diff --git a/compiler/erg_compiler/context/compare.rs b/compiler/erg_compiler/context/compare.rs
index 6dfa9127..2d9fa91f 100644
--- a/compiler/erg_compiler/context/compare.rs
+++ b/compiler/erg_compiler/context/compare.rs
@@ -606,10 +606,10 @@ impl Context {
                 self.poly_supertype_of(lhs, lparams, rparams)
             }
             (MonoQVar(name), r) | (PolyQVar { name, .. }, r) => {
-                panic!("Not instantiated type variable: {name}, r: {r}")
+                panic!("internal error: not instantiated type variable: '{name}, r: {r}")
             }
             (l, MonoQVar(name)) | (l, PolyQVar { name, .. }) => {
-                panic!("Not instantiated type variable: {name}, l: {l}")
+                panic!("internal error: not instantiated type variable: '{name}, l: {l}")
             }
             (MonoProj { .. }, _) => todo!(),
             (_, MonoProj { .. }) => todo!(),
diff --git a/compiler/erg_compiler/context/instantiate.rs b/compiler/erg_compiler/context/instantiate.rs
index f7645de3..6a6d9f5c 100644
--- a/compiler/erg_compiler/context/instantiate.rs
+++ b/compiler/erg_compiler/context/instantiate.rs
@@ -133,6 +133,7 @@ impl TyVarContext {
         params
             .into_iter()
             .map(|p| {
+                erg_common::log!(err "p: {p}, {:?}", p.tvar_name());
                 if let Some(name) = p.tvar_name() {
                     let tp = self.instantiate_qtp(p);
                     self.push_or_init_typaram(&name, &tp);
@@ -243,7 +244,7 @@ impl TyVarContext {
                 }
             }
             TyParam::Type(t) => {
-                if let Type::MonoQVar(n) = *t {
+                if let Some(n) = t.as_ref().tvar_name() {
                     if let Some(t) = self.get_typaram(&n) {
                         t.clone()
                     } else if let Some(t) = self.get_tyvar(&n) {
@@ -254,7 +255,7 @@ impl TyVarContext {
                         TyParam::t(tv)
                     }
                 } else {
-                    todo!("{t}")
+                    unreachable!("{t}")
                 }
             }
             TyParam::UnaryOp { op, val } => {
@@ -336,6 +337,7 @@ impl TyVarContext {
     }
 }
 
+/// TODO: this struct will be removed when const functions are implemented.
 #[derive(Debug, Clone, PartialEq, Eq, Hash)]
 pub enum ConstTemplate {
     Obj(ValueObj),
@@ -766,6 +768,9 @@ impl Context {
                 let t = Self::instantiate_t(*t, tv_ctx, loc)?;
                 Ok(TyParam::t(t))
             }
+            TyParam::FreeVar(fv) if fv.is_linked() => {
+                Self::instantiate_tp(fv.crack().clone(), tv_ctx, loc)
+            }
             p @ (TyParam::Value(_) | TyParam::Mono(_) | TyParam::FreeVar(_)) => Ok(p),
             other => todo!("{other}"),
         }
@@ -867,6 +872,7 @@ impl Context {
             Quantified(_) => {
                 panic!("a quantified type should not be instantiated, instantiate the inner type")
             }
+            FreeVar(fv) if fv.is_linked() => Self::instantiate_t(fv.crack().clone(), tv_ctx, loc),
             other if other.is_monomorphic() => Ok(other),
             other => todo!("{other}"),
         }
diff --git a/compiler/erg_type/lib.rs b/compiler/erg_type/lib.rs
index 1176d89f..20c2538c 100644
--- a/compiler/erg_type/lib.rs
+++ b/compiler/erg_type/lib.rs
@@ -1817,6 +1817,7 @@ impl Type {
 
     pub fn tvar_name(&self) -> Option<Str> {
         match self {
+            Self::FreeVar(fv) if fv.is_linked() => fv.crack().tvar_name(),
             Self::FreeVar(fv) => fv.unbound_name(),
             Self::MonoQVar(name) => Some(name.clone()),
             _ => None,
diff --git a/compiler/erg_type/typaram.rs b/compiler/erg_type/typaram.rs
index 2be0a1bd..a96cfe37 100644
--- a/compiler/erg_type/typaram.rs
+++ b/compiler/erg_type/typaram.rs
@@ -509,6 +509,7 @@ impl TyParam {
     pub fn name(&self) -> Option<Str> {
         match self {
             Self::Type(t) => Some(t.name()),
+            Self::FreeVar(fv) if fv.is_linked() => fv.crack().name(),
             Self::Mono(name) => Some(name.clone()),
             Self::MonoQVar(name) => Some(name.clone()),
             _ => None,
@@ -518,6 +519,7 @@ impl TyParam {
     pub fn tvar_name(&self) -> Option<Str> {
         match self {
             Self::Type(t) => t.tvar_name(),
+            Self::FreeVar(fv) if fv.is_linked() => fv.crack().tvar_name(),
             Self::FreeVar(fv) => fv.unbound_name(),
             Self::MonoQVar(name) => Some(name.clone()),
             _ => None,