diff --git a/compiler/can/src/annotation.rs b/compiler/can/src/annotation.rs
index a3c8ed95d2..51a36c1b53 100644
--- a/compiler/can/src/annotation.rs
+++ b/compiler/can/src/annotation.rs
@@ -234,7 +234,12 @@ fn can_annotation_help(
                     // instantiate variables
                     actual.substitute(&substitutions);
 
-                    Type::Alias(symbol, vars, Box::new(actual))
+                    Type::Alias {
+                        symbol,
+                        type_arguments: vars,
+                        lambda_set_variables: alias.lambda_set_variables.clone(),
+                        actual: Box::new(actual),
+                    }
                 }
                 None => {
                     let mut args = Vec::new();
@@ -378,7 +383,12 @@ fn can_annotation_help(
                         actual_var,
                     }
                 } else {
-                    Type::Alias(symbol, vars, Box::new(alias.typ.clone()))
+                    Type::Alias {
+                        symbol,
+                        type_arguments: vars,
+                        lambda_set_variables: alias.lambda_set_variables.clone(),
+                        actual: Box::new(alias.typ.clone()),
+                    }
                 }
             }
             _ => {
diff --git a/compiler/can/src/constraint.rs b/compiler/can/src/constraint.rs
index dfac99f49e..931c43f9b5 100644
--- a/compiler/can/src/constraint.rs
+++ b/compiler/can/src/constraint.rs
@@ -76,7 +76,7 @@ fn subtract(declared: &Declared, detail: &VariableDetail, accum: &mut VariableDe
         }
 
         if !declared.flex_vars.contains(&var.into_inner()) {
-            accum.lambda_set_variables.insert(*var);
+            accum.lambda_set_variables.push(*var);
         }
     }
 
diff --git a/compiler/can/src/def.rs b/compiler/can/src/def.rs
index b4a4652924..336d9cc7f2 100644
--- a/compiler/can/src/def.rs
+++ b/compiler/can/src/def.rs
@@ -1634,7 +1634,7 @@ fn make_tag_union_recursive<'a>(
             typ.substitute_alias(symbol, &Type::Variable(rec_var));
         }
         Type::RecursiveTagUnion(_, _, _) => {}
-        Type::Alias(_, _, actual) => make_tag_union_recursive(
+        Type::Alias { actual, .. } => make_tag_union_recursive(
             env,
             symbol,
             region,
diff --git a/compiler/can/src/scope.rs b/compiler/can/src/scope.rs
index 9037d6e193..ecfb3fa03b 100644
--- a/compiler/can/src/scope.rs
+++ b/compiler/can/src/scope.rs
@@ -47,7 +47,7 @@ impl Scope {
             let alias = Alias {
                 region,
                 typ,
-                lambda_set_variables: MutSet::default(),
+                lambda_set_variables: Vec::new(),
                 recursion_variables: MutSet::default(),
                 type_variables: variables,
             };
diff --git a/compiler/constrain/src/builtins.rs b/compiler/constrain/src/builtins.rs
index 4704c67539..c47a1e5796 100644
--- a/compiler/constrain/src/builtins.rs
+++ b/compiler/constrain/src/builtins.rs
@@ -2,7 +2,7 @@ use roc_can::constraint::Constraint::{self, *};
 use roc_can::constraint::LetConstraint;
 use roc_can::expected::Expected::{self, *};
 use roc_collections::all::SendMap;
-use roc_module::ident::TagName;
+use roc_module::ident::{Lowercase, TagName};
 use roc_module::symbol::Symbol;
 use roc_region::all::Region;
 use roc_types::subs::Variable;
@@ -89,9 +89,23 @@ pub fn str_type() -> Type {
     builtin_type(Symbol::STR_STR, Vec::new())
 }
 
+#[inline(always)]
+fn builtin_alias(
+    symbol: Symbol,
+    type_arguments: Vec<(Lowercase, Type)>,
+    actual: Box<Type>,
+) -> Type {
+    Type::Alias {
+        symbol,
+        type_arguments,
+        actual,
+        lambda_set_variables: vec![],
+    }
+}
+
 #[inline(always)]
 pub fn num_float(range: Type) -> Type {
-    Type::Alias(
+    builtin_alias(
         Symbol::NUM_FLOAT,
         vec![("range".into(), range.clone())],
         Box::new(num_num(num_floatingpoint(range))),
@@ -108,7 +122,7 @@ pub fn num_floatingpoint(range: Type) -> Type {
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(
+    builtin_alias(
         Symbol::NUM_FLOATINGPOINT,
         vec![("range".into(), range)],
         Box::new(alias_content),
@@ -122,12 +136,12 @@ pub fn num_binary64() -> Type {
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(Symbol::NUM_BINARY64, vec![], Box::new(alias_content))
+    builtin_alias(Symbol::NUM_BINARY64, vec![], Box::new(alias_content))
 }
 
 #[inline(always)]
 pub fn num_int(range: Type) -> Type {
-    Type::Alias(
+    builtin_alias(
         Symbol::NUM_INT,
         vec![("range".into(), range.clone())],
         Box::new(num_num(num_integer(range))),
@@ -141,7 +155,7 @@ pub fn num_signed64() -> Type {
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(Symbol::NUM_SIGNED64, vec![], Box::new(alias_content))
+    builtin_alias(Symbol::NUM_SIGNED64, vec![], Box::new(alias_content))
 }
 
 #[inline(always)]
@@ -154,7 +168,7 @@ pub fn num_integer(range: Type) -> Type {
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(
+    builtin_alias(
         Symbol::NUM_INTEGER,
         vec![("range".into(), range)],
         Box::new(alias_content),
@@ -168,7 +182,7 @@ pub fn num_num(typ: Type) -> Type {
         Box::new(Type::EmptyTagUnion),
     );
 
-    Type::Alias(
+    builtin_alias(
         Symbol::NUM_NUM,
         vec![("range".into(), typ)],
         Box::new(alias_content),
diff --git a/compiler/load/src/effect_module.rs b/compiler/load/src/effect_module.rs
index 5dab90a4f8..798c7b45c3 100644
--- a/compiler/load/src/effect_module.rs
+++ b/compiler/load/src/effect_module.rs
@@ -1,3 +1,4 @@
+use roc_can::annotation::IntroducedVariables;
 use roc_can::def::{Declaration, Def};
 use roc_can::env::Env;
 use roc_can::expr::{Expr, Recursive};
@@ -160,25 +161,22 @@ fn build_effect_always(
         (function_var, closure)
     };
 
-    use roc_can::annotation::IntroducedVariables;
-
     let mut introduced_variables = IntroducedVariables::default();
 
     let signature = {
         // Effect.always : a -> Effect a
         let var_a = var_store.fresh();
-
         introduced_variables.insert_named("a".into(), var_a);
 
-        let effect_a = {
-            let actual = build_effect_actual(effect_tag_name, Type::Variable(var_a), var_store);
-
-            Type::Alias(
-                effect_symbol,
-                vec![("a".into(), Type::Variable(var_a))],
-                Box::new(actual),
-            )
-        };
+        let effect_a = build_effect_alias(
+            effect_symbol,
+            effect_tag_name,
+            "a",
+            var_a,
+            Type::Variable(var_a),
+            var_store,
+            &mut introduced_variables,
+        );
 
         let closure_var = var_store.fresh();
         introduced_variables.insert_wildcard(closure_var);
@@ -353,8 +351,6 @@ fn build_effect_map(
         loc_body: Box::new(Located::at_zero(body)),
     };
 
-    use roc_can::annotation::IntroducedVariables;
-
     let mut introduced_variables = IntroducedVariables::default();
 
     let signature = {
@@ -365,26 +361,25 @@ fn build_effect_map(
         introduced_variables.insert_named("a".into(), var_a);
         introduced_variables.insert_named("b".into(), var_b);
 
-        let effect_a = {
-            let actual =
-                build_effect_actual(effect_tag_name.clone(), Type::Variable(var_a), var_store);
+        let effect_a = build_effect_alias(
+            effect_symbol,
+            effect_tag_name.clone(),
+            "a",
+            var_a,
+            Type::Variable(var_a),
+            var_store,
+            &mut introduced_variables,
+        );
 
-            Type::Alias(
-                effect_symbol,
-                vec![("a".into(), Type::Variable(var_a))],
-                Box::new(actual),
-            )
-        };
-
-        let effect_b = {
-            let actual = build_effect_actual(effect_tag_name, Type::Variable(var_b), var_store);
-
-            Type::Alias(
-                effect_symbol,
-                vec![("b".into(), Type::Variable(var_b))],
-                Box::new(actual),
-            )
-        };
+        let effect_b = build_effect_alias(
+            effect_symbol,
+            effect_tag_name,
+            "b",
+            var_b,
+            Type::Variable(var_b),
+            var_store,
+            &mut introduced_variables,
+        );
 
         let closure_var = var_store.fresh();
         introduced_variables.insert_wildcard(closure_var);
@@ -526,8 +521,6 @@ fn build_effect_after(
         loc_body: Box::new(Located::at_zero(to_effect_call)),
     };
 
-    use roc_can::annotation::IntroducedVariables;
-
     let mut introduced_variables = IntroducedVariables::default();
 
     let signature = {
@@ -537,26 +530,25 @@ fn build_effect_after(
         introduced_variables.insert_named("a".into(), var_a);
         introduced_variables.insert_named("b".into(), var_b);
 
-        let effect_a = {
-            let actual =
-                build_effect_actual(effect_tag_name.clone(), Type::Variable(var_a), var_store);
+        let effect_a = build_effect_alias(
+            effect_symbol,
+            effect_tag_name.clone(),
+            "a",
+            var_a,
+            Type::Variable(var_a),
+            var_store,
+            &mut introduced_variables,
+        );
 
-            Type::Alias(
-                effect_symbol,
-                vec![("a".into(), Type::Variable(var_a))],
-                Box::new(actual),
-            )
-        };
-
-        let effect_b = {
-            let actual = build_effect_actual(effect_tag_name, Type::Variable(var_b), var_store);
-
-            Type::Alias(
-                effect_symbol,
-                vec![("b".into(), Type::Variable(var_b))],
-                Box::new(actual),
-            )
-        };
+        let effect_b = build_effect_alias(
+            effect_symbol,
+            effect_tag_name,
+            "b",
+            var_b,
+            Type::Variable(var_b),
+            var_store,
+            &mut introduced_variables,
+        );
 
         let closure_var = var_store.fresh();
         introduced_variables.insert_wildcard(closure_var);
@@ -763,6 +755,40 @@ pub fn build_host_exposed_def(
     }
 }
 
+fn build_effect_alias(
+    effect_symbol: Symbol,
+    effect_tag_name: TagName,
+    a_name: &str,
+    a_var: Variable,
+    a_type: Type,
+    var_store: &mut VarStore,
+    introduced_variables: &mut IntroducedVariables,
+) -> Type {
+    let closure_var = var_store.fresh();
+    introduced_variables.insert_wildcard(closure_var);
+
+    let actual = {
+        Type::TagUnion(
+            vec![(
+                effect_tag_name,
+                vec![Type::Function(
+                    vec![Type::EmptyRec],
+                    Box::new(Type::Variable(closure_var)),
+                    Box::new(a_type),
+                )],
+            )],
+            Box::new(Type::EmptyTagUnion),
+        )
+    };
+
+    Type::Alias {
+        symbol: effect_symbol,
+        type_arguments: vec![(a_name.into(), Type::Variable(a_var))],
+        lambda_set_variables: vec![roc_types::subs::LambdaSet(closure_var)],
+        actual: Box::new(actual),
+    }
+}
+
 pub fn build_effect_actual(
     effect_tag_name: TagName,
     a_type: Type,
diff --git a/compiler/solve/src/solve.rs b/compiler/solve/src/solve.rs
index 914c7149b7..16f969d045 100644
--- a/compiler/solve/src/solve.rs
+++ b/compiler/solve/src/solve.rs
@@ -790,8 +790,14 @@ fn type_to_variable(
 
             tag_union_var
         }
-        Alias(Symbol::BOOL_BOOL, _, _) => Variable::BOOL,
-        Alias(symbol, args, alias_type) => {
+
+        Type::Alias {
+            symbol,
+            type_arguments: args,
+            actual: alias_type,
+            lambda_set_variables,
+        } => {
+            dbg!(lambda_set_variables);
             let mut arg_vars = Vec::with_capacity(args.len());
 
             for (arg, arg_type) in args {
diff --git a/compiler/types/src/solved_types.rs b/compiler/types/src/solved_types.rs
index 4bf65f0966..d091ea8413 100644
--- a/compiler/types/src/solved_types.rs
+++ b/compiler/types/src/solved_types.rs
@@ -183,6 +183,7 @@ pub enum SolvedType {
     Erroneous(Problem),
 
     /// A type alias
+    /// TODO transmit lambda sets!
     Alias(Symbol, Vec<(Lowercase, SolvedType)>, Box<SolvedType>),
 
     HostExposedAlias {
@@ -293,11 +294,16 @@ impl SolvedType {
                 )
             }
             Erroneous(problem) => SolvedType::Erroneous(problem.clone()),
-            Alias(symbol, args, box_type) => {
+            Alias {
+                symbol,
+                type_arguments,
+                actual: box_type,
+                ..
+            } => {
                 let solved_type = Self::from_type(solved_subs, box_type);
-                let mut solved_args = Vec::with_capacity(args.len());
+                let mut solved_args = Vec::with_capacity(type_arguments.len());
 
-                for (name, var) in args {
+                for (name, var) in type_arguments {
                     solved_args.push((name.clone(), Self::from_type(solved_subs, var)));
                 }
 
@@ -617,7 +623,12 @@ pub fn to_type(
 
             let actual = to_type(solved_actual, free_vars, var_store);
 
-            Type::Alias(*symbol, type_variables, Box::new(actual))
+            Type::Alias {
+                symbol: *symbol,
+                type_arguments: type_variables,
+                lambda_set_variables: vec![], // TODO transfer lambda sets
+                actual: Box::new(actual),
+            }
         }
         HostExposedAlias {
             name,
diff --git a/compiler/types/src/subs.rs b/compiler/types/src/subs.rs
index fa240dad0c..5875fc8924 100644
--- a/compiler/types/src/subs.rs
+++ b/compiler/types/src/subs.rs
@@ -206,7 +206,7 @@ impl UnifyKey for Variable {
 }
 
 #[derive(Copy, Clone, PartialEq, Eq, Hash, PartialOrd, Ord)]
-pub struct LambdaSet(Variable);
+pub struct LambdaSet(pub Variable);
 
 impl fmt::Debug for LambdaSet {
     fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
diff --git a/compiler/types/src/types.rs b/compiler/types/src/types.rs
index 7e0e54d3f4..56f7443f6d 100644
--- a/compiler/types/src/types.rs
+++ b/compiler/types/src/types.rs
@@ -12,6 +12,11 @@ pub const TYPE_NUM: &str = "Num";
 pub const TYPE_INTEGER: &str = "Integer";
 pub const TYPE_FLOATINGPOINT: &str = "FloatingPoint";
 
+const GREEK_LETTERS: &[char] = &[
+    'α', 'ν', 'β', 'ξ', 'γ', 'ο', 'δ', 'π', 'ε', 'ρ', 'ζ', 'σ', 'η', 'τ', 'θ', 'υ', 'ι', 'φ', 'κ',
+    'χ', 'λ', 'ψ', 'μ', 'ω', 'ς',
+];
+
 ///
 /// Intuitively
 ///
@@ -142,7 +147,12 @@ pub enum Type {
     Record(SendMap<Lowercase, RecordField<Type>>, Box<Type>),
     TagUnion(Vec<(TagName, Vec<Type>)>, Box<Type>),
     FunctionOrTagUnion(TagName, Symbol, Box<Type>),
-    Alias(Symbol, Vec<(Lowercase, Type)>, Box<Type>),
+    Alias {
+        symbol: Symbol,
+        type_arguments: Vec<(Lowercase, Type)>,
+        lambda_set_variables: Vec<LambdaSet>,
+        actual: Box<Type>,
+    },
     HostExposedAlias {
         name: Symbol,
         arguments: Vec<(Lowercase, Type)>,
@@ -198,13 +208,22 @@ impl fmt::Debug for Type {
 
                 write!(f, ")")
             }
-            Type::Alias(symbol, args, _actual) => {
+            Type::Alias {
+                symbol,
+                type_arguments,
+                lambda_set_variables,
+                ..
+            } => {
                 write!(f, "Alias {:?}", symbol)?;
 
-                for (_, arg) in args {
+                for (_, arg) in type_arguments {
                     write!(f, " {:?}", arg)?;
                 }
 
+                for (_, greek_letter) in lambda_set_variables.iter().zip(GREEK_LETTERS.iter()) {
+                    write!(f, " {:?}", greek_letter)?;
+                }
+
                 // Sometimes it's useful to see the expansion of the alias
                 // write!(f, "[ but actually {:?} ]", _actual)?;
 
@@ -442,11 +461,16 @@ impl Type {
                 }
                 ext.substitute(substitutions);
             }
-            Alias(_, zipped, actual_type) => {
-                for (_, value) in zipped.iter_mut() {
+            Alias {
+                type_arguments,
+                actual,
+                ..
+            } => {
+                for (_, value) in type_arguments.iter_mut() {
                     value.substitute(substitutions);
                 }
-                actual_type.substitute(substitutions);
+
+                actual.substitute(substitutions);
             }
             HostExposedAlias {
                 arguments,
@@ -497,8 +521,11 @@ impl Type {
                 }
                 ext.substitute_alias(rep_symbol, actual);
             }
-            Alias(_, _, actual_type) => {
-                actual_type.substitute_alias(rep_symbol, actual);
+            Alias {
+                actual: alias_actual,
+                ..
+            } => {
+                alias_actual.substitute_alias(rep_symbol, actual);
             }
             HostExposedAlias {
                 actual: actual_type,
@@ -547,9 +574,11 @@ impl Type {
                 ext.contains_symbol(rep_symbol)
                     || fields.values().any(|arg| arg.contains_symbol(rep_symbol))
             }
-            Alias(alias_symbol, _, actual_type) => {
-                alias_symbol == &rep_symbol || actual_type.contains_symbol(rep_symbol)
-            }
+            Alias {
+                symbol: alias_symbol,
+                actual: actual_type,
+                ..
+            } => alias_symbol == &rep_symbol || actual_type.contains_symbol(rep_symbol),
             HostExposedAlias { name, actual, .. } => {
                 name == &rep_symbol || actual.contains_symbol(rep_symbol)
             }
@@ -585,7 +614,10 @@ impl Type {
                         .values()
                         .any(|arg| arg.contains_variable(rep_variable))
             }
-            Alias(_, _, actual_type) => actual_type.contains_variable(rep_variable),
+            Alias {
+                actual: actual_type,
+                ..
+            } => actual_type.contains_variable(rep_variable),
             HostExposedAlias { actual, .. } => actual.contains_variable(rep_variable),
             Apply(_, args) => args.iter().any(|arg| arg.contains_variable(rep_variable)),
             EmptyRec | EmptyTagUnion | Erroneous(_) => false,
@@ -602,7 +634,7 @@ impl Type {
     /// a shallow dealias, continue until the first constructor is not an alias.
     pub fn shallow_dealias(&self) -> &Self {
         match self {
-            Type::Alias(_, _, actual) => actual.shallow_dealias(),
+            Type::Alias { actual, .. } => actual.shallow_dealias(),
             _ => self,
         }
     }
@@ -646,7 +678,11 @@ impl Type {
                 actual: actual_type,
                 ..
             }
-            | Alias(_, type_args, actual_type) => {
+            | Alias {
+                type_arguments: type_args,
+                actual: actual_type,
+                ..
+            } => {
                 for arg in type_args {
                     arg.1
                         .instantiate_aliases(region, aliases, var_store, introduced);
@@ -737,13 +773,19 @@ impl Type {
                         }
                         ext.substitute(&substitution);
 
-                        *self = Type::Alias(
-                            *symbol,
-                            named_args,
-                            Box::new(Type::RecursiveTagUnion(new_rec_var, tags, ext)),
-                        );
+                        *self = Type::Alias {
+                            symbol: *symbol,
+                            type_arguments: named_args,
+                            lambda_set_variables: alias.lambda_set_variables.clone(),
+                            actual: Box::new(Type::RecursiveTagUnion(new_rec_var, tags, ext)),
+                        };
                     } else {
-                        *self = Type::Alias(*symbol, named_args, Box::new(actual));
+                        *self = Type::Alias {
+                            symbol: *symbol,
+                            type_arguments: named_args,
+                            lambda_set_variables: alias.lambda_set_variables.clone(),
+                            actual: Box::new(actual),
+                        };
                     }
                 } else {
                     // one of the special-cased Apply types.
@@ -789,7 +831,11 @@ fn symbols_help(tipe: &Type, accum: &mut ImSet<Symbol>) {
                 }
             });
         }
-        Alias(alias_symbol, _, actual_type) => {
+        Alias {
+            symbol: alias_symbol,
+            actual: actual_type,
+            ..
+        } => {
             accum.insert(*alias_symbol);
             symbols_help(&actual_type, accum);
         }
@@ -859,8 +905,12 @@ fn variables_help(tipe: &Type, accum: &mut ImSet<Variable>) {
             // this rec var doesn't need to be in flex_vars or rigid_vars
             accum.remove(rec);
         }
-        Alias(_, args, actual) => {
-            for (_, arg) in args {
+        Alias {
+            type_arguments,
+            actual,
+            ..
+        } => {
+            for (_, arg) in type_arguments {
                 variables_help(arg, accum);
             }
             variables_help(actual, accum);
@@ -884,7 +934,7 @@ fn variables_help(tipe: &Type, accum: &mut ImSet<Variable>) {
 #[derive(Default)]
 pub struct VariableDetail {
     pub type_variables: MutSet<Variable>,
-    pub lambda_set_variables: MutSet<LambdaSet>,
+    pub lambda_set_variables: Vec<LambdaSet>,
     pub recursion_variables: MutSet<Variable>,
 }
 
@@ -911,7 +961,7 @@ fn variables_help_detailed(tipe: &Type, accum: &mut VariableDetail) {
                 variables_help_detailed(arg, accum);
             }
             if let Type::Variable(v) = **closure {
-                accum.lambda_set_variables.insert(LambdaSet::from(v));
+                accum.lambda_set_variables.push(LambdaSet::from(v));
             } else {
                 variables_help_detailed(closure, accum);
             }
@@ -957,8 +1007,12 @@ fn variables_help_detailed(tipe: &Type, accum: &mut VariableDetail) {
 
             accum.recursion_variables.insert(*rec);
         }
-        Alias(_, args, actual) => {
-            for (_, arg) in args {
+        Alias {
+            type_arguments,
+            actual,
+            ..
+        } => {
+            for (_, arg) in type_arguments {
                 variables_help_detailed(arg, accum);
             }
             variables_help_detailed(actual, accum);
@@ -1106,7 +1160,7 @@ pub struct Alias {
 
     /// lambda set variables, e.g. the one annotating the arrow in
     /// a |c|-> b
-    pub lambda_set_variables: MutSet<LambdaSet>,
+    pub lambda_set_variables: Vec<LambdaSet>,
 
     pub recursion_variables: MutSet<Variable>,
 
diff --git a/editor/src/lang/solve.rs b/editor/src/lang/solve.rs
index f248cc4999..7271701782 100644
--- a/editor/src/lang/solve.rs
+++ b/editor/src/lang/solve.rs
@@ -767,7 +767,6 @@ fn type_to_variable<'a>(
             register(subs, rank, pools, content)
         }
 
-        Alias(Symbol::BOOL_BOOL, _, _) => roc_types::subs::Variable::BOOL,
         Alias(symbol, args, alias_type_id) => {
             // TODO cache in uniqueness inference gives problems! all Int's get the same uniqueness var!
             // Cache aliases without type arguments. Commonly used aliases like `Int` would otherwise get O(n)