diff --git a/chalk-solve/src/clauses.rs b/chalk-solve/src/clauses.rs
index 20932413746..bd22b8ceacd 100644
--- a/chalk-solve/src/clauses.rs
+++ b/chalk-solve/src/clauses.rs
@@ -416,6 +416,12 @@ fn match_ty<I: Interner>(
 ) -> Result<(), Floundered> {
     let interner = builder.interner();
     Ok(match ty.data(interner) {
+        TyData::Apply(ApplicationTy {
+            name: TypeName::Scalar(_),
+            ..
+        }) => {
+            builder.push_fact(WellFormed::Ty(ty.clone()));
+        }
         TyData::Apply(application_ty) => match_type_name(builder, application_ty.name),
         TyData::Placeholder(_) => {
             builder.push_clause(WellFormed::Ty(ty.clone()), Some(FromEnv::Ty(ty.clone())));
diff --git a/libstd.chalk b/libstd.chalk
index 6d94f246667..c94b6047924 100644
--- a/libstd.chalk
+++ b/libstd.chalk
@@ -10,12 +10,10 @@ trait Clone { }
 trait Copy where Self: Clone { }
 trait Sized { }
 
-struct i32 { }
 impl Copy for i32 { }
 impl Clone for i32 { }
 impl Sized for i32 { }
 
-struct u32 { }
 impl Copy for u32 { }
 impl Clone for u32 { }
 impl Sized for u32 { }
diff --git a/tests/lowering/mod.rs b/tests/lowering/mod.rs
index 8665a3f8465..10e17c38a39 100644
--- a/tests/lowering/mod.rs
+++ b/tests/lowering/mod.rs
@@ -471,7 +471,7 @@ fn scalars() {
         }
 
         error_msg {
-            "parse error: UnrecognizedToken { token: (8, Token(45, \"i32\"), 11), expected: [\"r#\\\"([A-Za-z]|_)([A-Za-z0-9]|_)*\\\"#\"] }"
+            "parse error: UnrecognizedToken { token: (8, Token(49, \"i32\"), 11), expected: [\"r#\\\"([A-Za-z]|_)([A-Za-z0-9]|_)*\\\"#\"] }"
         }
     }
 }
diff --git a/tests/test/projection.rs b/tests/test/projection.rs
index c0673344008..cde486084f1 100644
--- a/tests/test/projection.rs
+++ b/tests/test/projection.rs
@@ -207,7 +207,6 @@ fn projection_equality_priority2() {
                 type Type;
             }
 
-            struct u32 {}
             struct S1 {}
             struct S2 {}
             struct S3 {}
@@ -286,8 +285,6 @@ fn projection_equality_from_env() {
             trait Trait1 {
                 type Type;
             }
-
-            struct u32 {}
         }
 
         goal {
@@ -314,8 +311,6 @@ fn projection_equality_nested() {
             trait Iterator {
                 type Item;
             }
-
-            struct u32 {}
         }
 
         goal {
@@ -360,8 +355,6 @@ fn iterator_flatten() {
             {
                 type Item = <U as Iterator>::Item;
             }
-
-            struct u32 {}
         }
 
         goal {
diff --git a/tests/test/scalars.rs b/tests/test/scalars.rs
index bbd91d521c2..d612e135f64 100644
--- a/tests/test/scalars.rs
+++ b/tests/test/scalars.rs
@@ -112,3 +112,27 @@ fn scalar_trait_impl() {
 
     }
 }
+
+#[test]
+fn scalars_are_well_formed() {
+    test! {
+        program { }
+
+        goal { WellFormed(i8) } yields { "Unique" }
+        goal { WellFormed(i16) } yields { "Unique" }
+        goal { WellFormed(i32) } yields { "Unique" }
+        goal { WellFormed(i64) } yields { "Unique" }
+        goal { WellFormed(i128) } yields { "Unique" }
+        goal { WellFormed(isize) } yields { "Unique" }
+        goal { WellFormed(u8) } yields { "Unique" }
+        goal { WellFormed(u16) } yields { "Unique" }
+        goal { WellFormed(u32) } yields { "Unique" }
+        goal { WellFormed(u64) } yields { "Unique" }
+        goal { WellFormed(u128) } yields { "Unique" }
+        goal { WellFormed(usize) } yields { "Unique" }
+        goal { WellFormed(f32) } yields { "Unique" }
+        goal { WellFormed(f64) } yields { "Unique" }
+        goal { WellFormed(bool) } yields { "Unique" }
+        goal { WellFormed(char) } yields { "Unique" }
+    }
+}