diff --git a/compiler/noirc_frontend/src/monomorphization/mod.rs b/compiler/noirc_frontend/src/monomorphization/mod.rs
index edb831b2158..79ac02710d9 100644
--- a/compiler/noirc_frontend/src/monomorphization/mod.rs
+++ b/compiler/noirc_frontend/src/monomorphization/mod.rs
@@ -845,6 +845,14 @@ impl<'interner> Monomorphizer<'interner> {
             return self.resolve_trait_method_expr(expr_id, typ, method);
         }
 
+        // Ensure all instantiation bindings are bound.
+        // This ensures even unused type variables like `fn foo<T>() {}` have concrete types
+        if let Some(bindings) = self.interner.try_get_instantiation_bindings(expr_id) {
+            for (_, binding) in bindings.values() {
+                Self::check_type(binding, ident.location)?;
+            }
+        }
+
         let definition = self.interner.definition(ident.id);
         let ident = match &definition.kind {
             DefinitionKind::Function(func_id) => {
diff --git a/compiler/noirc_frontend/src/node_interner.rs b/compiler/noirc_frontend/src/node_interner.rs
index 2c0426f6938..4837028b80f 100644
--- a/compiler/noirc_frontend/src/node_interner.rs
+++ b/compiler/noirc_frontend/src/node_interner.rs
@@ -1289,6 +1289,10 @@ impl NodeInterner {
         &self.instantiation_bindings[&expr_id]
     }
 
+    pub fn try_get_instantiation_bindings(&self, expr_id: ExprId) -> Option<&TypeBindings> {
+        self.instantiation_bindings.get(&expr_id)
+    }
+
     pub fn get_field_index(&self, expr_id: ExprId) -> usize {
         self.field_indices[&expr_id]
     }
diff --git a/noir_stdlib/src/collections/map.nr b/noir_stdlib/src/collections/map.nr
index bd50f345356..4607b06d667 100644
--- a/noir_stdlib/src/collections/map.nr
+++ b/noir_stdlib/src/collections/map.nr
@@ -77,10 +77,10 @@ impl<K, V> Slot<K, V> {
 // While conducting lookup, we iterate attempt from 0 to N - 1 due to heuristic,
 // that if we have went that far without finding desired, 
 // it is very unlikely to be after - performance will be heavily degraded.
-impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
+impl<K, V, let N: u32, B> HashMap<K, V, N, B> {
     // Creates a new instance of HashMap with specified BuildHasher.
     // docs:start:with_hasher
-    pub fn with_hasher(_build_hasher: B) -> Self
+    pub fn with_hasher<H>(_build_hasher: B) -> Self
     where
         B: BuildHasher<H> {
         // docs:end:with_hasher
@@ -99,7 +99,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // Returns true if the map contains a value for the specified key.
     // docs:start:contains_key
-    pub fn contains_key(
+    pub fn contains_key<H>(
         self,
         key: K
     ) -> bool
@@ -183,7 +183,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // For each key-value entry applies mutator function.
     // docs:start:iter_mut
-    pub fn iter_mut(
+    pub fn iter_mut<H>(
         &mut self,
         f: fn(K, V) -> (K, V)
     )
@@ -208,7 +208,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // For each key applies mutator function.
     // docs:start:iter_keys_mut
-    pub fn iter_keys_mut(
+    pub fn iter_keys_mut<H>(
         &mut self,
         f: fn(K) -> K
     ) 
@@ -278,7 +278,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // Get the value by key. If it does not exist, returns none().
     // docs:start:get
-    pub fn get(
+    pub fn get<H>(
         self,
         key: K
     ) -> Option<V>
@@ -313,7 +313,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // Insert key-value entry. In case key was already present, value is overridden. 
     // docs:start:insert
-    pub fn insert(
+    pub fn insert<H>(
         &mut self,
         key: K,
         value: V
@@ -356,7 +356,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
 
     // Removes a key-value entry. If key is not present, HashMap remains unchanged.
     // docs:start:remove
-    pub fn remove(
+    pub fn remove<H>(
         &mut self,
         key: K
     )
@@ -388,7 +388,7 @@ impl<K, V, let N: u32, B, H> HashMap<K, V, N, B> {
     }
 
     // Apply HashMap's hasher onto key to obtain pre-hash for probing.
-    fn hash(
+    fn hash<H>(
         self,
         key: K
     ) -> u32
diff --git a/noir_stdlib/src/collections/umap.nr b/noir_stdlib/src/collections/umap.nr
index 86ae79ea644..c552c053a92 100644
--- a/noir_stdlib/src/collections/umap.nr
+++ b/noir_stdlib/src/collections/umap.nr
@@ -76,10 +76,10 @@ impl<K, V> Slot<K, V> {
 // While conducting lookup, we iterate attempt from 0 to N - 1 due to heuristic,
 // that if we have went that far without finding desired, 
 // it is very unlikely to be after - performance will be heavily degraded.
-impl<K, V, B, H> UHashMap<K, V, B> {
+impl<K, V, B> UHashMap<K, V, B> {
     // Creates a new instance of UHashMap with specified BuildHasher.
     // docs:start:with_hasher
-    pub fn with_hasher(_build_hasher: B) -> Self
+    pub fn with_hasher<H>(_build_hasher: B) -> Self
     where
         B: BuildHasher<H> {
         // docs:end:with_hasher
@@ -88,7 +88,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
         Self { _table, _len, _build_hasher }
     }
 
-    pub fn with_hasher_and_capacity(_build_hasher: B, capacity: u32) -> Self
+    pub fn with_hasher_and_capacity<H>(_build_hasher: B, capacity: u32) -> Self
     where
         B: BuildHasher<H> {
         // docs:end:with_hasher
@@ -110,7 +110,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // Returns true if the map contains a value for the specified key.
     // docs:start:contains_key
-    pub fn contains_key(
+    pub fn contains_key<H>(
         self,
         key: K
     ) -> bool
@@ -194,7 +194,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // For each key-value entry applies mutator function.
     // docs:start:iter_mut
-    unconstrained pub fn iter_mut(
+    unconstrained pub fn iter_mut<H>(
         &mut self,
         f: fn(K, V) -> (K, V)
     )
@@ -216,7 +216,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // For each key applies mutator function.
     // docs:start:iter_keys_mut
-    unconstrained pub fn iter_keys_mut(
+    unconstrained pub fn iter_keys_mut<H>(
         &mut self,
         f: fn(K) -> K
     ) 
@@ -283,7 +283,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // Get the value by key. If it does not exist, returns none().
     // docs:start:get
-    unconstrained pub fn get(
+    unconstrained pub fn get<H>(
         self,
         key: K
     ) -> Option<V>
@@ -315,7 +315,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // Insert key-value entry. In case key was already present, value is overridden. 
     // docs:start:insert
-    unconstrained pub fn insert(
+    unconstrained pub fn insert<H>(
         &mut self,
         key: K,
         value: V
@@ -353,7 +353,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
         }
     }
 
-    unconstrained fn try_resize(&mut self)
+    unconstrained fn try_resize<H>(&mut self)
         where B: BuildHasher<H>, K: Eq + Hash, H: Hasher {
         if self.len() + 1 >= self.capacity() / 2 {
             let capacity = self.capacity() * 2;
@@ -368,7 +368,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
 
     // Removes a key-value entry. If key is not present, UHashMap remains unchanged.
     // docs:start:remove
-    unconstrained pub fn remove(
+    unconstrained pub fn remove<H>(
         &mut self,
         key: K
     )
@@ -397,7 +397,7 @@ impl<K, V, B, H> UHashMap<K, V, B> {
     }
 
     // Apply UHashMap's hasher onto key to obtain pre-hash for probing.
-    fn hash(
+    fn hash<H>(
         self,
         key: K
     ) -> u32
diff --git a/noir_stdlib/src/hash/sha256.nr b/noir_stdlib/src/hash/sha256.nr
index 55cdd984003..352df656068 100644
--- a/noir_stdlib/src/hash/sha256.nr
+++ b/noir_stdlib/src/hash/sha256.nr
@@ -122,7 +122,7 @@ pub fn sha256_var<let N: u32>(msg: [u8; N], message_size: u64) -> [u8; 32] {
     msg_block[msg_byte_ptr] = 1 << 7;
     msg_byte_ptr = msg_byte_ptr + 1;
     unsafe {
-        let (new_msg_block, new_msg_byte_ptr)= pad_msg_block(msg_block, msg_byte_ptr);
+        let (new_msg_block, new_msg_byte_ptr) = pad_msg_block(msg_block, msg_byte_ptr);
         msg_block = new_msg_block;
         if crate::runtime::is_unconstrained() {
             msg_byte_ptr = new_msg_byte_ptr;
@@ -188,10 +188,7 @@ pub fn sha256_var<let N: u32>(msg: [u8; N], message_size: u64) -> [u8; 32] {
     hash_final_block(msg_block, h)
 }
 
-unconstrained fn pad_msg_block<let N: u32>(
-    mut msg_block: [u8; 64],
-    mut msg_byte_ptr: u64
-) -> ([u8; 64], u64) {
+unconstrained fn pad_msg_block(mut msg_block: [u8; 64], mut msg_byte_ptr: u64) -> ([u8; 64], u64) {
     // If i >= 57, there aren't enough bits in the current message block to accomplish this, so
     // the 1 and 0s fill up the current block, which we then compress accordingly.
     if msg_byte_ptr >= 57 {
@@ -208,7 +205,7 @@ unconstrained fn pad_msg_block<let N: u32>(
     (msg_block, msg_byte_ptr)
 }
 
-unconstrained fn attach_len_to_msg_block<let N: u32>(
+unconstrained fn attach_len_to_msg_block(
     mut msg_block: [u8; 64],
     mut msg_byte_ptr: u64,
     message_size: u64
diff --git a/noir_stdlib/src/option.nr b/noir_stdlib/src/option.nr
index 8d6d9ef970d..5b6b36679f8 100644
--- a/noir_stdlib/src/option.nr
+++ b/noir_stdlib/src/option.nr
@@ -116,7 +116,7 @@ impl<T> Option<T> {
     }
 
     /// If self is Some, return self. Otherwise, return `default()`.
-    pub fn or_else<U, Env>(self, default: fn[Env]() -> Self) -> Self {
+    pub fn or_else<Env>(self, default: fn[Env]() -> Self) -> Self {
         if self._is_some { self } else { default() }
     }
 
diff --git a/test_programs/compile_failure/unspecified_generic/Nargo.toml b/test_programs/compile_failure/unspecified_generic/Nargo.toml
new file mode 100644
index 00000000000..15b97018f2d
--- /dev/null
+++ b/test_programs/compile_failure/unspecified_generic/Nargo.toml
@@ -0,0 +1,7 @@
+[package]
+name = "unspecified_generic"
+type = "bin"
+authors = [""]
+compiler_version = ">=0.33.0"
+
+[dependencies]
diff --git a/test_programs/compile_failure/unspecified_generic/src/main.nr b/test_programs/compile_failure/unspecified_generic/src/main.nr
new file mode 100644
index 00000000000..f26d794d567
--- /dev/null
+++ b/test_programs/compile_failure/unspecified_generic/src/main.nr
@@ -0,0 +1,5 @@
+fn foo<T>() {}
+
+fn main() {
+    foo();
+}
diff --git a/test_programs/compile_success_empty/method_call_regression/src/main.nr b/test_programs/compile_success_empty/method_call_regression/src/main.nr
index 88b8dc57196..de58271cae6 100644
--- a/test_programs/compile_success_empty/method_call_regression/src/main.nr
+++ b/test_programs/compile_success_empty/method_call_regression/src/main.nr
@@ -1,14 +1,14 @@
 fn main() {
-    // s: Struct<?, ()>
-    let s = Struct { b: () };
+    // s: Struct<?PolymorphicIntOrField, ()>
+    let s = Struct { a: 0, b: () };
     // Regression for #3089
     s.foo();
 }
 
-struct Struct<A, B> { b: B }
+struct Struct<A, B> { a: A, b: B }
 
 // Before the fix, this candidate is searched first, binding ? to `u8` permanently.
-impl<B> Struct<u8, u8> {
+impl Struct<u8, u8> {
     fn foo(self) {}
 }
 
@@ -18,6 +18,6 @@ impl<B> Struct<u8, u8> {
 // With the fix, the type of `s` correctly no longer changes until a
 // method is actually selected. So this candidate is now valid since
 // `Struct<u32, ()>` unifies with `Struct<?, ()>` with `? = u32`.
-impl<A> Struct<u32, ()> {
+impl Struct<u32, ()> {
     fn foo(self) {}
 }
diff --git a/test_programs/compile_success_empty/option/src/main.nr b/test_programs/compile_success_empty/option/src/main.nr
index c5f321256b1..d135b2d88b8 100644
--- a/test_programs/compile_success_empty/option/src/main.nr
+++ b/test_programs/compile_success_empty/option/src/main.nr
@@ -1,6 +1,6 @@
 fn main() {
     let ten = 10; // giving this a name, to ensure that the Option functions work with closures
-    let none = Option::none();
+    let none: Option<Field> = Option::none();
     let some = Option::some(3);
 
     assert(none.is_none());