diff --git a/crates/erg_compiler/context/compare.rs b/crates/erg_compiler/context/compare.rs
index 5707af044..f6125066d 100644
--- a/crates/erg_compiler/context/compare.rs
+++ b/crates/erg_compiler/context/compare.rs
@@ -816,6 +816,7 @@ impl Context {
             }
             // Int or Str :> Str or Int == (Int :> Str && Str :> Int) || (Int :> Int && Str :> Str) == true
             // Int or Str or NoneType :> Str or Int
+            // Int or Str or NoneType :> Str or NoneType or Nat
             (Or(l), Or(r)) => r.iter().all(|r| l.iter().any(|l| self.supertype_of(l, r))),
             // not Nat :> not Int == true
             (Not(l), Not(r)) => self.subtype_of(l, r),
diff --git a/crates/erg_compiler/context/unify.rs b/crates/erg_compiler/context/unify.rs
index 3df47f5c5..fea7e0dcc 100644
--- a/crates/erg_compiler/context/unify.rs
+++ b/crates/erg_compiler/context/unify.rs
@@ -156,6 +156,7 @@ impl<'c, 'l, 'u, L: Locational> Unifier<'c, 'l, 'u, L> {
                 }
                 Ok(())
             }
+            // FIXME: This is not correct, we must visit all permutations of the types
             (And(l), And(r)) if l.len() == r.len() => {
                 let mut r = r.clone();
                 for _ in 0..r.len() {
@@ -1297,65 +1298,58 @@ impl<'c, 'l, 'u, L: Locational> Unifier<'c, 'l, 'u, L> {
                 // self.sub_unify(&lsub, &union, loc, param_name)?;
                 maybe_sup.update_tyvar(union, intersec, self.undoable, false);
             }
+            // TODO: Preferentially compare same-structure types (e.g. K(?T) <: K(?U))
             (And(ltys), And(rtys)) => {
-                let mut rtys = rtys.clone();
-                for _ in 0..rtys.len() {
-                    if ltys
-                        .iter()
-                        .zip(rtys.iter())
-                        .all(|(l, r)| self.ctx.subtype_of(l, r))
-                    {
-                        for (l, r) in ltys.iter().zip(rtys.iter()) {
-                            self.sub_unify(l, r)?;
+                let mut ltys_ = ltys.clone();
+                let mut rtys_ = rtys.clone();
+                // Show and EqHash and T <: Eq and Show and Ord
+                // => EqHash and T <: Eq and Ord
+                for lty in ltys.iter() {
+                    if let Some(idx) = rtys_.iter().position(|r| r == lty) {
+                        rtys_.remove(idx);
+                        let idx = ltys_.iter().position(|l| l == lty).unwrap();
+                        ltys_.remove(idx);
+                    }
+                }
+                // EqHash and T <: Eq and Ord
+                for lty in ltys_.iter() {
+                    // lty: EqHash
+                    // rty: Eq, Ord
+                    for rty in rtys_.iter() {
+                        if self.ctx.subtype_of(lty, rty) {
+                            self.sub_unify(lty, rty)?;
+                            continue;
                         }
-                        return Ok(());
                     }
-                    rtys.rotate_left(1);
                 }
-                return Err(TyCheckErrors::from(TyCheckError::type_mismatch_error(
-                    self.ctx.cfg.input.clone(),
-                    line!() as usize,
-                    self.loc.loc(),
-                    self.ctx.caused_by(),
-                    self.param_name.as_ref().unwrap_or(&Str::ever("_")),
-                    None,
-                    maybe_sup,
-                    maybe_sub,
-                    self.ctx.get_candidates(maybe_sub),
-                    self.ctx.get_simple_type_mismatch_hint(maybe_sup, maybe_sub),
-                )));
             }
+            // TODO: Preferentially compare same-structure types (e.g. K(?T) <: K(?U))
+            // Nat or Str or NoneType <: NoneType or ?T or Int
+            // => Str <: ?T
             // (Int or ?T) <: (?U or Int)
             // OK: (Int <: Int); (?T <: ?U)
             // NG: (Int <: ?U); (?T <: Int)
             (Or(ltys), Or(rtys)) => {
-                let ltys = ltys.to_vec();
-                let mut rtys = rtys.to_vec();
-                for _ in 0..rtys.len() {
-                    if ltys
-                        .iter()
-                        .zip(rtys.iter())
-                        .all(|(l, r)| self.ctx.subtype_of(l, r))
-                    {
-                        for (l, r) in ltys.iter().zip(rtys.iter()) {
-                            self.sub_unify(l, r)?;
+                let mut ltys_ = ltys.clone();
+                let mut rtys_ = rtys.clone();
+                // Nat or T or Str <: Str or Int or NoneType
+                // => Nat or T <: Int or NoneType
+                for lty in ltys {
+                    if rtys_.linear_remove(lty) {
+                        ltys_.linear_remove(lty);
+                    }
+                }
+                // Nat or T <: Int or NoneType
+                for lty in ltys_.iter() {
+                    // lty: Nat
+                    // rty: Int, NoneType
+                    for rty in rtys_.iter() {
+                        if self.ctx.subtype_of(lty, rty) {
+                            self.sub_unify(lty, rty)?;
+                            continue;
                         }
-                        return Ok(());
                     }
-                    rtys.rotate_left(1);
                 }
-                return Err(TyCheckErrors::from(TyCheckError::type_mismatch_error(
-                    self.ctx.cfg.input.clone(),
-                    line!() as usize,
-                    self.loc.loc(),
-                    self.ctx.caused_by(),
-                    self.param_name.as_ref().unwrap_or(&Str::ever("_")),
-                    None,
-                    maybe_sup,
-                    maybe_sub,
-                    self.ctx.get_candidates(maybe_sub),
-                    self.ctx.get_simple_type_mismatch_hint(maybe_sup, maybe_sub),
-                )));
             }
             // NG: Nat <: ?T or Int ==> Nat or Int (?T = Nat)
             // OK: Nat <: ?T or Int ==> ?T or Int
diff --git a/tests/should_err/and.er b/tests/should_err/and.er
new file mode 100644
index 000000000..a16daf02c
--- /dev/null
+++ b/tests/should_err/and.er
@@ -0,0 +1,3 @@
+a as Eq and Hash and Show and Add(Str) = "a"
+f _: Ord and Eq and Show and Hash = None
+f a # ERR
diff --git a/tests/should_err/or.er b/tests/should_err/or.er
new file mode 100644
index 000000000..20e8937da
--- /dev/null
+++ b/tests/should_err/or.er
@@ -0,0 +1,3 @@
+a as Int or Str or NoneType = 1
+f _: Nat or NoneType or Str = None
+f a # ERR
diff --git a/tests/should_ok/and.er b/tests/should_ok/and.er
new file mode 100644
index 000000000..4f3bee0d7
--- /dev/null
+++ b/tests/should_ok/and.er
@@ -0,0 +1,7 @@
+a as Eq and Hash and Show = 1
+f _: Eq and Show and Hash = None
+f a
+
+b as Eq and Hash and Ord and Show = 1
+g _: Ord and Eq and Show and Hash = None
+g b
diff --git a/tests/should_ok/or.er b/tests/should_ok/or.er
new file mode 100644
index 000000000..2e36f19b0
--- /dev/null
+++ b/tests/should_ok/or.er
@@ -0,0 +1,7 @@
+a as Nat or Str or NoneType = 1
+f _: Int or NoneType or Str = None
+f a
+
+b as Nat or Str or NoneType or Bool = 1
+g _: Int or NoneType or Bool or Str = None
+g b
diff --git a/tests/test.rs b/tests/test.rs
index 3259eee09..4ed20fb92 100644
--- a/tests/test.rs
+++ b/tests/test.rs
@@ -16,6 +16,11 @@ fn exec_advanced_type_spec() -> Result<(), ()> {
     expect_success("tests/should_ok/advanced_type_spec.er", 5)
 }
 
+#[test]
+fn exec_and() -> Result<(), ()> {
+    expect_success("tests/should_ok/and.er", 0)
+}
+
 #[test]
 fn exec_args_expansion() -> Result<(), ()> {
     expect_success("tests/should_ok/args_expansion.er", 0)
@@ -327,6 +332,11 @@ fn exec_operators() -> Result<(), ()> {
     expect_success("tests/should_ok/operators.er", 0)
 }
 
+#[test]
+fn exec_or() -> Result<(), ()> {
+    expect_success("tests/should_ok/or.er", 0)
+}
+
 #[test]
 fn exec_patch() -> Result<(), ()> {
     expect_success("examples/patch.er", 0)
@@ -527,6 +537,11 @@ fn exec_list_member_err() -> Result<(), ()> {
     expect_failure("tests/should_err/list_member.er", 0, 3)
 }
 
+#[test]
+fn exec_and_err() -> Result<(), ()> {
+    expect_failure("tests/should_err/and.er", 0, 1)
+}
+
 #[test]
 fn exec_as() -> Result<(), ()> {
     expect_failure("tests/should_err/as.er", 0, 6)
@@ -634,6 +649,11 @@ fn exec_move_check() -> Result<(), ()> {
     expect_failure("examples/move_check.er", 1, 1)
 }
 
+#[test]
+fn exec_or_err() -> Result<(), ()> {
+    expect_failure("tests/should_err/or.er", 0, 1)
+}
+
 #[test]
 fn exec_poly_type_spec_err() -> Result<(), ()> {
     expect_failure("tests/should_err/poly_type_spec.er", 0, 3)