diff --git a/Cargo.lock b/Cargo.lock
index 3a81399..18418e4 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -253,8 +253,7 @@ checksum = "7fcaabb2fef8c910e7f4c7ce9f67a1283a1715879a7c230ca9d6d1ae31f16d91"
 [[package]]
 name = "els"
 version = "0.1.19-nightly.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "fc21e1a7815740ad6debfd616bd9f5551dc4b10fa1b4e0e2cec42ddf57dbc7d8"
+source = "git+https://github.com/erg-lang/erg?branch=main#0f0d04202014c002fbbafa88ff9d42067d57f201"
 dependencies = [
  "erg_common",
  "erg_compiler",
@@ -275,8 +274,7 @@ dependencies = [
 [[package]]
 name = "erg_common"
 version = "0.6.7-nightly.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d8d2357638900c5d5f2ee751b4fd2254932fda6a1c50939ffbc8a7acd5903ce9"
+source = "git+https://github.com/erg-lang/erg?branch=main#0f0d04202014c002fbbafa88ff9d42067d57f201"
 dependencies = [
  "backtrace-on-stack-overflow",
  "hermit-abi",
@@ -287,8 +285,7 @@ dependencies = [
 [[package]]
 name = "erg_compiler"
 version = "0.6.7-nightly.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "682faa374e190771be607591426293f6fb56f22f8ed08c3d424a27615bb261cd"
+source = "git+https://github.com/erg-lang/erg?branch=main#0f0d04202014c002fbbafa88ff9d42067d57f201"
 dependencies = [
  "erg_common",
  "erg_parser",
@@ -297,8 +294,7 @@ dependencies = [
 [[package]]
 name = "erg_parser"
 version = "0.6.7-nightly.0"
-source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "e3e3ee6c10e35b83fe0c6c675ab1697aa72d175e4d10cbcf9a8057485192a604"
+source = "git+https://github.com/erg-lang/erg?branch=main#0f0d04202014c002fbbafa88ff9d42067d57f201"
 dependencies = [
  "erg_common",
  "unicode-xid 0.2.4",
@@ -920,9 +916,9 @@ checksum = "73473c0e59e6d5812c5dfe2a064a6444949f089e20eec9a2e5506596494e4623"
 
 [[package]]
 name = "syn"
-version = "1.0.108"
+version = "1.0.109"
 source = "registry+https://github.com/rust-lang/crates.io-index"
-checksum = "d56e159d99e6c2b93995d171050271edb50ecc5288fbc7cc17de8fdce4e58c14"
+checksum = "72b64191b275b66ffe2469e8af2c1cfe3bafa67b529ead792a6d0160888b4237"
 dependencies = [
  "proc-macro2",
  "quote",
diff --git a/Cargo.toml b/Cargo.toml
index 626319e..d743794 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -22,13 +22,13 @@ edition = "2021"
 repository = "https://github.com/mtshiba/pylyzer"
 
 [workspace.dependencies]
-erg_common = { version = "0.6.7-nightly.0", features = ["py_compatible", "els"] }
-erg_compiler = { version = "0.6.7-nightly.0", features = ["py_compatible", "els"] }
-els = { version = "0.1.19-nightly.0", features = ["py_compatible"] }
+# erg_common = { version = "0.6.7-nightly.0", features = ["py_compatible", "els"] }
+# erg_compiler = { version = "0.6.7-nightly.0", features = ["py_compatible", "els"] }
+# els = { version = "0.1.19-nightly.0", features = ["py_compatible"] }
 rustpython-parser = "0.1.2"
-# erg_compiler = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible", "els"] }
-# erg_common = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible", "els"] }
-# els = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible"] }
+erg_compiler = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible", "els"] }
+erg_common = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible", "els"] }
+els = { git = "https://github.com/erg-lang/erg", branch = "main", features = ["py_compatible"] }
 
 [features]
 debug = ["erg_compiler/debug", "erg_common/debug", "py2erg/debug"]
diff --git a/README.md b/README.md
index 95ec148..3c9357e 100644
--- a/README.md
+++ b/README.md
@@ -90,7 +90,11 @@ pylyzer converts Python ASTs to Erg ASTs and passes them to Erg's type checker.
 * [x] local scripts resolving
 * [ ] local packages resolving
 * [ ] compound type checking
-* [ ] type assertion
+  * [x] `Union`
+  * [x] `Optional`
+  * [x] `list`
+  * [ ] others
+* [ ] type assertion (`typing.cast`)
 
 ---
 
diff --git a/crates/py2erg/convert.rs b/crates/py2erg/convert.rs
index 940d970..7f5a2a3 100644
--- a/crates/py2erg/convert.rs
+++ b/crates/py2erg/convert.rs
@@ -6,12 +6,13 @@ use erg_common::traits::{Locational, Stream};
 use erg_common::{log, set};
 use erg_compiler::artifact::IncompleteArtifact;
 use erg_compiler::erg_parser::ast::{
-    Accessor, Args, Array, BinOp, Block, ClassAttr, ClassAttrs, ClassDef, ConstArgs, Decorator,
-    Def, DefBody, DefId, DefaultParamSignature, Dict, Dummy, Expr, Identifier, KeyValue, Lambda,
-    LambdaSignature, Literal, Methods, Module, NonDefaultParamSignature, NormalArray, NormalDict,
-    NormalRecord, NormalSet, NormalTuple, ParamPattern, Params, PosArg, PreDeclTypeSpec, ReDef,
-    Record, RecordAttrs, Set, Signature, SimpleTypeSpec, SubrSignature, Tuple, TypeAscription,
-    TypeBoundSpecs, TypeSpec, TypeSpecWithOp, UnaryOp, VarName, VarPattern, VarSignature,
+    Accessor, Args, Array, ArrayTypeSpec, BinOp, Block, ClassAttr, ClassAttrs, ClassDef,
+    ConstAccessor, ConstArgs, ConstExpr, Decorator, Def, DefBody, DefId, DefaultParamSignature,
+    Dict, Dummy, Expr, Identifier, KeyValue, Lambda, LambdaSignature, Literal, Methods, Module,
+    NonDefaultParamSignature, NormalArray, NormalDict, NormalRecord, NormalSet, NormalTuple,
+    ParamPattern, Params, PosArg, PreDeclTypeSpec, ReDef, Record, RecordAttrs, Set, Signature,
+    SimpleTypeSpec, SubrSignature, Tuple, TypeAscription, TypeBoundSpecs, TypeSpec, TypeSpecWithOp,
+    UnaryOp, VarName, VarPattern, VarSignature,
 };
 use erg_compiler::erg_parser::token::{Token, TokenKind, COLON, DOT, EQUAL};
 use erg_compiler::error::CompileErrors;
@@ -502,17 +503,89 @@ impl ASTConverter {
         Lambda::new(sig, op, Block::new(body), DefId(0))
     }
 
+    fn convert_ident_type_spec(&mut self, name: String, loc: PyLocation) -> SimpleTypeSpec {
+        SimpleTypeSpec::new(self.convert_ident(name, loc), ConstArgs::empty())
+    }
+
+    fn gen_dummy_type_spec(loc: PyLocation) -> TypeSpec {
+        TypeSpec::Infer(Token::new(
+            TokenKind::UBar,
+            "_",
+            loc.row() as u32,
+            loc.column() as u32 - 1,
+        ))
+    }
+
+    // TODO:
+    fn convert_compound_type_spec(
+        &mut self,
+        name: String,
+        args: Located<ExpressionType>,
+    ) -> TypeSpec {
+        match &name[..] {
+            "Union" => {
+                let ExpressionType::Tuple { mut elements } = args.node else {
+                    return Self::gen_dummy_type_spec(args.location);
+                };
+                let lhs = self.convert_type_spec(elements.remove(0));
+                let rhs = self.convert_type_spec(elements.remove(0));
+                TypeSpec::or(lhs, rhs)
+            }
+            "Optional" => {
+                let loc = args.location;
+                let t = self.convert_type_spec(args);
+                let ident = Identifier::private_with_line("NoneType".into(), loc.row() as u32);
+                let none = TypeSpec::PreDeclTy(PreDeclTypeSpec::Simple(SimpleTypeSpec::new(
+                    ident,
+                    ConstArgs::empty(),
+                )));
+                TypeSpec::or(t, none)
+            }
+            "list" => {
+                let len = ConstExpr::Accessor(ConstAccessor::Local(
+                    self.convert_ident("_".into(), args.location),
+                ));
+                let elem_t = self.convert_type_spec(args);
+                TypeSpec::Array(ArrayTypeSpec::new(elem_t, len))
+            }
+            _ => Self::gen_dummy_type_spec(args.location),
+        }
+    }
+
     fn convert_type_spec(&mut self, expr: Located<ExpressionType>) -> TypeSpec {
+        #[allow(clippy::collapsible_match)]
         match expr.node {
             ExpressionType::Identifier { name } => TypeSpec::PreDeclTy(PreDeclTypeSpec::Simple(
-                SimpleTypeSpec::new(self.convert_ident(name, expr.location), ConstArgs::empty()),
-            )),
-            _other => TypeSpec::Infer(Token::new(
-                TokenKind::UBar,
-                "_",
-                expr.location.row() as u32,
-                expr.location.column() as u32 - 1,
+                self.convert_ident_type_spec(name, expr.location),
             )),
+            ExpressionType::Attribute { value, name } => {
+                let namespace = Box::new(self.convert_expr(*value));
+                let t = self.convert_ident_type_spec(name, expr.location);
+                let predecl = PreDeclTypeSpec::Attr { namespace, t };
+                TypeSpec::PreDeclTy(predecl)
+            }
+            ExpressionType::Subscript { a, b } => match a.node {
+                ExpressionType::Identifier { name } => self.convert_compound_type_spec(name, *b),
+                other => {
+                    log!(err "unknown: {other:?}");
+                    Self::gen_dummy_type_spec(a.location)
+                }
+            },
+            ExpressionType::Binop { a, op, b } => {
+                match op {
+                    // A | B
+                    Operator::BitOr => {
+                        let lhs = self.convert_type_spec(*a);
+                        let rhs = self.convert_type_spec(*b);
+                        TypeSpec::or(lhs, rhs)
+                    }
+                    _ => Self::gen_dummy_type_spec(expr.location),
+                }
+            }
+            other => {
+                log!(err "unknown: {other:?}");
+                Self::gen_dummy_type_spec(expr.location)
+            }
         }
     }
 
diff --git a/tests/test.rs b/tests/test.rs
index 0bd8e7e..339c9f7 100644
--- a/tests/test.rs
+++ b/tests/test.rs
@@ -70,3 +70,8 @@ fn exec_errors() {
 fn exec_warns() {
     expect("tests/warns.py", 2, 0);
 }
+
+#[test]
+fn exec_typespec() {
+    expect("tests/typespec.py", 0, 2);
+}
diff --git a/tests/typespec.py b/tests/typespec.py
new file mode 100644
index 0000000..f445b7c
--- /dev/null
+++ b/tests/typespec.py
@@ -0,0 +1,8 @@
+from typing import Union, Optional
+
+i: Union[int, str] = 1 # OK
+j: Union[int, str] = "aa" # OK
+k: Union[list[int], str] = 1 # ERR
+l: Union[list[int], str] = [1] # OK
+o: Optional[int] = None # OK
+p: Optional[int] = "a" # ERR