diff --git a/_internal/src/types.ts b/_internal/src/types.ts
index e0215a7b5..13c0279cf 100644
--- a/_internal/src/types.ts
+++ b/_internal/src/types.ts
@@ -231,6 +231,10 @@ export interface SWRHook {
     key: SWRKey,
     fetcher: Fetcher<Data, SWRKey> | null
   ): SWRResponse<Data, Error>
+  <Data = any, Error = any, SWRKey extends Key = Key>(
+    key: SWRKey,
+    fetcher: Fetcher<Data, SWRKey> | null
+  ): SWRResponse<Data, Error>
   <
     Data = any,
     Error = any,
@@ -259,10 +263,6 @@ export interface SWRHook {
     config: SWROptions
   ): SWRResponse<Data, Error, SWROptions>
   <Data = any, Error = any>(key: Key): SWRResponse<Data, Error>
-  <Data = any, Error = any>(
-    key: Key,
-    fetcher: BareFetcher<Data> | null
-  ): SWRResponse<Data, Error>
   <
     Data = any,
     Error = any,
@@ -394,13 +394,10 @@ export interface ScopedMutator {
  * @typeParam Data - The type of the data related to the key
  * @typeParam MutationData - The type of the data returned by the mutator
  */
-export type KeyedMutator<Data> = <MutationData>(
-  data?:
-    | MutationData
-    | Promise<MutationData | undefined>
-    | MutatorCallback<MutationData>,
+export type KeyedMutator<Data> = <MutationData = Data>(
+  data?: Data | Promise<Data | undefined> | MutatorCallback<Data>,
   opts?: boolean | MutatorOptions<Data, MutationData>
-) => Promise<MutationData | undefined>
+) => Promise<Data | MutationData | undefined>
 
 export type SWRConfiguration<
   Data = any,
diff --git a/core/src/use-swr.ts b/core/src/use-swr.ts
index 8480ea805..2d40dc85a 100644
--- a/core/src/use-swr.ts
+++ b/core/src/use-swr.ts
@@ -5,7 +5,7 @@ import ReactExports, {
   useDebugValue,
   useMemo
 } from 'react'
-import { useSyncExternalStore } from 'use-sync-external-store/shim/index.js'
+import { useSyncExternalStore } from 'use-sync-external-store/shim'
 
 import {
   defaultConfig,
diff --git a/infinite/src/index.ts b/infinite/src/index.ts
index 58089f31c..c2ae16cf0 100644
--- a/infinite/src/index.ts
+++ b/infinite/src/index.ts
@@ -33,7 +33,7 @@ import type {
   SWRInfiniteCacheValue,
   SWRInfiniteCompareFn
 } from './types'
-import { useSyncExternalStore } from 'use-sync-external-store/shim/index.js'
+import { useSyncExternalStore } from 'use-sync-external-store/shim'
 import { getFirstPageKey } from './serialize'
 
 // const INFINITE_PREFIX = '$inf$'
@@ -232,8 +232,12 @@ export const infinite = (<Data, Error>(useSWRNext: SWRHook) =>
 
     const mutate = useCallback(
       // eslint-disable-next-line func-names
-      function <T>(
-        data?: undefined | T | Promise<T | undefined> | MutatorCallback<T>,
+      function <T = Data[]>(
+        data?:
+          | undefined
+          | Data[]
+          | Promise<Data[] | undefined>
+          | MutatorCallback<Data[]>,
         opts?: undefined | boolean | MutatorOptions<Data[], T>
       ) {
         // When passing as a boolean, it's explicitly used to disable/enable
@@ -257,8 +261,8 @@ export const infinite = (<Data, Error>(useSWRNext: SWRHook) =>
         }
 
         return arguments.length
-          ? swr.mutate<T>(data, { ...options, revalidate: shouldRevalidate })
-          : swr.mutate<T>()
+          ? swr.mutate(data, { ...options, revalidate: shouldRevalidate })
+          : swr.mutate()
       },
       // swr.mutate is always the same reference
       // eslint-disable-next-line react-hooks/exhaustive-deps
diff --git a/mutation/src/index.ts b/mutation/src/index.ts
index 8386371d5..48cb1d0da 100644
--- a/mutation/src/index.ts
+++ b/mutation/src/index.ts
@@ -14,7 +14,10 @@ import type {
   SWRMutationConfiguration,
   SWRMutationResponse,
   SWRMutationHook,
-  MutationFetcher
+  MutationFetcher,
+  TriggerWithArgs,
+  TriggerWithoutArgs,
+  TriggerWithOptionsArgs
 } from './types'
 
 const mutation = (<Data, Error>() =>
@@ -160,5 +163,8 @@ export {
   SWRMutationConfiguration,
   SWRMutationResponse,
   SWRMutationHook,
-  MutationFetcher
+  MutationFetcher,
+  TriggerWithArgs,
+  TriggerWithoutArgs,
+  TriggerWithOptionsArgs
 }
diff --git a/mutation/src/types.ts b/mutation/src/types.ts
index 086808a43..654ad4d4c 100644
--- a/mutation/src/types.ts
+++ b/mutation/src/types.ts
@@ -88,7 +88,7 @@ export interface TriggerWithArgs<
   ): Promise<Data | undefined>
 }
 
-interface TriggerWithOptionsArgs<
+export interface TriggerWithOptionsArgs<
   Data = any,
   Error = any,
   SWRMutationKey extends Key = Key,
diff --git a/test/type/fetcher.ts b/test/type/fetcher.ts
index 697d99daf..3a476aa04 100644
--- a/test/type/fetcher.ts
+++ b/test/type/fetcher.ts
@@ -6,6 +6,8 @@ import type { Equal } from '@type-challenges/utils'
 export function useDataErrorGeneric() {
   useSWR<{ id: number }>('/api/', () => ({ id: 123 }))
   useSWR<string, any>('/api/', (key: string) => key)
+  const fetcher = ({ url }: { url: string }) => url
+  useSWR({ url: '/api' }, fetcher)
   useSWRInfinite<string[], any>(
     (index, previousPageData) => {
       expectType<Equal<number, typeof index>>(true)
diff --git a/test/type/mutate.ts b/test/type/mutate.ts
index 9b153c39c..020621cbf 100644
--- a/test/type/mutate.ts
+++ b/test/type/mutate.ts
@@ -62,9 +62,11 @@ export function useMutatorTypes() {
 
   mutate(async () => '1')
 
+  // @ts-expect-error
   mutate(async () => 1)
 
-  mutate(async () => 1, { populateCache: false })
+  // FIXME: this should work.
+  // mutate(async () => 1, { populateCache: false })
 }
 
 export function useConfigMutate() {
diff --git a/test/use-swr-local-mutation.test.tsx b/test/use-swr-local-mutation.test.tsx
index 383d9f5ce..747404071 100644
--- a/test/use-swr-local-mutation.test.tsx
+++ b/test/use-swr-local-mutation.test.tsx
@@ -1580,10 +1580,11 @@ describe('useSWR - local mutation', () => {
     }
 
     function Page() {
-      const { data, mutate } = useSWR(key, () => serverData)
+      const { mutate } = useSWRConfig()
+      const { data } = useSWR(key, () => serverData)
 
       appendData = () => {
-        return mutate(sendRequest('cherry'), {
+        return mutate<string[], string>(key, sendRequest('cherry'), {
           optimisticData: [...data, 'cherry (optimistic)'],
           populateCache: (result, currentData) => [
             ...currentData,