diff --git a/drimc_rs/src/main.rs b/drimc_rs/src/main.rs
index 9ff0951..7563091 100644
--- a/drimc_rs/src/main.rs
+++ b/drimc_rs/src/main.rs
@@ -2,13 +2,13 @@
 
 use std::{error::Error, fmt::Display, fs::File, io::Write, process::exit, str::FromStr};
 
+use clap::Parser;
 use drimc_rs::{
     ast2ir::ast2ir,
     backends,
     parser::{parser, ParserError, ParserMeta},
     typeck::typeck,
 };
-use clap::Parser;
 
 /// Optimization levels.
 #[derive(Debug)]
@@ -256,7 +256,7 @@ fn main() {
         let source = std::fs::read_to_string(&args.source_file)?;
         let meta = ParserMeta::default();
         let ast = chumsky::Parser::parse(&parser(&meta), source).map_err(ParserError)?;
-        typeck(&ast)?;
+        let ast = typeck(ast)?;
 
         let ir = ast2ir(ast);
 
diff --git a/drimc_rs/src/syntax.rs b/drimc_rs/src/syntax.rs
index f295b05..d834951 100644
--- a/drimc_rs/src/syntax.rs
+++ b/drimc_rs/src/syntax.rs
@@ -2,6 +2,8 @@
 
 use num_bigint::BigUint;
 
+use crate::typeck;
+
 /// A concrete syntax tree. This represents the full content of a Drim program, including all
 /// whitespace, comments, and tokens: the source code of the original program can be recovered
 /// completely using the syntax tree.
@@ -68,7 +70,7 @@ pub enum ClassMember {
 
         /// The type of the overall function; this is filled in by the typechecker, and is left
         /// blank by the parser.
-        typ: Option<Type>,
+        typ: Option<typeck::Type>,
     },
 
     /// Declaration of a type that is a literal alias for another type.
@@ -98,7 +100,7 @@ pub struct Expr {
     pub kind: ExprKind,
 
     /// An optional type signature, left as `None` by the parser and added by the type checker.
-    pub typ: Option<Type>,
+    pub typ: Option<typeck::Type>,
 }
 
 /// The different kinds of expressions.
@@ -266,7 +268,7 @@ pub enum Pattern {
 }
 
 /// Namespaced identifiers.
-#[derive(Clone, Debug)]
+#[derive(Clone, Debug, Hash, PartialEq)]
 pub struct Identifier {
     /// The elements of the identifier; there must be at least one of these.
     pub elems: Vec<String>,
diff --git a/drimc_rs/src/typeck.rs b/drimc_rs/src/typeck.rs
index 56de735..d12647e 100644
--- a/drimc_rs/src/typeck.rs
+++ b/drimc_rs/src/typeck.rs
@@ -1,8 +1,10 @@
 //! Type checker.
 
-use std::{error::Error, fmt::Display};
+use std::{collections::BTreeMap, error::Error, fmt::Display};
 
-use crate::syntax::SyntaxTree;
+use num_bigint::BigInt;
+
+use crate::syntax::{Identifier, SyntaxTree};
 
 /// A compile-time type error from the user's source code.
 #[derive(Debug)]
@@ -16,7 +18,39 @@ impl Display for TypeError {
 
 impl Error for TypeError {}
 
+/// A type known at compile time. While this resembles the AST `Type` structure, this enum is
+/// optimized for unifying types against one another and representing compiler-generated types
+/// rather than strictly representing named types.
+#[derive(Debug, Clone, PartialEq)]
+pub enum Type {
+    /// `Foo`
+    Named(Identifier),
+
+    /// `List Int`
+    Application {
+        /// The function being applied. This must be a generic type.
+        function: Box<Type>,
+
+        /// The type given as an argument to the type.
+        expression: Box<Type>,
+    },
+
+    /// `(a, b)`
+    Tuple(Vec<Type>),
+
+    /// `{ a: x, b: y }`
+    Record(BTreeMap<String, Type>),
+
+    /// Compiler-internal type representing an arbitrary-precision integer whose value is known at
+    /// compile time. This is the default type of integer literals. A `CompInt` can be converted to
+    /// an actual integer type via implicit application of the `fromCompInt` generic function.
+    CompInt(BigInt),
+
+    /// Compiler-internal type representing a string literal. See `CompInt`.
+    CompString(String),
+}
+
 /// Type-checks the syntax tree.
-pub fn typeck(_: &SyntaxTree) -> Result<(), TypeError> {
+pub fn typeck(_: SyntaxTree) -> Result<SyntaxTree, TypeError> {
     todo!()
 }