diff --git a/crates/fayalite/src/phantom_const.rs b/crates/fayalite/src/phantom_const.rs
index b8f3f09..dd6cff6 100644
--- a/crates/fayalite/src/phantom_const.rs
+++ b/crates/fayalite/src/phantom_const.rs
@@ -4,6 +4,11 @@
 use serde::{de::DeserializeOwned, Deserialize, Serialize};
 
 use crate::{
+    expr::{
+        ops::{ExprPartialEq, ExprPartialOrd},
+        Expr, ToExpr,
+    },
+    int::Bool,
     intern::{Intern, Interned, InternedCompare, LazyInterned, Memoize},
     source_location::SourceLocation,
     ty::{impl_match_variant_as_self, CanonicalType, StaticType, Type, TypeProperties},
@@ -272,3 +277,37 @@ where
     const TYPE_PROPERTIES: TypeProperties = <()>::TYPE_PROPERTIES;
     const MASK_TYPE_PROPERTIES: TypeProperties = <()>::TYPE_PROPERTIES;
 }
+
+impl<T: ?Sized + PhantomConstValue> ExprPartialEq<Self> for PhantomConst<T> {
+    fn cmp_eq(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        true.to_expr()
+    }
+
+    fn cmp_ne(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        false.to_expr()
+    }
+}
+
+impl<T: ?Sized + PhantomConstValue> ExprPartialOrd<Self> for PhantomConst<T> {
+    fn cmp_lt(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        false.to_expr()
+    }
+
+    fn cmp_le(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        true.to_expr()
+    }
+
+    fn cmp_gt(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        false.to_expr()
+    }
+
+    fn cmp_ge(lhs: Expr<Self>, rhs: Expr<Self>) -> Expr<Bool> {
+        assert_eq!(Expr::ty(lhs), Expr::ty(rhs));
+        true.to_expr()
+    }
+}