diff --git a/src/Illuminate/Auth/Access/HandlesAuthorization.php b/src/Illuminate/Auth/Access/HandlesAuthorization.php
index 3afa863e06d8..66e5786e38e8 100644
--- a/src/Illuminate/Auth/Access/HandlesAuthorization.php
+++ b/src/Illuminate/Auth/Access/HandlesAuthorization.php
@@ -19,7 +19,7 @@ protected function allow($message = null, $code = null)
     /**
      * Throws an unauthorized exception.
      *
-     * @param  string  $message
+     * @param  string|null  $message
      * @param  mixed|null  $code
      * @return \Illuminate\Auth\Access\Response
      */
diff --git a/src/Illuminate/Cookie/CookieJar.php b/src/Illuminate/Cookie/CookieJar.php
index 261f3567aee8..a880e898eb43 100755
--- a/src/Illuminate/Cookie/CookieJar.php
+++ b/src/Illuminate/Cookie/CookieJar.php
@@ -118,7 +118,7 @@ public function hasQueued($key, $path = null)
      *
      * @param  string  $key
      * @param  mixed  $default
-     * @param  string  $path
+     * @param  string|null  $path
      * @return \Symfony\Component\HttpFoundation\Cookie
      */
     public function queued($key, $default = null, $path = null)
diff --git a/src/Illuminate/Database/Concerns/BuildsQueries.php b/src/Illuminate/Database/Concerns/BuildsQueries.php
index e19995da0c00..a43b9befc1e1 100644
--- a/src/Illuminate/Database/Concerns/BuildsQueries.php
+++ b/src/Illuminate/Database/Concerns/BuildsQueries.php
@@ -117,8 +117,8 @@ public function chunkById($count, callable $callback, $column = null, $alias = n
      *
      * @param  callable  $callback
      * @param  int  $count
-     * @param  string  $column
-     * @param  string  $alias
+     * @param  string|null  $column
+     * @param  string|null  $alias
      * @return bool
      */
     public function eachById(callable $callback, $count = 1000, $column = null, $alias = null)
diff --git a/src/Illuminate/Database/Eloquent/Builder.php b/src/Illuminate/Database/Eloquent/Builder.php
index 7e2f57d8c4f2..00131c80054f 100755
--- a/src/Illuminate/Database/Eloquent/Builder.php
+++ b/src/Illuminate/Database/Eloquent/Builder.php
@@ -703,7 +703,7 @@ public function pluck($column, $key = null)
     /**
      * Paginate the given query.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int|null  $page
@@ -730,7 +730,7 @@ public function paginate($perPage = null, $columns = ['*'], $pageName = 'page',
     /**
      * Paginate the given query into a simple paginator.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int|null  $page
diff --git a/src/Illuminate/Database/Eloquent/Concerns/HasRelationships.php b/src/Illuminate/Database/Eloquent/Concerns/HasRelationships.php
index 3c5c928293fd..92c3758e15f9 100644
--- a/src/Illuminate/Database/Eloquent/Concerns/HasRelationships.php
+++ b/src/Illuminate/Database/Eloquent/Concerns/HasRelationships.php
@@ -48,8 +48,8 @@ trait HasRelationships
      * Define a one-to-one relationship.
      *
      * @param  string  $related
-     * @param  string  $foreignKey
-     * @param  string  $localKey
+     * @param  string|null  $foreignKey
+     * @param  string|null  $localKey
      * @return \Illuminate\Database\Eloquent\Relations\HasOne
      */
     public function hasOne($related, $foreignKey = null, $localKey = null)
@@ -125,9 +125,9 @@ protected function newHasOneThrough(Builder $query, Model $farParent, Model $thr
      *
      * @param  string  $related
      * @param  string  $name
-     * @param  string  $type
-     * @param  string  $id
-     * @param  string  $localKey
+     * @param  string|null  $type
+     * @param  string|null  $id
+     * @param  string|null  $localKey
      * @return \Illuminate\Database\Eloquent\Relations\MorphOne
      */
     public function morphOne($related, $name, $type = null, $id = null, $localKey = null)
@@ -162,9 +162,9 @@ protected function newMorphOne(Builder $query, Model $parent, $type, $id, $local
      * Define an inverse one-to-one or many relationship.
      *
      * @param  string  $related
-     * @param  string  $foreignKey
-     * @param  string  $ownerKey
-     * @param  string  $relation
+     * @param  string|null  $foreignKey
+     * @param  string|null  $ownerKey
+     * @param  string|null  $relation
      * @return \Illuminate\Database\Eloquent\Relations\BelongsTo
      */
     public function belongsTo($related, $foreignKey = null, $ownerKey = null, $relation = null)
@@ -213,10 +213,10 @@ protected function newBelongsTo(Builder $query, Model $child, $foreignKey, $owne
     /**
      * Define a polymorphic, inverse one-to-one or many relationship.
      *
-     * @param  string  $name
-     * @param  string  $type
-     * @param  string  $id
-     * @param  string  $ownerKey
+     * @param  string|null  $name
+     * @param  string|null  $type
+     * @param  string|null  $id
+     * @param  string|null  $ownerKey
      * @return \Illuminate\Database\Eloquent\Relations\MorphTo
      */
     public function morphTo($name = null, $type = null, $id = null, $ownerKey = null)
@@ -318,8 +318,8 @@ protected function guessBelongsToRelation()
      * Define a one-to-many relationship.
      *
      * @param  string  $related
-     * @param  string  $foreignKey
-     * @param  string  $localKey
+     * @param  string|null  $foreignKey
+     * @param  string|null  $localKey
      * @return \Illuminate\Database\Eloquent\Relations\HasMany
      */
     public function hasMany($related, $foreignKey = null, $localKey = null)
@@ -397,9 +397,9 @@ protected function newHasManyThrough(Builder $query, Model $farParent, Model $th
      *
      * @param  string  $related
      * @param  string  $name
-     * @param  string  $type
-     * @param  string  $id
-     * @param  string  $localKey
+     * @param  string|null  $type
+     * @param  string|null  $id
+     * @param  string|null  $localKey
      * @return \Illuminate\Database\Eloquent\Relations\MorphMany
      */
     public function morphMany($related, $name, $type = null, $id = null, $localKey = null)
@@ -437,12 +437,12 @@ protected function newMorphMany(Builder $query, Model $parent, $type, $id, $loca
      * Define a many-to-many relationship.
      *
      * @param  string  $related
-     * @param  string  $table
-     * @param  string  $foreignPivotKey
-     * @param  string  $relatedPivotKey
-     * @param  string  $parentKey
-     * @param  string  $relatedKey
-     * @param  string  $relation
+     * @param  string|null  $table
+     * @param  string|null  $foreignPivotKey
+     * @param  string|null  $relatedPivotKey
+     * @param  string|null  $parentKey
+     * @param  string|null  $relatedKey
+     * @param  string|null  $relation
      * @return \Illuminate\Database\Eloquent\Relations\BelongsToMany
      */
     public function belongsToMany($related, $table = null, $foreignPivotKey = null, $relatedPivotKey = null,
@@ -502,11 +502,11 @@ protected function newBelongsToMany(Builder $query, Model $parent, $table, $fore
      *
      * @param  string  $related
      * @param  string  $name
-     * @param  string  $table
-     * @param  string  $foreignPivotKey
-     * @param  string  $relatedPivotKey
-     * @param  string  $parentKey
-     * @param  string  $relatedKey
+     * @param  string|null  $table
+     * @param  string|null  $foreignPivotKey
+     * @param  string|null  $relatedPivotKey
+     * @param  string|null  $parentKey
+     * @param  string|null  $relatedKey
      * @param  bool  $inverse
      * @return \Illuminate\Database\Eloquent\Relations\MorphToMany
      */
@@ -554,7 +554,7 @@ public function morphToMany($related, $name, $table = null, $foreignPivotKey = n
      * @param  string  $relatedPivotKey
      * @param  string  $parentKey
      * @param  string  $relatedKey
-     * @param  string  $relationName
+     * @param  string|null  $relationName
      * @param  bool  $inverse
      * @return \Illuminate\Database\Eloquent\Relations\MorphToMany
      */
@@ -571,11 +571,11 @@ protected function newMorphToMany(Builder $query, Model $parent, $name, $table,
      *
      * @param  string  $related
      * @param  string  $name
-     * @param  string  $table
-     * @param  string  $foreignPivotKey
-     * @param  string  $relatedPivotKey
-     * @param  string  $parentKey
-     * @param  string  $relatedKey
+     * @param  string|null  $table
+     * @param  string|null  $foreignPivotKey
+     * @param  string|null  $relatedPivotKey
+     * @param  string|null  $parentKey
+     * @param  string|null  $relatedKey
      * @return \Illuminate\Database\Eloquent\Relations\MorphToMany
      */
     public function morphedByMany($related, $name, $table = null, $foreignPivotKey = null,
diff --git a/src/Illuminate/Database/Eloquent/Relations/BelongsToMany.php b/src/Illuminate/Database/Eloquent/Relations/BelongsToMany.php
index 7175d6953f36..cf8b902b6bea 100755
--- a/src/Illuminate/Database/Eloquent/Relations/BelongsToMany.php
+++ b/src/Illuminate/Database/Eloquent/Relations/BelongsToMany.php
@@ -344,7 +344,7 @@ public function as($accessor)
      * Set a where clause for a pivot table column.
      *
      * @param  string  $column
-     * @param  string  $operator
+     * @param  string|null  $operator
      * @param  mixed  $value
      * @param  string  $boolean
      * @return $this
@@ -376,7 +376,7 @@ public function wherePivotIn($column, $values, $boolean = 'and', $not = false)
      * Set an "or where" clause for a pivot table column.
      *
      * @param  string  $column
-     * @param  string  $operator
+     * @param  string|null  $operator
      * @param  mixed  $value
      * @return $this
      */
@@ -681,7 +681,7 @@ protected function aliasedPivotColumns()
     /**
      * Get a paginator for the "select" statement.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int|null  $page
@@ -699,7 +699,7 @@ public function paginate($perPage = null, $columns = ['*'], $pageName = 'page',
     /**
      * Paginate the given query into a simple paginator.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int|null  $page
diff --git a/src/Illuminate/Database/Eloquent/Relations/HasManyThrough.php b/src/Illuminate/Database/Eloquent/Relations/HasManyThrough.php
index df1c5ea332e4..1372f628da78 100644
--- a/src/Illuminate/Database/Eloquent/Relations/HasManyThrough.php
+++ b/src/Illuminate/Database/Eloquent/Relations/HasManyThrough.php
@@ -373,7 +373,7 @@ public function get($columns = ['*'])
     /**
      * Get a paginator for the "select" statement.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int  $page
@@ -389,7 +389,7 @@ public function paginate($perPage = null, $columns = ['*'], $pageName = 'page',
     /**
      * Paginate the given query into a simple paginator.
      *
-     * @param  int  $perPage
+     * @param  int|null  $perPage
      * @param  array  $columns
      * @param  string  $pageName
      * @param  int|null  $page
diff --git a/src/Illuminate/Database/Eloquent/Relations/MorphToMany.php b/src/Illuminate/Database/Eloquent/Relations/MorphToMany.php
index a7bcd1ead43b..e4f4c42b6c22 100644
--- a/src/Illuminate/Database/Eloquent/Relations/MorphToMany.php
+++ b/src/Illuminate/Database/Eloquent/Relations/MorphToMany.php
@@ -42,7 +42,7 @@ class MorphToMany extends BelongsToMany
      * @param  string  $relatedPivotKey
      * @param  string  $parentKey
      * @param  string  $relatedKey
-     * @param  string  $relationName
+     * @param  string|null  $relationName
      * @param  bool  $inverse
      * @return void
      */
diff --git a/src/Illuminate/Foundation/helpers.php b/src/Illuminate/Foundation/helpers.php
index f9337f2f4007..36fc1b5728ff 100644
--- a/src/Illuminate/Foundation/helpers.php
+++ b/src/Illuminate/Foundation/helpers.php
@@ -918,7 +918,7 @@ function __($key = null, $replace = [], $locale = null)
     /**
      * Generate a url for the application.
      *
-     * @param  string  $path
+     * @param  string|null  $path
      * @param  mixed  $parameters
      * @param  bool|null  $secure
      * @return \Illuminate\Contracts\Routing\UrlGenerator|string
diff --git a/src/Illuminate/Support/Facades/Cookie.php b/src/Illuminate/Support/Facades/Cookie.php
index ad0be149e9d7..245ed1ec71b3 100755
--- a/src/Illuminate/Support/Facades/Cookie.php
+++ b/src/Illuminate/Support/Facades/Cookie.php
@@ -25,7 +25,7 @@ public static function has($key)
     /**
      * Retrieve a cookie from the request.
      *
-     * @param  string  $key
+     * @param  string|null  $key
      * @param  mixed  $default
      * @return string|array|null
      */
diff --git a/src/Illuminate/Support/MessageBag.php b/src/Illuminate/Support/MessageBag.php
index 4931595fb56b..1fb862a59408 100755
--- a/src/Illuminate/Support/MessageBag.php
+++ b/src/Illuminate/Support/MessageBag.php
@@ -150,8 +150,8 @@ public function hasAny($keys = [])
     /**
      * Get the first message from the message bag for a given key.
      *
-     * @param  string  $key
-     * @param  string  $format
+     * @param  string|null  $key
+     * @param  string|null  $format
      * @return string
      */
     public function first($key = null, $format = null)
diff --git a/src/Illuminate/Support/ServiceProvider.php b/src/Illuminate/Support/ServiceProvider.php
index 5a0077e83f7c..983940bdc875 100755
--- a/src/Illuminate/Support/ServiceProvider.php
+++ b/src/Illuminate/Support/ServiceProvider.php
@@ -227,8 +227,8 @@ protected function addPublishGroup($group, $paths)
     /**
      * Get the paths to publish.
      *
-     * @param  string  $provider
-     * @param  string  $group
+     * @param  string|null  $provider
+     * @param  string|null  $group
      * @return array
      */
     public static function pathsToPublish($provider = null, $group = null)
diff --git a/src/Illuminate/Support/Str.php b/src/Illuminate/Support/Str.php
index 9c9ed49113a7..7f2ddebfd15f 100644
--- a/src/Illuminate/Support/Str.php
+++ b/src/Illuminate/Support/Str.php
@@ -281,7 +281,7 @@ public static function kebab($value)
      * Return the length of the given string.
      *
      * @param  string  $value
-     * @param  string  $encoding
+     * @param  string|null  $encoding
      * @return int
      */
     public static function length($value, $encoding = null)
diff --git a/src/Illuminate/Support/Traits/EnumeratesValues.php b/src/Illuminate/Support/Traits/EnumeratesValues.php
index d24a9fe906eb..ea7934ee2e80 100644
--- a/src/Illuminate/Support/Traits/EnumeratesValues.php
+++ b/src/Illuminate/Support/Traits/EnumeratesValues.php
@@ -825,7 +825,7 @@ protected function getArrayableItems($items)
      * Get an operator checker callback.
      *
      * @param  string  $key
-     * @param  string  $operator
+     * @param  string|string  $operator
      * @param  mixed  $value
      * @return \Closure
      */