diff --git a/src/ast2/intern.rs b/src/ast2/intern.rs
index 1c8d27e..09df5f6 100644
--- a/src/ast2/intern.rs
+++ b/src/ast2/intern.rs
@@ -22,6 +22,12 @@ pub enum SimpleType {
     USize,
     ISize,
     ComptimeInt,
+    /// Top type: this is the supertype of all types, and any value can coerce into it.
+    /// Although Rust's `()` is not a top type, it can be thought of as a top type in some contexts.
+    Top,
+    /// Bottom type: this is the subtype of all types, and it can coerce into a value of any type.
+    /// Akin to Rust's `!`.
+    Bottom,
 }
 
 impl From<u8> for SimpleType {
@@ -52,6 +58,8 @@ impl Display for SimpleType {
                 SimpleType::USize => "usize",
                 SimpleType::ISize => "isize",
                 SimpleType::ComptimeInt => "comptime_int",
+                SimpleType::Top => "⊤",
+                SimpleType::Bottom => "⊥",
             }
         )
     }
@@ -527,6 +535,8 @@ macro_rules! static_keys {
 }
 
 static_keys!(
+    TOP => Key::SimpleType {ty: SimpleType::Top,},
+    BOTTOM => Key::SimpleType {ty: SimpleType::Bottom,},
     BOOL => Key::SimpleType {ty: SimpleType::Bool,},
     F32 => Key::SimpleType {ty: SimpleType::F32,},
     F64 => Key::SimpleType {ty: SimpleType::F64,},
@@ -632,6 +642,18 @@ impl InternPool {
     pub fn get_i64_type(&self) -> Index {
         self.get_assume_present(&Key::SIntType { bit_width: 64 })
     }
+
+    pub fn get_top_type(&self) -> Index {
+        self.get_assume_present(&Key::SimpleType {
+            ty: SimpleType::Top,
+        })
+    }
+
+    pub fn get_bottom_type(&self) -> Index {
+        self.get_assume_present(&Key::SimpleType {
+            ty: SimpleType::Bottom,
+        })
+    }
 }
 
 #[derive(Debug, Clone, Copy)]
@@ -740,8 +762,8 @@ impl InternPool {
                     todo!("void can't be turned into a mir type")
                 }
                 SimpleType::ISize | SimpleType::USize => Type::QWord,
-                SimpleType::ComptimeInt => {
-                    panic!("comptime int can't be turned into a mir type")
+                SimpleType::Top | SimpleType::Bottom | SimpleType::ComptimeInt => {
+                    panic!("{ty} can't be turned into a mir type")
                 }
             },
             Key::ArrayType { .. } => {
@@ -816,6 +838,9 @@ impl InternPool {
                 },
                 SimpleType::USize => ptr_size,
                 SimpleType::ISize => ptr_size,
+                SimpleType::Top | SimpleType::Bottom => {
+                    panic!("top and bottom types are not sized")
+                }
                 SimpleType::ComptimeInt => panic!("comptime int is unsized"),
             },
             Key::PointerType { .. } => ptr_size,
@@ -953,6 +978,9 @@ impl InternPool {
                 SimpleType::USize => Type::Integer(IntegralType::new(false, pointer_bits)),
                 SimpleType::ISize => Type::Integer(IntegralType::new(true, pointer_bits)),
                 SimpleType::ComptimeInt => Type::comptime_number(),
+                SimpleType::Top | SimpleType::Bottom => {
+                    panic!("top and bottom types cannot be converted to ast1 types")
+                }
             },
             Key::PointerType { pointee, flags } => Type::Pointer {
                 constness: flags.is_const,
diff --git a/src/ast2/ir.rs b/src/ast2/ir.rs
index b92efff..aef9354 100644
--- a/src/ast2/ir.rs
+++ b/src/ast2/ir.rs
@@ -1,11 +1,12 @@
+#![allow(unused_variables)]
 use std::collections::HashMap;
 
 use crate::{
     ast2::{
-        intern::{self, AMD64_POINTER_TYPE_INFO},
         Index,
+        intern::{self, AMD64_POINTER_TYPE_INFO},
     },
-    triples::{self, Inst, IR},
+    triples::{self, IR, Inst},
 };
 
 #[derive(Debug, thiserror::Error)]
@@ -15,9 +16,9 @@ enum Error {
 }
 
 use super::{
+    Ast, Data, PlaceOrValue, Tag, TypeCache,
     intern::InternPoolWrapper as InternPool,
     visitor::{AstExt, AstVisitorTrait},
-    Ast, Data, PlaceOrValue, Tag, TypeCache,
 };
 
 struct IrBuilder {
diff --git a/src/ast2/mod.rs b/src/ast2/mod.rs
index dde901a..14597b6 100644
--- a/src/ast2/mod.rs
+++ b/src/ast2/mod.rs
@@ -5,7 +5,7 @@ use std::{
     fmt::{Debug, Display},
 };
 
-use intern::{InternPoolWrapper as InternPool, PointerFlags, StructFlags, AMD64_POINTER_TYPE_INFO};
+use intern::{AMD64_POINTER_TYPE_INFO, InternPoolWrapper as InternPool, PointerFlags, StructFlags};
 use num_bigint::BigInt;
 
 use crate::{
@@ -2251,6 +2251,9 @@ where
                 };
                 ComptimeNumber::Integral(ComptimeInt::Comptime(bigint))
             }
+            intern::SimpleType::Top | intern::SimpleType::Bottom => {
+                unreachable!()
+            }
         },
         _ => {
             unreachable!()
diff --git a/src/ast2/typecheck.rs b/src/ast2/typecheck.rs
index fef8123..da52c77 100644
--- a/src/ast2/typecheck.rs
+++ b/src/ast2/typecheck.rs
@@ -1,10 +1,17 @@
+//! Type checking for the AST.
+//! This module implements a bi-unification type-checking algorithm to infer
+//! types for each node in the AST.
+
+// Visitor pattern has lots of unused arguments
+#![allow(unused_variables)]
+
 use crate::variant;
 
 use super::{
+    Ast, Data, Index, Tag,
     intern::{self},
     tag::{AstNode, AstNodeExt},
     visitor::{AstExt, AstVisitorTrait},
-    Ast, Data, Index, Tag,
 };
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]