diff --git a/lib/tokenize.cpp b/lib/tokenize.cpp
index 14e5831ad..8dd6c585e 100644
--- a/lib/tokenize.cpp
+++ b/lib/tokenize.cpp
@@ -695,6 +695,15 @@ namespace {
                     mRangeAfterVar.second = mEndToken;
                     return;
                 }
+                if (Token::Match(type, "%name% (") && Token::simpleMatch(type->linkAt(1), ") ;") && !type->isStandardType()) {
+                    mNameToken = type;
+                    mEndToken = type->linkAt(1)->next();
+                    mRangeType.first = start;
+                    mRangeType.second = type;
+                    mRangeAfterVar.first = mNameToken->next();
+                    mRangeAfterVar.second = mEndToken;
+                    return;
+                }
             }
             // TODO: handle all typedefs
             if ((false))
@@ -710,6 +719,15 @@ namespace {
             return mUsed;
         }
 
+        bool isInvalidConstFunctionType(const std::map<std::string, TypedefSimplifier>& m) const {
+            if (!Token::Match(mTypedefToken, "typedef const %name% %name% ;"))
+                return false;
+            const auto it = m.find(mTypedefToken->strAt(2));
+            if (it == m.end())
+                return false;
+            return Token::Match(it->second.mNameToken, "%name% (");
+        }
+
         bool fail() const {
             return mFail;
         }
@@ -823,6 +841,15 @@ namespace {
             Token *after = tok3;
             while (Token::Match(after, "%name%|*|&|&&|::"))
                 after = after->next();
+            if (Token::Match(mNameToken, "%name% (") && Token::simpleMatch(tok3->next(), "*")) {
+                while (Token::Match(after, "(|["))
+                    after = after->link()->next();
+                if (after) {
+                    tok3->insertToken("(");
+                    after->previous()->insertToken(")");
+                    Token::createMutualLinks(tok3->next(), after->previous());
+                }
+            }
 
             bool useAfterVarRange = true;
             if (Token::simpleMatch(mRangeAfterVar.first, "[")) {
@@ -920,6 +947,8 @@ namespace {
                 return true;
             if (Token::Match(tok->previous(), "; %name% ;"))
                 return false;
+            if (Token::Match(tok->previous(), "<|, %name% * ,|>"))
+                return true;
             for (const Token* after = tok->next(); after; after = after->next()) {
                 if (Token::Match(after, "%name%|::|&|*|&&"))
                     continue;
@@ -1014,6 +1043,9 @@ void Tokenizer::simplifyTypedef()
         if (indentlevel == 0 && tok->str() == "typedef") {
             TypedefSimplifier ts(tok, typeNum);
             if (!ts.fail() && numberOfTypedefs[ts.name()] == 1) {
+                if (mSettings->severity.isEnabled(Severity::portability) && ts.isInvalidConstFunctionType(typedefs))
+                    reportError(tok->next(), Severity::portability, "invalidConstFunctionType",
+                                "It is unspecified behavior to const qualify a function type.");
                 typedefs.emplace(ts.name(), ts);
                 if (!ts.isStructEtc())
                     tok = ts.endToken();
diff --git a/test/testsimplifytypedef.cpp b/test/testsimplifytypedef.cpp
index 6a7fc9a91..52f3ca5c4 100644
--- a/test/testsimplifytypedef.cpp
+++ b/test/testsimplifytypedef.cpp
@@ -42,7 +42,7 @@ public:
 private:
     // If there are unused templates, keep those
     const Settings settings0 = settingsBuilder().severity(Severity::style).checkUnusedTemplates().build();
-    const Settings settings1 = settingsBuilder().checkUnusedTemplates().build();
+    const Settings settings1 = settingsBuilder().severity(Severity::portability).checkUnusedTemplates().build();
     const Settings settings2 = settingsBuilder().severity(Severity::style).checkUnusedTemplates().build();
 
     void run() override {
@@ -57,6 +57,9 @@ private:
         TEST_CASE(cstruct3);
         TEST_CASE(cstruct3);
         TEST_CASE(cstruct4);
+        TEST_CASE(cfunction1);
+        TEST_CASE(cfunction2);
+        TEST_CASE(cfunction3);
         TEST_CASE(cfp1);
         TEST_CASE(cfp2);
         TEST_CASE(cfp4);
@@ -382,6 +385,26 @@ private:
         ASSERT_EQUALS("struct s { int a ; int b ; } ; struct s x { } ;", simplifyTypedefC(code));
     }
 
+    void cfunction1() {
+        const char code[] = "typedef int callback(int);\n"
+                            "callback* cb;";
+        ASSERT_EQUALS("int ( * cb ) ( int ) ;", simplifyTypedefC(code));
+    }
+
+    void cfunction2() {
+        const char code[] = "typedef int callback(int);\n"
+                            "typedef callback* callbackPtr;\n"
+                            "callbackPtr cb;";
+        ASSERT_EQUALS("int ( * cb ) ( int ) ;", simplifyTypedefC(code));
+    }
+
+    void cfunction3() {
+        const char code[] = "typedef int f(int);\n"
+                            "typedef const f cf;\n";
+        simplifyTypedefC(code);
+        ASSERT_EQUALS("[file.c:2]: (portability) It is unspecified behavior to const qualify a function type.\n", errout.str());
+    }
+
     void cfp1() {
         const char code[] = "typedef void (*fp)(void * p);\n"
                             "fp x;";
@@ -3532,7 +3555,7 @@ private:
                                 "func7 f7;";
 
             // The expected result..
-            const char expected[] = "; C f1 ( ) ; "
+            const char expected[] = "C f1 ( ) ; "
                                     "C ( * f2 ) ( ) ; "
                                     "C ( & f3 ) ( ) ; "
                                     "C ( * f4 ) ( ) ; "
@@ -3561,7 +3584,7 @@ private:
 
             // The expected result..
             // C const -> const C
-            const char expected[] = "; const C f1 ( ) ; "
+            const char expected[] = "const C f1 ( ) ; "
                                     "const C ( * f2 ) ( ) ; "
                                     "const C ( & f3 ) ( ) ; "
                                     "const C ( * f4 ) ( ) ; "
@@ -3589,7 +3612,7 @@ private:
                                 "func7 f7;";
 
             // The expected result..
-            const char expected[] = "; const C f1 ( ) ; "
+            const char expected[] = "const C f1 ( ) ; "
                                     "const C ( * f2 ) ( ) ; "
                                     "const C ( & f3 ) ( ) ; "
                                     "const C ( * f4 ) ( ) ; "
@@ -3617,7 +3640,7 @@ private:
                                 "func7 f7;";
 
             // The expected result..
-            const char expected[] = "; C * f1 ( ) ; "
+            const char expected[] = "C * f1 ( ) ; "
                                     "C * ( * f2 ) ( ) ; "
                                     "C * ( & f3 ) ( ) ; "
                                     "C * ( * f4 ) ( ) ; "
@@ -3645,7 +3668,7 @@ private:
                                 "func7 f7;";
 
             // The expected result..
-            const char expected[] = "; const C * f1 ( ) ; "
+            const char expected[] = "const C * f1 ( ) ; "
                                     "const C * ( * f2 ) ( ) ; "
                                     "const C * ( & f3 ) ( ) ; "
                                     "const C * ( * f4 ) ( ) ; "
@@ -3674,7 +3697,7 @@ private:
 
             // The expected result..
             // C const -> const C
-            const char expected[] = "; const C * f1 ( ) ; "
+            const char expected[] = "const C * f1 ( ) ; "
                                     "const C * ( * f2 ) ( ) ; "
                                     "const C * ( & f3 ) ( ) ; "
                                     "const C * ( * f4 ) ( ) ; "
diff --git a/test/testtokenize.cpp b/test/testtokenize.cpp
index 488ba5549..1bf9ed682 100644
--- a/test/testtokenize.cpp
+++ b/test/testtokenize.cpp
@@ -3599,7 +3599,7 @@ private:
         ASSERT_EQUALS("unsigned int ( * f ) ( ) ;", tokenizeAndStringify("unsigned int (*f)();"));
         ASSERT_EQUALS("unsigned int * ( * f ) ( ) ;", tokenizeAndStringify("unsigned int * (*f)();"));
         ASSERT_EQUALS("void ( * f [ 2 ] ) ( ) ;", tokenizeAndStringify("void (*f[2])();"));
-        TODO_ASSERT_EQUALS("void ( * f [ 2 ] ) ( ) ;", "void ( * f ) ( void ) [ 2 ] ;", tokenizeAndStringify("typedef void func_t(void); func_t *f[2];"));
+        ASSERT_EQUALS("void ( * f [ 2 ] ) ( void ) ;", tokenizeAndStringify("typedef void func_t(void); func_t *f[2];"));
     }
 
     void simplifyFunctionPointers2() {