  return std::nullopt;
+}
+
 int64_t DimLvlExpr::castConstantValue() const {
   return expr.cast<AffineConstantExpr>().getValue();
 }
 
-std::optional<int64_t> DimLvlExpr::tryGetConstantValue() const {
+std::optional<int64_t> DimLvlExpr::dyn_castConstantValue() const {
   const auto k = expr.dyn_cast_or_null<AffineConstantExpr>();
   return k ? std::make_optional(k.getValue()) : std::nullopt;
 }
@@ -98,7 +125,7 @@
       return MatchNeg{DimLvlExpr{expr.getExprKind(), AffineExpr()}, val};
   }
   if (op == AffineExprKind::Mul)
-    if (const auto rval = rhs.tryGetConstantValue(); rval && *rval < 0)
+    if (const auto rval = rhs.dyn_castConstantValue(); rval && *rval < 0)
       return MatchNeg{lhs, *rval};
   return std::nullopt;
 }