diff --git a/compiler/constrain/src/expr.rs b/compiler/constrain/src/expr.rs
index eac7d8f1fc..c0356f2368 100644
--- a/compiler/constrain/src/expr.rs
+++ b/compiler/constrain/src/expr.rs
@@ -739,11 +739,10 @@ pub fn constrain_expr(
                 region,
             );
 
-            let ext = Type::Variable(*closure_var);
-            let lambda_set = Type::TagUnion(
-                vec![(TagName::Closure(*closure_name), vec![])],
-                Box::new(ext),
-            );
+            let lambda_set = Type::ClosureTag {
+                name: *closure_name,
+                ext: *closure_var,
+            };
 
             let function_type = Type::Function(
                 vec![record_type],
@@ -1416,7 +1415,7 @@ fn constrain_closure_size(
         ));
     }
 
-    let tag_name = roc_module::ident::TagName::Closure(name);
+    let tag_name = TagName::Closure(name);
     let closure_type = Type::TagUnion(
         vec![(tag_name, tag_arguments)],
         Box::new(Type::Variable(closure_ext_var)),
diff --git a/compiler/solve/src/solve.rs b/compiler/solve/src/solve.rs
index c4a4eb98dc..d9ce0d3153 100644
--- a/compiler/solve/src/solve.rs
+++ b/compiler/solve/src/solve.rs
@@ -690,6 +690,19 @@ fn type_to_variable<'a>(
         EmptyRec => Variable::EMPTY_RECORD,
         EmptyTagUnion => Variable::EMPTY_TAG_UNION,
 
+        ClosureTag { name, ext } => {
+            let tag_name = TagName::Closure(*name);
+            let tag_names = SubsSlice::new(subs.tag_names.len() as u32, 1);
+
+            subs.tag_names.push(tag_name);
+
+            let union_tags = UnionTags::from_slices(tag_names, SubsSlice::default());
+
+            let content = Content::Structure(FlatType::TagUnion(union_tags, *ext));
+
+            register(subs, rank, pools, content)
+        }
+
         // This case is important for the rank of boolean variables
         Function(arguments, closure_type, ret_type) => {
             let new_arguments = VariableSubsSlice::reserve_into_subs(subs, arguments.len());
diff --git a/compiler/types/src/solved_types.rs b/compiler/types/src/solved_types.rs
index 2473597a35..3fe67edf2f 100644
--- a/compiler/types/src/solved_types.rs
+++ b/compiler/types/src/solved_types.rs
@@ -130,6 +130,11 @@ impl SolvedType {
                     ext: Box::new(solved_ext),
                 }
             }
+            ClosureTag { name, ext } => {
+                let solved_ext = Self::from_type(solved_subs, &Type::Variable(*ext));
+                let solved_tags = vec![(TagName::Closure(*name), vec![])];
+                SolvedType::TagUnion(solved_tags, Box::new(solved_ext))
+            }
             TagUnion(tags, box_ext) => {
                 let solved_ext = Self::from_type(solved_subs, box_ext);
                 let mut solved_tags = Vec::with_capacity(tags.len());
diff --git a/compiler/types/src/types.rs b/compiler/types/src/types.rs
index 96e0190a43..04130e2484 100644
--- a/compiler/types/src/types.rs
+++ b/compiler/types/src/types.rs
@@ -169,6 +169,11 @@ pub enum Type {
     Record(SendMap<Lowercase, RecordField<Type>>, Box<Type>),
     TagUnion(Vec<(TagName, Vec<Type>)>, Box<Type>),
     FunctionOrTagUnion(TagName, Symbol, Box<Type>),
+    /// A function name that is used in our defunctionalization algorithm
+    ClosureTag {
+        name: Symbol,
+        ext: Variable,
+    },
     Alias {
         symbol: Symbol,
         type_arguments: Vec<(Lowercase, Type)>,
@@ -378,6 +383,15 @@ impl fmt::Debug for Type {
                     }
                 }
             }
+            Type::ClosureTag { name, ext } => {
+                write!(f, "ClosureTag(")?;
+
+                name.fmt(f)?;
+                write!(f, ", ")?;
+                ext.fmt(f)?;
+
+                write!(f, ")")
+            }
             Type::RecursiveTagUnion(rec, tags, ext) => {
                 write!(f, "[")?;
 
@@ -462,7 +476,7 @@ impl Type {
         use Type::*;
 
         match self {
-            Variable(v) => {
+            ClosureTag { ext: v, .. } | Variable(v) => {
                 if let Some(replacement) = substitutions.get(v) {
                     *self = replacement.clone();
                 }
@@ -590,7 +604,7 @@ impl Type {
                     arg.substitute_alias(rep_symbol, actual);
                 }
             }
-            EmptyRec | EmptyTagUnion | Erroneous(_) | Variable(_) => {}
+            EmptyRec | EmptyTagUnion | ClosureTag { .. } | Erroneous(_) | Variable(_) => {}
         }
     }
 
@@ -627,7 +641,7 @@ impl Type {
             }
             Apply(symbol, _) if *symbol == rep_symbol => true,
             Apply(_, args) => args.iter().any(|arg| arg.contains_symbol(rep_symbol)),
-            EmptyRec | EmptyTagUnion | Erroneous(_) | Variable(_) => false,
+            EmptyRec | EmptyTagUnion | ClosureTag { .. } | Erroneous(_) | Variable(_) => false,
         }
     }
 
@@ -635,7 +649,7 @@ impl Type {
         use Type::*;
 
         match self {
-            Variable(v) => *v == rep_variable,
+            ClosureTag { ext: v, .. } | Variable(v) => *v == rep_variable,
             Function(args, closure, ret) => {
                 ret.contains_variable(rep_variable)
                     || closure.contains_variable(rep_variable)
@@ -819,7 +833,7 @@ impl Type {
                     }
                 }
             }
-            EmptyRec | EmptyTagUnion | Erroneous(_) | Variable(_) => {}
+            EmptyRec | EmptyTagUnion | ClosureTag { .. } | Erroneous(_) | Variable(_) => {}
         }
     }
 }
@@ -872,7 +886,7 @@ fn symbols_help(tipe: &Type, accum: &mut ImSet<Symbol>) {
             accum.insert(*symbol);
             args.iter().for_each(|arg| symbols_help(arg, accum));
         }
-        EmptyRec | EmptyTagUnion | Erroneous(_) | Variable(_) => {}
+        EmptyRec | EmptyTagUnion | ClosureTag { .. } | Erroneous(_) | Variable(_) => {}
     }
 }
 
@@ -882,7 +896,7 @@ fn variables_help(tipe: &Type, accum: &mut ImSet<Variable>) {
     match tipe {
         EmptyRec | EmptyTagUnion | Erroneous(_) => (),
 
-        Variable(v) => {
+        ClosureTag { ext: v, .. } | Variable(v) => {
             accum.insert(*v);
         }
 
@@ -979,7 +993,7 @@ fn variables_help_detailed(tipe: &Type, accum: &mut VariableDetail) {
     match tipe {
         EmptyRec | EmptyTagUnion | Erroneous(_) => (),
 
-        Variable(v) => {
+        ClosureTag { ext: v, .. } | Variable(v) => {
             accum.type_variables.insert(*v);
         }