diff --git a/compiler/erg_common/error.rs b/compiler/erg_common/error.rs
index 90e16a86..e00438bc 100644
--- a/compiler/erg_common/error.rs
+++ b/compiler/erg_common/error.rs
@@ -488,8 +488,22 @@ pub trait ErrorDisplay {
                 }
                 res + RESET
             }
-            Location::LineRange(_begin, _end) => {
-                todo!()
+            Location::LineRange(ln_begin, ln_end) => {
+                let codes = if self.input() == &Input::REPL {
+                    vec![self.input().reread()]
+                } else {
+                    self.input().reread_lines(ln_begin, ln_end)
+                };
+                let mut res = CYAN.to_string();
+                for (i, lineno) in (ln_begin..=ln_end).enumerate() {
+                    let mut pointer = " ".repeat(lineno.to_string().len() + 2); // +2 means `| `
+                    pointer += &"^".repeat(cmp::max(1, codes[i].len()));
+                    res += &format!(
+                        "{lineno}{VBAR_UNICODE} {code}\n{pointer}\n",
+                        code = codes[i]
+                    );
+                }
+                res + RESET
             }
             Location::Line(lineno) => {
                 let code = if self.input() == &Input::REPL {
diff --git a/compiler/erg_common/vis.rs b/compiler/erg_common/vis.rs
index 4a43778c..ad1c8079 100644
--- a/compiler/erg_common/vis.rs
+++ b/compiler/erg_common/vis.rs
@@ -22,8 +22,8 @@ impl Visibility {
 /// same structure as `Identifier`, but only for Record fields.
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub struct Field {
-    vis: Visibility,
-    symbol: Str,
+    pub vis: Visibility,
+    pub symbol: Str,
 }
 
 impl fmt::Display for Field {
diff --git a/compiler/erg_compiler/codegen.rs b/compiler/erg_compiler/codegen.rs
index 837fc64f..7d6e8733 100644
--- a/compiler/erg_compiler/codegen.rs
+++ b/compiler/erg_compiler/codegen.rs
@@ -13,21 +13,25 @@ use erg_common::Str;
 use erg_common::{
     debug_power_assert, enum_unwrap, fn_name_full, impl_stream_for_wrapper, log, switch_unreachable,
 };
+use erg_parser::ast::DefId;
 use erg_type::codeobj::{CodeObj, CodeObjFlags};
 use Opcode::*;
 
-use erg_parser::ast::{Identifier, ParamPattern, Params, VarName};
+use erg_parser::ast::{Identifier, ParamPattern, ParamSignature, Params, VarName};
 use erg_parser::token::{Token, TokenKind};
 
+use erg_type::free::fresh_varname;
 use erg_type::value::TypeKind;
 use erg_type::value::ValueObj;
-use erg_type::{HasType, TypeCode, TypePair};
+use erg_type::{HasType, Type, TypeCode, TypePair};
 
 use crate::compile::{AccessKind, Name, StoreLoadKind};
 use crate::context::eval::eval_lit;
 use crate::error::{CompileError, CompileErrors, CompileResult};
+use crate::hir::AttrDef;
+use crate::hir::Attribute;
 use crate::hir::{
-    Accessor, Args, Array, Block, Call, ClassDef, DefBody, Expr, Local, RecordAttrs, Signature,
+    Accessor, Args, Array, Block, Call, ClassDef, Def, DefBody, Expr, Local, Signature,
     SubrSignature, Tuple, VarSignature, HIR,
 };
 use AccessKind::*;
@@ -197,6 +201,7 @@ fn convert_to_python_attr(class: &str, uniq_obj_name: Option<&str>, name: Str) -
         ("Array!", _, "push!") => Str::ever("append"),
         ("Complex" | "Real" | "Int" | "Nat" | "Float", _, "Real") => Str::ever("real"),
         ("Complex" | "Real" | "Int" | "Nat" | "Float", _, "Imag") => Str::ever("imag"),
+        ("Type", _, "new" | "__new__") => Str::ever("__call__"),
         ("StringIO!", _, "getvalue!") => Str::ever("getvalue"),
         ("Module", Some("importlib"), "reload!") => Str::ever("reload"),
         ("Module", Some("random"), "randint!") => Str::ever("randint"),
@@ -644,6 +649,25 @@ impl CodeGenerator {
         self.stack_dec();
     }
 
+    fn store_acc(&mut self, acc: Accessor) {
+        match acc {
+            Accessor::Local(local) => {
+                self.emit_store_instr(Identifier::new(None, VarName::new(local.name)), Name);
+            }
+            Accessor::Public(public) => {
+                self.emit_store_instr(
+                    Identifier::new(Some(public.dot), VarName::new(public.name)),
+                    Name,
+                );
+            }
+            Accessor::Attr(attr) => {
+                self.codegen_expr(*attr.obj);
+                self.emit_store_instr(Identifier::new(None, VarName::new(attr.name)), Attr);
+            }
+            acc => todo!("store: {acc}"),
+        }
+    }
+
     fn emit_pop_top(&mut self) {
         self.write_instr(Opcode::POP_TOP);
         self.write_arg(0u8);
@@ -686,38 +710,46 @@ impl CodeGenerator {
             .collect()
     }
 
-    fn emit_linked_type_def(&mut self, type_def: ClassDef) {
-        match type_def.def.sig {
-            Signature::Var(var) => match type_def.kind {
-                TypeKind::Class => self.emit_mono_class_def(var, type_def.public_methods),
-                TypeKind::InheritedClass => {
-                    todo!()
-                }
-                other => todo!("{other:?} is not supported"),
-            },
-            Signature::Subr(_) => todo!("polymorphic type definition"),
-        }
-    }
-
-    fn emit_mono_class_def(&mut self, sig: VarSignature, methods: RecordAttrs) {
+    fn emit_class_def(&mut self, class_def: ClassDef) {
+        let ident = class_def.sig.ident().clone();
+        let kind = class_def.kind;
+        let require_or_sup = class_def.require_or_sup.clone();
         self.write_instr(Opcode::LOAD_BUILD_CLASS);
         self.write_arg(0);
         self.stack_inc();
-        let code = self.codegen_typedef_block(sig.inspect().clone(), methods);
+        let code = self.codegen_typedef_block(class_def);
         self.emit_load_const(code);
-        self.emit_load_const(sig.inspect().clone());
+        self.emit_load_const(ident.inspect().clone());
         self.write_instr(Opcode::MAKE_FUNCTION);
         self.write_arg(0);
-        self.emit_load_const(sig.inspect().clone());
+        self.emit_load_const(ident.inspect().clone());
+        let subclasses_len = self.emit_require_type(kind, *require_or_sup);
+        // LOAD subclasses
         self.write_instr(Opcode::CALL_FUNCTION);
-        self.write_arg(2);
-        self.stack_dec_n((1 + 2) - 1);
-        self.emit_store_instr(sig.ident, Name);
+        self.write_arg(2 + subclasses_len as u8);
+        self.stack_dec_n((1 + 2 + subclasses_len) - 1);
+        self.emit_store_instr(ident, Name);
     }
 
     // NOTE: use `TypeVar`, `Generic` in `typing` module
     // fn emit_poly_type_def(&mut self, sig: SubrSignature, body: DefBody) {}
 
+    fn emit_require_type(&mut self, kind: TypeKind, require_or_sup: Expr) -> usize {
+        match kind {
+            TypeKind::Class => 0,
+            TypeKind::Subclass => {
+                self.codegen_expr(require_or_sup);
+                1 // TODO: not always 1
+            }
+            _ => todo!(),
+        }
+    }
+
+    fn emit_attr_def(&mut self, attr_def: AttrDef) {
+        self.codegen_frameless_block(attr_def.block, vec![]);
+        self.store_acc(attr_def.attr);
+    }
+
     fn emit_var_def(&mut self, sig: VarSignature, mut body: DefBody) {
         if body.block.len() == 1 {
             self.codegen_expr(body.block.remove(0));
@@ -971,6 +1003,9 @@ impl CodeGenerator {
     }
 
     fn emit_call_method(&mut self, obj: Expr, method_name: Token, mut args: Args) {
+        if &method_name.inspect()[..] == "update!" {
+            return self.emit_call_update(obj, args);
+        }
         let class = obj.ref_t().name(); // これは必ずmethodのあるクラスになっている
         let uniq_obj_name = obj.__name__().map(Str::rc);
         self.codegen_expr(obj);
@@ -1005,6 +1040,21 @@ impl CodeGenerator {
         self.stack_dec_n((1 + argc + kwsc) - 1);
     }
 
+    /// X.update! x -> x + 1
+    /// X = (x -> x + 1)(X)
+    /// X = X + 1
+    fn emit_call_update(&mut self, obj: Expr, mut args: Args) {
+        let acc = enum_unwrap!(obj, Expr::Accessor);
+        let func = args.remove_left_or_key("f").unwrap();
+        self.codegen_expr(func);
+        self.codegen_acc(acc.clone());
+        self.write_instr(CALL_FUNCTION);
+        self.write_arg(1 as u8);
+        // (1 (subroutine) + argc) input objects -> 1 return object
+        self.stack_dec_n((1 + 1) - 1);
+        self.store_acc(acc);
+    }
+
     // assert takes 1 or 2 arguments (0: cond, 1: message)
     fn emit_assert_instr(&mut self, mut args: Args) -> CompileResult<()> {
         self.codegen_expr(args.remove(0));
@@ -1066,7 +1116,8 @@ impl CodeGenerator {
                 Signature::Subr(sig) => self.emit_subr_def(sig, def.body),
                 Signature::Var(sig) => self.emit_var_def(sig, def.body),
             },
-            Expr::ClassDef(def) => self.emit_linked_type_def(def),
+            Expr::ClassDef(class) => self.emit_class_def(class),
+            Expr::AttrDef(attr) => self.emit_attr_def(attr),
             // TODO:
             Expr::Lambda(lambda) => {
                 let params = self.gen_param_names(&lambda.params);
@@ -1323,22 +1374,42 @@ impl CodeGenerator {
         self.cancel_pop_top();
     }
 
-    fn codegen_typedef_block(&mut self, name: Str, methods: RecordAttrs) -> CodeObj {
+    fn codegen_typedef_block(&mut self, class: ClassDef) -> CodeObj {
+        let name = class.sig.ident().inspect().clone();
         self.unit_size += 1;
+        let firstlineno = match (
+            class.private_methods.get(0).and_then(|def| def.ln_begin()),
+            class.public_methods.get(0).and_then(|def| def.ln_begin()),
+        ) {
+            (Some(l), Some(r)) => l.min(r),
+            (Some(line), None) | (None, Some(line)) => line,
+            (None, None) => class.sig.ln_begin().unwrap(),
+        };
         self.units.push(CodeGenUnit::new(
             self.unit_size,
             vec![],
             Str::rc(self.cfg.input.enclosed_name()),
             &name,
-            methods[0].ln_begin().unwrap(),
+            firstlineno,
         ));
         let mod_name = self.toplevel_block_codeobj().name.clone();
         self.emit_load_const(mod_name);
         self.emit_store_instr(Identifier::public("__module__"), Attr);
         self.emit_load_const(name);
         self.emit_store_instr(Identifier::public("__qualname__"), Attr);
+        if class.need_to_gen_new {
+            self.emit_auto_new(&class.sig, class.__new__);
+        }
         // TODO: サブルーチンはT.subという書式でSTORE
-        for def in methods.into_iter() {
+        for def in class.private_methods.into_iter() {
+            self.codegen_expr(Expr::Def(def));
+            // TODO: discard
+            if self.cur_block().stack_len == 1 {
+                self.emit_pop_top();
+            }
+        }
+        for mut def in class.public_methods.into_iter() {
+            def.sig.ident_mut().dot = Some(Token::dummy());
             self.codegen_expr(Expr::Def(def));
             // TODO: discard
             if self.cur_block().stack_len == 1 {
@@ -1378,6 +1449,62 @@ impl CodeGenerator {
         unit.codeobj
     }
 
+    fn emit_auto_new(&mut self, sig: &Signature, __new__: Type) {
+        let line = sig.ln_begin().unwrap();
+        let ident = Identifier::private_with_line(Str::ever("__new__"), line);
+        let param_name = fresh_varname();
+        let param = VarName::from_str_and_line(Str::from(param_name.clone()), line);
+        let params = Params::new(
+            vec![ParamSignature::new(
+                ParamPattern::VarName(param),
+                None,
+                None,
+            )],
+            None,
+            vec![],
+            None,
+        );
+        let sig = Signature::Subr(SubrSignature::new(ident, params.clone(), __new__.clone()));
+        let mut attrs = vec![];
+        match __new__.non_default_params().unwrap()[0].typ() {
+            // {x = Int; y = Int}
+            // self.x = %x.x; self.y = %x.y
+            Type::Record(rec) => {
+                for field in rec.keys() {
+                    let obj = Expr::Accessor(Accessor::local(
+                        Token::symbol_with_line(&param_name[..], line),
+                        Type::Failure,
+                    ));
+                    let attr = Accessor::Attr(Attribute::new(
+                        obj,
+                        Token::symbol(&field.symbol[..]),
+                        Type::Failure,
+                    ));
+                    let obj = Expr::Accessor(Accessor::local(
+                        Token::symbol_with_line("self", line),
+                        Type::Failure,
+                    ));
+                    let expr = Expr::Accessor(Accessor::Attr(Attribute::new(
+                        obj,
+                        Token::symbol(&field.symbol[..]),
+                        Type::Failure,
+                    )));
+                    let attr_def = AttrDef::new(attr, Block::new(vec![expr]));
+                    attrs.push(Expr::AttrDef(attr_def));
+                }
+            }
+            other => todo!("{other}"),
+        }
+        let block = Block::new(attrs);
+        let body = DefBody::new(Token::dummy(), block, DefId(0));
+        let private_new_def = Def::new(sig, body.clone());
+        self.codegen_expr(Expr::Def(private_new_def));
+        let ident = Identifier::public_with_line(Token::dummy(), Str::ever("new"), line);
+        let sig = Signature::Subr(SubrSignature::new(ident, params, __new__));
+        let new_def = Def::new(sig, body);
+        self.codegen_expr(Expr::Def(new_def));
+    }
+
     fn codegen_block(&mut self, block: Block, opt_name: Option<Str>, params: Vec<Str>) -> CodeObj {
         self.unit_size += 1;
         let name = if let Some(name) = opt_name {
diff --git a/compiler/erg_compiler/context/initialize/const_func.rs b/compiler/erg_compiler/context/initialize/const_func.rs
index a454f509..863739e0 100644
--- a/compiler/erg_compiler/context/initialize/const_func.rs
+++ b/compiler/erg_compiler/context/initialize/const_func.rs
@@ -1,6 +1,8 @@
+use std::mem;
+
 use erg_common::Str;
 
-use erg_type::constructors::mono;
+use erg_type::constructors::{and, mono};
 use erg_type::value::{TypeKind, TypeObj, ValueObj};
 use erg_type::Type;
 use erg_type::ValueArgs;
@@ -19,9 +21,9 @@ fn value_obj_to_t(value: ValueObj) -> TypeObj {
 
 /// Requirement: Type, Impl := Type -> Class
 pub fn class_func(mut args: ValueArgs, __name__: Option<Str>) -> ValueObj {
-    let require = args.pos_args.remove(0);
+    let require = args.remove_left_or_key("Requirement").unwrap();
     let require = value_obj_to_t(require);
-    let impls = args.pos_args.pop().or_else(|| args.kw_args.remove("Impl"));
+    let impls = args.remove_left_or_key("Impl");
     let impls = impls.map(|v| value_obj_to_t(v));
     let t = mono(__name__.unwrap_or(Str::ever("<Lambda>")));
     ValueObj::gen_t(TypeKind::Class, t, require, impls, None)
@@ -29,21 +31,34 @@ pub fn class_func(mut args: ValueArgs, __name__: Option<Str>) -> ValueObj {
 
 /// Super: Type, Impl := Type, Additional := Type -> Class
 pub fn inherit_func(mut args: ValueArgs, __name__: Option<Str>) -> ValueObj {
-    let sup = args.pos_args.remove(0);
+    let sup = args.remove_left_or_key("Super").unwrap();
     let sup = value_obj_to_t(sup);
-    let impls = args.pos_args.pop().or_else(|| args.kw_args.remove("Impl"));
+    let impls = args.remove_left_or_key("Impl");
     let impls = impls.map(|v| value_obj_to_t(v));
-    let additional = args
-        .pos_args
-        .pop()
-        .or_else(|| args.kw_args.remove("Additional"));
+    let additional = args.remove_left_or_key("Additional");
     let additional = additional.map(|v| value_obj_to_t(v));
     let t = mono(__name__.unwrap_or(Str::ever("<Lambda>")));
-    ValueObj::gen_t(TypeKind::InheritedClass, t, sup, impls, additional)
+    ValueObj::gen_t(TypeKind::Subclass, t, sup, impls, additional)
 }
 
-/// Class -> Class
+/// Class -> Class (with `Inheritable`)
 /// This function is used by the compiler to mark a class as inheritable and does nothing in terms of actual operation.
 pub fn inheritable_func(args: ValueArgs, __name__: Option<Str>) -> ValueObj {
-    args.pos_args.into_iter().next().unwrap()
+    let class = args.pos_args.into_iter().next().unwrap();
+    match class {
+        ValueObj::Type(TypeObj::Generated(mut gen)) => {
+            if let Some(typ) = &mut gen.impls {
+                match typ.as_mut() {
+                    TypeObj::Generated(gen) => {
+                        gen.t = and(mem::take(&mut gen.t), mono("Inheritable"));
+                    }
+                    TypeObj::Builtin(t) => {
+                        *t = and(mem::take(t), mono("Inheritable"));
+                    }
+                }
+            }
+            ValueObj::Type(TypeObj::Generated(gen))
+        }
+        _ => todo!(),
+    }
 }
diff --git a/compiler/erg_compiler/context/initialize/mod.rs b/compiler/erg_compiler/context/initialize/mod.rs
index cedbd159..1cfb15d3 100644
--- a/compiler/erg_compiler/context/initialize/mod.rs
+++ b/compiler/erg_compiler/context/initialize/mod.rs
@@ -57,6 +57,7 @@ impl Context {
         if self.rec_get_const_obj(name).is_some() {
             panic!("already registered: {name}");
         } else {
+            // TODO: not all value objects are comparable
             let vi = VarInfo::new(enum_t(set! {obj.clone()}), Const, Private, Builtin);
             self.consts.insert(VarName::from_str(Str::rc(name)), obj);
             self.locals.insert(VarName::from_str(Str::rc(name)), vi);
@@ -360,8 +361,6 @@ impl Context {
         obj.register_builtin_impl("__dict__", fn0_met(Obj, dict(Str, Obj)), Immutable, Public);
         obj.register_builtin_impl("__bytes__", fn0_met(Obj, mono("Bytes")), Immutable, Public);
         obj.register_builtin_const("MutType!", ValueObj::builtin_t(mono("Obj!")));
-        // let mut record = Self::mono_trait("Record", vec![Obj], Self::TOP_LEVEL);
-        // let mut class = Self::mono_class("Class", vec![Type, Obj], Self::TOP_LEVEL);
         let mut int = Self::mono_class(
             "Int",
             vec![Ratio, Obj],
@@ -1089,7 +1088,7 @@ impl Context {
             vec![param_t("Impl", Type)],
             Class,
         );
-        let class = ConstSubr::Builtin(BuiltinConstSubr::new(class_func, class_t));
+        let class = ConstSubr::Builtin(BuiltinConstSubr::new("Class", class_func, class_t));
         self.register_builtin_const("Class", ValueObj::Subr(class));
         let inherit_t = func(
             vec![param_t("Super", Class)],
@@ -1097,11 +1096,15 @@ impl Context {
             vec![param_t("Impl", Type), param_t("Additional", Type)],
             Class,
         );
-        let inherit = ConstSubr::Builtin(BuiltinConstSubr::new(inherit_func, inherit_t));
+        let inherit = ConstSubr::Builtin(BuiltinConstSubr::new("Inherit", inherit_func, inherit_t));
         self.register_builtin_const("Inherit", ValueObj::Subr(inherit));
         // decorators
-        let inheritable =
-            ConstSubr::Builtin(BuiltinConstSubr::new(inheritable_func, func1(Class, Class)));
+        let inheritable_t = func1(Class, Class);
+        let inheritable = ConstSubr::Builtin(BuiltinConstSubr::new(
+            "Inheritable",
+            inheritable_func,
+            inheritable_t,
+        ));
         self.register_builtin_const("Inheritable", ValueObj::Subr(inheritable));
     }
 
diff --git a/compiler/erg_compiler/context/register.rs b/compiler/erg_compiler/context/register.rs
index 534fec46..34161f20 100644
--- a/compiler/erg_compiler/context/register.rs
+++ b/compiler/erg_compiler/context/register.rs
@@ -525,6 +525,7 @@ impl Context {
                     let gen = enum_unwrap!(t, TypeObj::Generated);
                     self.register_gen_type(gen);
                 }
+                // TODO: not all value objects are comparable
                 other => {
                     let id = DefId(get_hash(name));
                     let vi = VarInfo::new(
@@ -556,7 +557,7 @@ impl Context {
                     todo!()
                 }
             }
-            TypeKind::InheritedClass => {
+            TypeKind::Subclass => {
                 if gen.t.is_monomorphic() {
                     let super_classes = vec![gen.require_or_sup.typ().clone()];
                     let super_traits = gen.impls.iter().map(|to| to.typ().clone()).collect();
@@ -568,6 +569,8 @@ impl Context {
                             TypeObj::Builtin(t) => t,
                             TypeObj::Generated(t) => t.require_or_sup.as_ref().typ(),
                         };
+                        // `Super.Requirement := {x = Int}` and `Self.Additional := {y = Int}`
+                        // => `Self.Requirement := {x = Int; y = Int}`
                         let param_t = if let Some(additional) = &gen.additional {
                             self.rec_intersection(&param_t, additional.typ())
                         } else {
diff --git a/compiler/erg_compiler/context/tyvar.rs b/compiler/erg_compiler/context/tyvar.rs
index 5e4245a5..59ded596 100644
--- a/compiler/erg_compiler/context/tyvar.rs
+++ b/compiler/erg_compiler/context/tyvar.rs
@@ -493,6 +493,13 @@ impl Context {
                 }
                 Ok(())
             }
+            hir::Expr::AttrDef(attr_def) => {
+                // REVIEW: attr_def.attr is not dereferenced
+                for chunk in attr_def.block.iter_mut() {
+                    self.deref_expr_t(chunk)?;
+                }
+                Ok(())
+            }
         }
     }
 
diff --git a/compiler/erg_compiler/hir.rs b/compiler/erg_compiler/hir.rs
index 11f3294d..d439ae12 100644
--- a/compiler/erg_compiler/hir.rs
+++ b/compiler/erg_compiler/hir.rs
@@ -243,6 +243,22 @@ impl Args {
                 .map(|a| &a.expr)
         }
     }
+
+    pub fn remove_left_or_key(&mut self, key: &str) -> Option<Expr> {
+        if !self.pos_args.is_empty() {
+            Some(self.pos_args.remove(0).expr)
+        } else {
+            if let Some(pos) = self
+                .kw_args
+                .iter()
+                .position(|arg| &arg.keyword.inspect()[..] == key)
+            {
+                Some(self.kw_args.remove(pos).expr)
+            } else {
+                None
+            }
+        }
+    }
 }
 
 /// represents local variables
@@ -894,9 +910,9 @@ impl NestedDisplay for Call {
     fn fmt_nest(&self, f: &mut std::fmt::Formatter<'_>, level: usize) -> std::fmt::Result {
         writeln!(
             f,
-            "({}){}(: {}):",
+            "({}){} (: {}):",
             self.obj,
-            fmt_option!(pre ".", self.method_name),
+            fmt_option!(pre ".", self.method_name.as_ref().map(|t| t.inspect())),
             self.sig_t
         )?;
         self.args.fmt_nest(f, level + 1)
@@ -1011,6 +1027,7 @@ impl NestedDisplay for VarSignature {
 
 impl_display_from_nested!(VarSignature);
 impl_locational!(VarSignature, ident);
+impl_t!(VarSignature);
 
 impl VarSignature {
     pub const fn new(ident: Identifier, t: Type) -> Self {
@@ -1041,6 +1058,7 @@ impl NestedDisplay for SubrSignature {
 
 impl_display_from_nested!(SubrSignature);
 impl_locational!(SubrSignature, ident, params);
+impl_t!(SubrSignature);
 
 impl SubrSignature {
     pub const fn new(ident: Identifier, params: Params, t: Type) -> Self {
@@ -1096,6 +1114,7 @@ pub enum Signature {
 
 impl_nested_display_for_chunk_enum!(Signature; Var, Subr);
 impl_display_for_enum!(Signature; Var, Subr,);
+impl_t_for_enum!(Signature; Var, Subr);
 impl_locational_for_enum!(Signature; Var, Subr,);
 
 impl Signature {
@@ -1130,6 +1149,13 @@ impl Signature {
             Self::Subr(s) => &s.ident,
         }
     }
+
+    pub fn ident_mut(&mut self) -> &mut Identifier {
+        match self {
+            Self::Var(v) => &mut v.ident,
+            Self::Subr(s) => &mut s.ident,
+        }
+    }
 }
 
 /// represents a declaration of a variable
@@ -1254,23 +1280,23 @@ impl Def {
 }
 
 #[derive(Debug, Clone)]
-pub struct MethodDefs {
+pub struct Methods {
     pub class: TypeSpec,
     pub vis: Token,        // `.` or `::`
     pub defs: RecordAttrs, // TODO: allow declaration
 }
 
-impl NestedDisplay for MethodDefs {
+impl NestedDisplay for Methods {
     fn fmt_nest(&self, f: &mut fmt::Formatter<'_>, level: usize) -> fmt::Result {
         writeln!(f, "{}{}", self.class, self.vis.content)?;
         self.defs.fmt_nest(f, level + 1)
     }
 }
 
-impl_display_from_nested!(MethodDefs);
-impl_locational!(MethodDefs, class, defs);
+impl_display_from_nested!(Methods);
+impl_locational!(Methods, class, defs);
 
-impl HasType for MethodDefs {
+impl HasType for Methods {
     #[inline]
     fn ref_t(&self) -> &Type {
         Type::NONE
@@ -1289,7 +1315,7 @@ impl HasType for MethodDefs {
     }
 }
 
-impl MethodDefs {
+impl Methods {
     pub const fn new(class: TypeSpec, vis: Token, defs: RecordAttrs) -> Self {
         Self { class, vis, defs }
     }
@@ -1298,21 +1324,25 @@ impl MethodDefs {
 #[derive(Debug, Clone)]
 pub struct ClassDef {
     pub kind: TypeKind,
-    pub def: Def,
+    pub sig: Signature,
+    pub require_or_sup: Box<Expr>,
+    /// The type of `new` and `__new__` that is automatically defined if not defined
+    pub need_to_gen_new: bool,
+    pub __new__: Type,
     pub private_methods: RecordAttrs,
     pub public_methods: RecordAttrs,
 }
 
 impl NestedDisplay for ClassDef {
     fn fmt_nest(&self, f: &mut fmt::Formatter<'_>, level: usize) -> fmt::Result {
-        self.def.fmt_nest(f, level)?;
+        self.sig.fmt_nest(f, level)?;
         self.private_methods.fmt_nest(f, level)?;
         self.public_methods.fmt_nest(f, level + 1)
     }
 }
 
 impl_display_from_nested!(ClassDef);
-impl_locational!(ClassDef, def);
+impl_locational!(ClassDef, sig);
 
 impl HasType for ClassDef {
     #[inline]
@@ -1334,21 +1364,69 @@ impl HasType for ClassDef {
 }
 
 impl ClassDef {
-    pub const fn new(
+    pub fn new(
         kind: TypeKind,
-        def: Def,
+        sig: Signature,
+        require_or_sup: Expr,
+        need_to_gen_new: bool,
+        __new__: Type,
         private_methods: RecordAttrs,
         public_methods: RecordAttrs,
     ) -> Self {
         Self {
             kind,
-            def,
+            sig,
+            require_or_sup: Box::new(require_or_sup),
+            need_to_gen_new,
+            __new__,
             private_methods,
             public_methods,
         }
     }
 }
 
+#[derive(Debug, Clone)]
+pub struct AttrDef {
+    pub attr: Accessor,
+    pub block: Block,
+}
+
+impl NestedDisplay for AttrDef {
+    fn fmt_nest(&self, f: &mut fmt::Formatter<'_>, level: usize) -> fmt::Result {
+        self.attr.fmt_nest(f, level)?;
+        writeln!(f, " = ")?;
+        self.block.fmt_nest(f, level + 1)
+    }
+}
+
+impl_display_from_nested!(AttrDef);
+impl_locational!(AttrDef, attr, block);
+
+impl HasType for AttrDef {
+    #[inline]
+    fn ref_t(&self) -> &Type {
+        Type::NONE
+    }
+    #[inline]
+    fn ref_mut_t(&mut self) -> &mut Type {
+        todo!()
+    }
+    #[inline]
+    fn signature_t(&self) -> Option<&Type> {
+        None
+    }
+    #[inline]
+    fn signature_mut_t(&mut self) -> Option<&mut Type> {
+        None
+    }
+}
+
+impl AttrDef {
+    pub const fn new(attr: Accessor, block: Block) -> Self {
+        Self { attr, block }
+    }
+}
+
 #[derive(Debug, Clone)]
 pub enum Expr {
     Lit(Literal),
@@ -1365,12 +1443,13 @@ pub enum Expr {
     Decl(Decl),
     Def(Def),
     ClassDef(ClassDef),
+    AttrDef(AttrDef),
 }
 
-impl_nested_display_for_chunk_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef);
+impl_nested_display_for_chunk_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef, AttrDef);
 impl_display_from_nested!(Expr);
-impl_locational_for_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef);
-impl_t_for_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef);
+impl_locational_for_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef, AttrDef);
+impl_t_for_enum!(Expr; Lit, Accessor, Array, Tuple, Dict, Record, BinOp, UnaryOp, Call, Lambda, Decl, Def, ClassDef, AttrDef);
 
 impl Expr {
     pub fn receiver_t(&self) -> Option<&Type> {
diff --git a/compiler/erg_compiler/lower.rs b/compiler/erg_compiler/lower.rs
index 84055c79..59560f99 100644
--- a/compiler/erg_compiler/lower.rs
+++ b/compiler/erg_compiler/lower.rs
@@ -13,13 +13,14 @@ use erg_parser::token::{Token, TokenKind};
 use erg_type::constructors::{array, array_mut, free_var, func, mono, poly, proc, quant};
 use erg_type::free::Constraint;
 use erg_type::typaram::TyParam;
-use erg_type::value::{TypeKind, ValueObj};
+use erg_type::value::{TypeObj, ValueObj};
 use erg_type::{HasType, ParamTy, Type};
 
 use crate::context::{Context, ContextKind, RegistrationMode};
 use crate::error::{LowerError, LowerErrors, LowerResult, LowerWarnings};
 use crate::hir;
 use crate::hir::HIR;
+use crate::varinfo::VarKind;
 use Visibility::*;
 
 /// Singleton that checks types of an AST, and convert (lower) it into a HIR
@@ -548,7 +549,7 @@ impl ASTLowerer {
 
     fn lower_class_def(&mut self, class_def: ast::ClassDef) -> LowerResult<hir::ClassDef> {
         log!(info "entered {}({class_def})", fn_name!());
-        let hir_def = self.lower_def(class_def.def)?;
+        let mut hir_def = self.lower_def(class_def.def)?;
         let mut private_methods = hir::RecordAttrs::empty();
         let mut public_methods = hir::RecordAttrs::empty();
         for methods in class_def.methods_list.into_iter() {
@@ -581,22 +582,44 @@ impl ASTLowerer {
                 }
             }
         }
-        let definition = hir_def.body.block.first().unwrap();
-        let call = enum_unwrap!(definition, hir::Expr::Call);
-        // FIXME:
-        let kind = match &call.obj.var_full_name().unwrap()[..] {
-            "Class" | "Inheritable" => TypeKind::Class,
-            "Inherit" => TypeKind::InheritedClass,
-            _ => unreachable!(),
+        let (_, ctx) = self
+            .ctx
+            .rec_get_nominal_type_ctx(&mono(hir_def.sig.ident().inspect()))
+            .unwrap();
+        let type_obj = enum_unwrap!(self.ctx.rec_get_const_obj(hir_def.sig.ident().inspect()).unwrap(), ValueObj::Type:(TypeObj::Generated:(_)));
+        // vi.t.non_default_params().unwrap()[0].typ().clone()
+        let (__new__, need_to_gen_new) = if let Some(vi) = ctx.get_current_scope_var("new") {
+            (vi.t.clone(), vi.kind == VarKind::Auto)
+        } else {
+            todo!()
         };
+        let require_or_sup = self.get_require_or_sup(hir_def.body.block.remove(0));
         Ok(hir::ClassDef::new(
-            kind,
-            hir_def,
+            type_obj.kind,
+            hir_def.sig,
+            require_or_sup,
+            need_to_gen_new,
+            __new__,
             private_methods,
             public_methods,
         ))
     }
 
+    fn get_require_or_sup(&self, expr: hir::Expr) -> hir::Expr {
+        match expr {
+            acc @ hir::Expr::Accessor(_) => acc,
+            hir::Expr::Call(mut call) => match call.obj.var_full_name().as_ref().map(|s| &s[..]) {
+                Some("Class") => call.args.remove_left_or_key("Requirement").unwrap(),
+                Some("Inherit") => call.args.remove_left_or_key("Super").unwrap(),
+                Some("Inheritable") => {
+                    self.get_require_or_sup(call.args.remove_left_or_key("Class").unwrap())
+                }
+                _ => todo!(),
+            },
+            other => todo!("{other}"),
+        }
+    }
+
     // Call.obj == Accessor cannot be type inferred by itself (it can only be inferred with arguments)
     // so turn off type checking (check=false)
     fn lower_expr(&mut self, expr: ast::Expr) -> LowerResult<hir::Expr> {
diff --git a/compiler/erg_parser/ast.rs b/compiler/erg_parser/ast.rs
index badcd3c8..8d6e8e45 100644
--- a/compiler/erg_parser/ast.rs
+++ b/compiler/erg_parser/ast.rs
@@ -1872,13 +1872,17 @@ impl Identifier {
         Self::new(None, VarName::from_str_and_line(name, line))
     }
 
+    pub fn public_with_line(dot: Token, name: Str, line: usize) -> Self {
+        Self::new(Some(dot), VarName::from_str_and_line(name, line))
+    }
+
     pub fn is_const(&self) -> bool {
         self.name.is_const()
     }
 
     pub const fn vis(&self) -> Visibility {
         match &self.dot {
-            Some(_dot) => Visibility::Public,
+            Some(_) => Visibility::Public,
             None => Visibility::Private,
         }
     }
diff --git a/compiler/erg_parser/token.rs b/compiler/erg_parser/token.rs
index 52a78893..386a9117 100644
--- a/compiler/erg_parser/token.rs
+++ b/compiler/erg_parser/token.rs
@@ -376,6 +376,16 @@ impl Token {
         Self::from_str(TokenKind::Symbol, cont)
     }
 
+    #[inline]
+    pub fn symbol_with_line(cont: &str, line: usize) -> Self {
+        Token {
+            kind: TokenKind::Symbol,
+            content: Str::rc(cont),
+            lineno: line,
+            col_begin: 0,
+        }
+    }
+
     pub const fn static_symbol(s: &'static str) -> Self {
         Token {
             kind: TokenKind::Symbol,
diff --git a/compiler/erg_type/lib.rs b/compiler/erg_type/lib.rs
index 29eb2054..793df2bf 100644
--- a/compiler/erg_type/lib.rs
+++ b/compiler/erg_type/lib.rs
@@ -142,17 +142,36 @@ impl ValueArgs {
     pub const fn new(pos_args: Vec<ValueObj>, kw_args: Dict<Str, ValueObj>) -> Self {
         ValueArgs { pos_args, kw_args }
     }
+
+    pub fn remove_left_or_key(&mut self, key: &str) -> Option<ValueObj> {
+        if !self.pos_args.is_empty() {
+            Some(self.pos_args.remove(0))
+        } else {
+            self.kw_args.remove(key)
+        }
+    }
 }
 
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub struct BuiltinConstSubr {
+    name: &'static str,
     subr: fn(ValueArgs, Option<Str>) -> ValueObj,
     t: Type,
 }
 
+impl fmt::Display for BuiltinConstSubr {
+    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
+        write!(f, "<built-in const subroutine '{}'>", self.name)
+    }
+}
+
 impl BuiltinConstSubr {
-    pub const fn new(subr: fn(ValueArgs, Option<Str>) -> ValueObj, t: Type) -> Self {
-        Self { subr, t }
+    pub const fn new(
+        name: &'static str,
+        subr: fn(ValueArgs, Option<Str>) -> ValueObj,
+        t: Type,
+    ) -> Self {
+        Self { name, subr, t }
     }
 }
 
@@ -165,8 +184,10 @@ pub enum ConstSubr {
 impl fmt::Display for ConstSubr {
     fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
         match self {
-            ConstSubr::User(_) => write!(f, "<user-defined const subroutine>"),
-            ConstSubr::Builtin(_) => write!(f, "<builtin const subroutine>"),
+            ConstSubr::User(subr) => {
+                write!(f, "<user-defined const subroutine '{}'>", subr.code.name)
+            }
+            ConstSubr::Builtin(subr) => write!(f, "{subr}"),
         }
     }
 }
@@ -1840,6 +1861,13 @@ impl Type {
         }
     }
 
+    pub fn contains_intersec(&self, typ: &Type) -> bool {
+        match self {
+            Type::And(t1, t2) => t1.contains_intersec(typ) || t2.contains_intersec(typ),
+            _ => self == typ,
+        }
+    }
+
     pub fn tvar_name(&self) -> Option<Str> {
         match self {
             Self::FreeVar(fv) => fv.unbound_name(),
diff --git a/compiler/erg_type/value.rs b/compiler/erg_type/value.rs
index a67ed21c..b5d5622f 100644
--- a/compiler/erg_type/value.rs
+++ b/compiler/erg_type/value.rs
@@ -25,9 +25,9 @@ use crate::{ConstSubr, HasType, Predicate, Type};
 #[derive(Clone, Copy, Debug, PartialEq, Eq, Hash)]
 pub enum TypeKind {
     Class,
-    InheritedClass,
+    Subclass,
     Trait,
-    SubsumedTrait,
+    Subtrait,
     StructuralTrait,
 }
 
@@ -35,7 +35,7 @@ pub enum TypeKind {
 #[derive(Clone, Debug, PartialEq, Eq, Hash)]
 pub struct GenTypeObj {
     pub kind: TypeKind,
-    pub t: Type,
+    pub t: Type, // andやorが入る可能性あり
     pub require_or_sup: Box<TypeObj>,
     pub impls: Option<Box<TypeObj>>,
     pub additional: Option<Box<TypeObj>>,
@@ -66,8 +66,8 @@ impl GenTypeObj {
 
     pub fn meta_type(&self) -> Type {
         match self.kind {
-            TypeKind::Class | TypeKind::InheritedClass => Type::Class,
-            TypeKind::Trait | TypeKind::SubsumedTrait | TypeKind::StructuralTrait => Type::Trait,
+            TypeKind::Class | TypeKind::Subclass => Type::Class,
+            TypeKind::Trait | TypeKind::Subtrait | TypeKind::StructuralTrait => Type::Trait,
         }
     }
 }