diff --git a/compiler/erg_compiler/codegen.rs b/compiler/erg_compiler/codegen.rs
index ef63c8b0..186a6138 100644
--- a/compiler/erg_compiler/codegen.rs
+++ b/compiler/erg_compiler/codegen.rs
@@ -301,6 +301,7 @@ fn convert_to_python_name(name: Str) -> Str {
     }
 }
 
+/// This method obviously does not scale, so in the future all Python APIs will be replaced by declarations in d.er, and renaming will be done in `HIRDesugarer`.
 fn escape_name(ident: Identifier) -> Str {
     let vis = ident.vis();
     let mut name = convert_to_python_name(ident.name.into_token().content).to_string();
diff --git a/compiler/erg_compiler/lib/std/_erg_std_prelude.d.er b/compiler/erg_compiler/lib/std/_erg_std_prelude.d.er
new file mode 100644
index 00000000..e69de29b
diff --git a/compiler/erg_compiler/lib/std/_prelude.er b/compiler/erg_compiler/lib/std/_prelude.er
index 0f8386ee..a64816b3 100644
--- a/compiler/erg_compiler/lib/std/_prelude.er
+++ b/compiler/erg_compiler/lib/std/_prelude.er
@@ -13,8 +13,8 @@ PartialOrd(R := Self) = Trait {
 }
 Ord = Subsume PartialOrd()
 
-EqForOrd R = Patch Ord, Impl := Eq()
-EqForOrd(R).
+EqForOrd R = Patch Ord
+EqForOrd(R)|<: Eq()|.
     `==`(self, other: R): Bool = self.cmp(other) == Ordering.Equal
 
 LeForOrd = Patch Ord
@@ -36,9 +36,9 @@ Add(R := Self) = Trait {
 }
 Sub(R := Self) = Trait {
     .Output = Type
-    .`_-_` = (self: Self, R) -> Self.Output
+    .`-` = (self: Self, R) -> Self.Output
 }
-Mul(R := Self()) = Trait {
+Mul(R := Self) = Trait {
     .Output = Type
     .`*` = (self: Self, R) -> Self.Output
 }
@@ -46,7 +46,6 @@ Div(R := Self) = Trait {
     .Output = Type
     .`/` = (self: Self, R) -> Self.Output or Panic
 }
-Num: (R := Type) -> Type
 Num = Add and Sub and Mul
 
 Seq T = Trait {
@@ -54,29 +53,40 @@ Seq T = Trait {
     .get = (self: Ref(Self), Nat) -> T
 }
 
-`_+_`: |R: Type, A <: Add(R)| (A, R) -> A.AddO
-`_-_`: |R: Type, S <: Add(R)| (S, R) -> S.SubO
-`*`: |R, O: Type, M <: Add(R)| (M, R) -> M.MulO
-`/`: |R, O: Type, D <: Add(R)| (D, R) -> D.DivO
-
-AddForInt = Patch Int, Impl := Add()
-AddForInt.AddO = Int
-AddForInt.
-    `_+_`: (self: Self, other: Int) -> Int = magic("Add.`_+_`")
+AddForInt = Patch Int
+AddForInt|<: Add(Int)|.
+    AddO = Int
+    `_+_`(self: Self, other: Int): Int = magic("Add.`_+_`")
 
 # TODO: Mul and Div
-NumForInterval M, N, O, P: Int =
-    Patch M..N, Impl := Add(R := O..P) and Sub(R := O..P)
-NumForInterval(M, N, O, P).
-    `_+_`: (self: Self, other: O..P) -> M+O..N+P = magic("NumForInterval.`_+_`")
-    `_-_`: (self: Self, other: O..P) -> M-P..N-O = magic("NumForInterval.`_-_`")
+NumForInterval M, N, O, P: Int = Patch M..N
+NumForInterval(M, N, O, P)|<: Add(O..P)|.
+    Output = M+O..N+P
+    __add__(self: Self, other: O..P) = magic("NumForInterval.`_+_`")
+NumForInterval(M, N, O, P)|<: Sub(O..P)|.
+    Output = M-P..N-O
+    __sub__(self: Self, other: O..P) = magic("NumForInterval.`_-_`")
 
 Read = Trait {
-    .read = (self: Ref(Self)) -> Str
+    .read = (self: Ref(Self),) -> Str
 }
 Read! = Trait {
-    .read! = (self: Ref!(Self)) => Str
+    .read! = (self: Ref!(Self),) => Str
 }
 Write! = Trait {
     .write! = (self: Ref!(Self), Str) => ()
 }
+
+discard _x = None
+
+discard 1
+
+# if: |T, U|(Bool, T, U) -> T or U
+cond|T: Type|(c: Bool, then: T, else: T): T =
+    if c:
+        do then
+        do else
+
+assert cond(False, 1, 2) == 2
+# assert cond(True, 1, 3) == "a"
+# assert "a" == cond(True, 1, 3)
diff --git a/compiler/erg_compiler/lib/std/prelude.er b/compiler/erg_compiler/lib/std/prelude.er
deleted file mode 100644
index 5f01c9ea..00000000
--- a/compiler/erg_compiler/lib/std/prelude.er
+++ /dev/null
@@ -1,13 +0,0 @@
-discard _x = None
-
-discard 1
-
-# if: |T, U|(Bool, T, U) -> T or U
-cond|T: Type|(c: Bool, then: T, else: T): T =
-    if c:
-        do then
-        do else
-
-assert cond(False, 1, 2) == 2
-# assert cond(True, 1, 3) == "a"
-# assert "a" == cond(True, 1, 3)
diff --git a/compiler/erg_parser/lex.rs b/compiler/erg_parser/lex.rs
index e487b7c1..fb989393 100644
--- a/compiler/erg_parser/lex.rs
+++ b/compiler/erg_parser/lex.rs
@@ -186,7 +186,8 @@ impl Lexer /*<'a>*/ {
     fn is_definable_operator(s: &str) -> bool {
         matches!(
             s,
-            "+" | "-"
+            "+_" | "_+_"
+                | "-"
                 | "*"
                 | "/"
                 | "//"
@@ -1127,6 +1128,18 @@ impl Iterator for Lexer /*<'a>*/ {
                             return self.accept(Symbol, &op);
                         } else {
                             let token = self.emit_token(Illegal, &op);
+                            let hint = if op.contains('+') {
+                                Some(
+                                    switch_lang!(
+                                        "japanese" => "二項演算子の+は`_+_`、単項演算子の+は`+_`です",
+                                        "simplified_chinese" => "二元运算符+是`_+_`，一元运算符+是`+_`",
+                                        "traditional_chinese" => "二元運算符+是`_+_`，一元運算符+是`+_`",
+                                        "english" => "the binary operator + is `_+_`, the unary operator + is `+_`",
+                                    ).into(),
+                                )
+                            } else {
+                                None
+                            };
                             return Some(Err(LexError::syntax_error(
                                 0,
                                 token.loc(),
@@ -1136,7 +1149,7 @@ impl Iterator for Lexer /*<'a>*/ {
                                     "traditional_chinese" => format!("`{}`不能由用戶定義", &token.content),
                                     "english" => format!("`{}` cannot be defined by user", &token.content),
                                 ),
-                                None,
+                                hint,
                             )));
                         }
                     }
diff --git a/tests/test.rs b/tests/test.rs
index 3a8031cd..4254e143 100644
--- a/tests/test.rs
+++ b/tests/test.rs
@@ -66,11 +66,6 @@ fn exec_move_check() -> Result<(), ()> {
     expect_failure("examples/move_check.er")
 }
 
-#[test]
-fn exec_prelude() -> Result<(), ()> {
-    expect_success("compiler/erg_compiler/lib/std/prelude.er")
-}
-
 #[test]
 fn exec_pyimport() -> Result<(), ()> {
     expect_end_with("examples/pyimport.er", 111)