diff --git a/src/Nullability/NullableChecker.php b/src/Nullability/NullableChecker.php
index 94de481..a757977 100644
--- a/src/Nullability/NullableChecker.php
+++ b/src/Nullability/NullableChecker.php
@@ -121,11 +121,6 @@ public function visitClassString(Type\ClassStringType $type): mixed
         return false;
     }
 
-    public function visitCallableString(Type\CallableStringType $type): mixed
-    {
-        return false;
-    }
-
     public function visitInterfaceString(Type\InterfaceStringType $type): mixed
     {
         return false;
@@ -191,11 +186,6 @@ public function visitNonEmptyArray(Type\NonEmptyArrayType $type): mixed
         return false;
     }
 
-    public function visitCallableArray(Type\CallableArrayType $type): mixed
-    {
-        return false;
-    }
-
     public function visitArray(Type\ArrayType $type): mixed
     {
         return false;
diff --git a/src/PhpDocParser/ContextualPhpDocTypeReflector.php b/src/PhpDocParser/ContextualPhpDocTypeReflector.php
index fdd8ecb..b8a7133 100644
--- a/src/PhpDocParser/ContextualPhpDocTypeReflector.php
+++ b/src/PhpDocParser/ContextualPhpDocTypeReflector.php
@@ -165,11 +165,20 @@ private function reflectIdentifier(string $name, array $genericTypes = []): Type
             'array-key' => types::arrayKey,
             'literal-int' => types::literalInt,
             'literal-string' => types::literalString,
-            'callable-string' => types::callableString,
+            'callable-string' => types::intersection(
+                types::literalString,
+                types::callable(),
+            ),
             'interface-string' => types::interfaceString,
             'enum-string' => types::enumString,
             'trait-string' => types::traitString,
-            'callable-array' => types::callableArray,
+            'callable-array' => types::intersection(
+                types::arrayShape([
+                    types::union(types::classString, types::object),
+                    types::literalString,
+                ]),
+                types::callable(),
+            ),
             'resource' => types::resource,
             'closed-resource' => types::closedResource,
             'object' => types::object,
diff --git a/src/TypeResolver/RecursiveTypeReplacer.php b/src/TypeResolver/RecursiveTypeReplacer.php
index f897a79..284d24b 100644
--- a/src/TypeResolver/RecursiveTypeReplacer.php
+++ b/src/TypeResolver/RecursiveTypeReplacer.php
@@ -116,11 +116,6 @@ public function visitClassString(Type\ClassStringType $type): mixed
         return $type;
     }
 
-    public function visitCallableString(Type\CallableStringType $type): mixed
-    {
-        return $type;
-    }
-
     public function visitInterfaceString(Type\InterfaceStringType $type): mixed
     {
         return $type;
@@ -198,11 +193,6 @@ public function visitNonEmptyArray(Type\NonEmptyArrayType $type): mixed
         return types::nonEmptyArray($type->keyType->accept($this), $type->valueType->accept($this));
     }
 
-    public function visitCallableArray(Type\CallableArrayType $type): mixed
-    {
-        return $type;
-    }
-
     public function visitArray(Type\ArrayType $type): mixed
     {
         /** @psalm-suppress MixedArgumentTypeCoercion */
diff --git a/tests/unit/PhpDocParser/ContextualPhpDocTypeReflectorTest.php b/tests/unit/PhpDocParser/ContextualPhpDocTypeReflectorTest.php
index e067f40..5b9440d 100644
--- a/tests/unit/PhpDocParser/ContextualPhpDocTypeReflectorTest.php
+++ b/tests/unit/PhpDocParser/ContextualPhpDocTypeReflectorTest.php
@@ -71,7 +71,10 @@ public static function validTypes(): \Generator
         yield ['literal-string', types::literalString];
         yield ['numeric-string', types::numericString];
         yield ['class-string', types::classString];
-        yield ['callable-string', types::callableString];
+        yield ['callable-string', types::intersection(
+            types::literalString,
+            types::callable(),
+        )];
         yield ['interface-string', types::interfaceString];
         yield ['enum-string', types::enumString];
         yield ['trait-string', types::traitString];
@@ -81,7 +84,13 @@ public static function validTypes(): \Generator
         yield ['string', types::string];
         yield ['numeric', types::numeric];
         yield ['scalar', types::scalar];
-        yield ['callable-array', types::callableArray];
+        yield ['callable-array', types::intersection(
+            types::arrayShape([
+                types::union(types::classString, types::object),
+                types::literalString,
+            ]),
+            types::callable(),
+        )];
         yield ['object', types::object];
         yield ['resource', types::resource];
         yield ['closed-resource', types::closedResource];