diff --git a/src/Analyser/ExprHandler/Helper/ImplicitToStringCallHelper.php b/src/Analyser/ExprHandler/Helper/ImplicitToStringCallHelper.php
index 1b66bc7ba38..e7177fb9b4c 100644
--- a/src/Analyser/ExprHandler/Helper/ImplicitToStringCallHelper.php
+++ b/src/Analyser/ExprHandler/Helper/ImplicitToStringCallHelper.php
@@ -28,6 +28,15 @@ public function processImplicitToStringCall(Expr $expr, MutatingScope $scope): E
 		$impurePoints = [];
 
 		$exprType = $scope->getType($expr);
+		if ($exprType->isObject()->no()) {
+			return new ExpressionResult(
+				$scope,
+				hasYield: false,
+				isAlwaysTerminating: false,
+				throwPoints: [],
+				impurePoints: [],
+			);
+		}
 		$toStringMethod = $scope->getMethodReflection($exprType, '__toString');
 		if ($toStringMethod === null) {
 			return new ExpressionResult(
diff --git a/src/Type/TypeCombinator.php b/src/Type/TypeCombinator.php
index 901c78de7ee..990e6b57263 100644
--- a/src/Type/TypeCombinator.php
+++ b/src/Type/TypeCombinator.php
@@ -1399,6 +1399,52 @@ public static function intersect(Type ...$types): Type
 					continue;
 				}
 
+				if (
+					$types[$j] instanceof TemplateMixedType
+					&& !$types[$i] instanceof TemplateType
+					&& $types[$i]->isScalar()->yes()
+					&& !$types[$i]->isConstantScalarValue()->yes()
+					&& $types[$j]->getBound()->isSuperTypeOf($types[$i])->yes()
+				) {
+					$narrowed = TemplateTypeFactory::create(
+						$types[$j]->getScope(),
+						$types[$j]->getName(),
+						$types[$i],
+						$types[$j]->getVariance(),
+						$types[$j]->getStrategy(),
+						$types[$j]->getDefault(),
+					);
+					if (!$narrowed instanceof TemplateMixedType) {
+						$types[$j] = $narrowed;
+						array_splice($types, $i--, 1);
+						$typesCount--;
+						continue 2;
+					}
+				}
+
+				if (
+					$types[$i] instanceof TemplateMixedType
+					&& !$types[$j] instanceof TemplateType
+					&& $types[$j]->isScalar()->yes()
+					&& !$types[$j]->isConstantScalarValue()->yes()
+					&& $types[$i]->getBound()->isSuperTypeOf($types[$j])->yes()
+				) {
+					$narrowed = TemplateTypeFactory::create(
+						$types[$i]->getScope(),
+						$types[$i]->getName(),
+						$types[$j],
+						$types[$i]->getVariance(),
+						$types[$i]->getStrategy(),
+						$types[$i]->getDefault(),
+					);
+					if (!$narrowed instanceof TemplateMixedType) {
+						$types[$i] = $narrowed;
+						array_splice($types, $j--, 1);
+						$typesCount--;
+						continue;
+					}
+				}
+
 				if ($types[$i] instanceof IterableType) {
 					$isSuperTypeB = $types[$i]->isSuperTypeOfMixed($types[$j]);
 				} else {
diff --git a/tests/PHPStan/Analyser/nsrt/bug-4498.php b/tests/PHPStan/Analyser/nsrt/bug-4498.php
index ad07baa3db4..68e652b159a 100644
--- a/tests/PHPStan/Analyser/nsrt/bug-4498.php
+++ b/tests/PHPStan/Analyser/nsrt/bug-4498.php
@@ -38,7 +38,7 @@ public function fcn(iterable $iterable): iterable
 	public function bar(iterable $iterable): iterable
 	{
 		if (is_array($iterable)) {
-			assertType('array<((int&TKey (method Bug4498\Foo::bar(), argument))|(string&TKey (method Bug4498\Foo::bar(), argument))), TValue (method Bug4498\Foo::bar(), argument)>', $iterable);
+			assertType('array<(TKey of int (method Bug4498\Foo::bar(), argument)|TKey of string (method Bug4498\Foo::bar(), argument)), TValue (method Bug4498\Foo::bar(), argument)>', $iterable);
 			return $iterable;
 		}
 
diff --git a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
index a202c8e271d..e086b2ea02b 100644
--- a/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
+++ b/tests/PHPStan/Rules/Functions/CallToFunctionParametersRuleTest.php
@@ -725,11 +725,11 @@ public function testArrayUdiffCallback(): void
 				14,
 			],
 			[
-				'Parameter #1 $arr1 of function array_udiff expects array<(int&TK)|(string&TK), string>, null given.',
+				'Parameter #1 $arr1 of function array_udiff expects array<(TK of int)|TK of string, string>, null given.',
 				20,
 			],
 			[
-				'Parameter #2 $arr2 of function array_udiff expects array<(int&TK)|(string&TK), string>, null given.',
+				'Parameter #2 $arr2 of function array_udiff expects array<(TK of int)|TK of string, string>, null given.',
 				21,
 			],
 			[
diff --git a/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php b/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
index 9fa246f5552..8e172d035a0 100644
--- a/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
+++ b/tests/PHPStan/Rules/Pure/PureFunctionRuleTest.php
@@ -214,4 +214,9 @@ public function testBug14504(): void
 		$this->analyse([__DIR__ . '/data/bug-14504.php'], []);
 	}
 
+	public function testBug14511(): void
+	{
+		$this->analyse([__DIR__ . '/data/bug-14511.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php b/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
index 2b896c17b10..88bb38c5d40 100644
--- a/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
+++ b/tests/PHPStan/Rules/Pure/PureMethodRuleTest.php
@@ -383,4 +383,10 @@ public function testBug14504(): void
 		$this->analyse([__DIR__ . '/data/bug-14504-method.php'], []);
 	}
 
+	public function testBug14511(): void
+	{
+		$this->treatPhpDocTypesAsCertain = true;
+		$this->analyse([__DIR__ . '/data/bug-14511-method.php'], []);
+	}
+
 }
diff --git a/tests/PHPStan/Rules/Pure/data/bug-14511-method.php b/tests/PHPStan/Rules/Pure/data/bug-14511-method.php
new file mode 100644
index 00000000000..5b8b15030a5
--- /dev/null
+++ b/tests/PHPStan/Rules/Pure/data/bug-14511-method.php
@@ -0,0 +1,47 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14511Method;
+
+class Foo
+{
+
+	/**
+	 * @phpstan-pure
+	 * @template T of mixed
+	 * @param T $val
+	 */
+	public function testStringCast(mixed $val): ?string
+	{
+		if (is_int($val)) {
+			return (string) $val;
+		}
+		return null;
+	}
+
+	/**
+	 * @phpstan-pure
+	 * @template T of mixed
+	 * @param T $val
+	 */
+	public function testStringConcat(mixed $val): ?string
+	{
+		if (is_int($val)) {
+			return 'value: ' . $val;
+		}
+		return null;
+	}
+
+	/**
+	 * @phpstan-pure
+	 * @template T of mixed
+	 * @param T $val
+	 */
+	public function testEmptyNonArray(mixed $val): ?string
+	{
+		if (empty($val) && !\is_array($val)) {
+			return (string) $val;
+		}
+		return null;
+	}
+
+}
diff --git a/tests/PHPStan/Rules/Pure/data/bug-14511.php b/tests/PHPStan/Rules/Pure/data/bug-14511.php
new file mode 100644
index 00000000000..72569f7799a
--- /dev/null
+++ b/tests/PHPStan/Rules/Pure/data/bug-14511.php
@@ -0,0 +1,75 @@
+<?php declare(strict_types = 1);
+
+namespace Bug14511;
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testStringCast(mixed $val): ?string {
+	if (is_int($val)) {
+		return (string) $val;
+	}
+	return null;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testStringConcat(mixed $val): ?string {
+	if (is_int($val)) {
+		return 'value: ' . $val;
+	}
+	return null;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testFloatCast(mixed $val): ?string {
+	if (is_float($val)) {
+		return (string) $val;
+	}
+	return null;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testBoolCast(mixed $val): ?string {
+	if (is_bool($val)) {
+		return (string) $val;
+	}
+	return null;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testStringVal(mixed $val): ?string {
+	if (is_string($val)) {
+		return (string) $val;
+	}
+	return null;
+}
+
+/**
+ * @phpstan-pure
+ * @template T of mixed
+ * @param T $val
+ */
+function testEmptyNonArray(mixed $val): ?string {
+	if (empty($val) && !\is_array($val)) {
+		return (string) $val;
+	}
+	return null;
+}