diff --git a/axc/src/parser.rs b/axc/src/parser.rs
index fffc1c2..08680d5 100644
--- a/axc/src/parser.rs
+++ b/axc/src/parser.rs
@@ -3,7 +3,7 @@
 use std::{error::Error, fmt::Display};
 
 use chumsky::{
-    prelude::{choice, end, just, none_of, one_of, todo, Simple},
+    prelude::{choice, end, just, none_of, one_of, Simple},
     text::{ident, int, keyword, whitespace},
     Parser,
 };
@@ -303,6 +303,7 @@ fn parse_func_decl<'a>(
 
 fn parse_type_alias(m: &ParserMeta) -> impl Parser<char, ClassMember, Error = Simple<char>> {
     keyword("type")
+        .then_ignore(whitespace())
         .ignore_then(parse_type(m))
         .then(
             just('=')
@@ -481,11 +482,24 @@ fn parse_literal(_m: &ParserMeta) -> impl Parser<char, Expr, Error = Simple<char
         .map(Expr::Literal)
 }
 
-fn parse_type(_m: &ParserMeta) -> impl Parser<char, Type, Error = Simple<char>> {
-    todo()
+fn parse_type(m: &ParserMeta) -> impl Parser<char, Type, Error = Simple<char>> {
+    parse_named_type(m).repeated().at_least(1).map(|types| {
+        types
+            .into_iter()
+            .reduce(|l, r| Type::Application {
+                function: Box::new(l),
+                expression: Box::new(r),
+            })
+            .unwrap()
+    })
+}
+
+fn parse_named_type(_m: &ParserMeta) -> impl Parser<char, Type, Error = Simple<char>> {
+    ident().then_ignore(whitespace()).map(Type::Named)
 }
 
 fn parse_pattern(m: &ParserMeta) -> impl Parser<char, Pattern, Error = Simple<char>> {
+    // TODO: add all the patterns
     choice((parse_capture_pattern(m),))
 }