diff --git a/spec-trait-impl/crates/spec-trait-bin/src/all.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/all.rs
similarity index 99%
rename from spec-trait-impl/crates/spec-trait-bin/src/all.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/all.rs
index 932cc00..7be4d13 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/all.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/all.rs
@@ -294,7 +294,7 @@ impl<T> Foo4 for Vec<T> {
 }
 
 pub fn run() {
-    println!("\n- All Cases:");
+    println!("\n- All Examples:");
 
     let zst = ZST;
     let zst2 = ZST2;
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/base.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/base.rs
similarity index 82%
rename from spec-trait-impl/crates/spec-trait-bin/src/base.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/base.rs
index 613ebff..3d681fd 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/base.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/base.rs
@@ -40,8 +40,15 @@ impl<T, U> BaseTrait<T> for BaseType {
     }
 }
 
+#[when(not(T = &BaseType))]
+impl<T> BaseTrait<T> for BaseType {
+    fn base_method(&self, _x: T) {
+        println!("T is not &BaseType");
+    }
+}
+
 pub fn run() {
-    println!("\n- Base Cases:");
+    println!("\n- Base Examples:");
 
     let x = BaseType;
 
@@ -49,5 +56,6 @@ pub fn run() {
     spec! { x.base_method(1.2f32); BaseType; [f32]; f32: Copy } // T implements Copy
     spec! { x.base_method(1i32); BaseType; [i32] } // T is String or i32
     spec! { x.base_method(vec![1, 2, 3]); BaseType; [Vec<i32>]; i32: Copy } // T is a Vec of Copy
+    spec! { x.base_method(1i8); BaseType; [i8] } // T is not &BaseType
     spec! { x.base_method(&x); BaseType; [&BaseType] } // Default
 }
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/examples/higher.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/higher.rs
new file mode 100644
index 0000000..deb2ed3
--- /dev/null
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/higher.rs
@@ -0,0 +1,33 @@
+use spec_trait_macro::{spec, when};
+
+struct BaseType;
+
+#[allow(dead_code)]
+trait HigherOrderSpecTrait<F, T> {
+    fn higher_order_spec_method(&self, f: F, arg: T) -> T;
+}
+
+#[when(F = for<'a> fn(&'a T) -> T)]
+impl<F, T> HigherOrderSpecTrait<F, T> for BaseType {
+    fn higher_order_spec_method(&self, f: F, arg: T) -> T {
+        println!("T is generic");
+        f(&arg)
+    }
+}
+
+#[when(all(T = i32, F = for<'a> fn(&'a T) -> T))]
+impl<F, T> HigherOrderSpecTrait<F, T> for BaseType {
+    fn higher_order_spec_method(&self, f: F, arg: T) -> T {
+        println!("T is i32");
+        f(&arg)
+    }
+}
+
+pub fn run() {
+    println!("\n- Higher Order Specialization Examples:");
+
+    let x = BaseType;
+
+    let _: i32 = spec! { x.higher_order_spec_method(|v: &i32| *v, 1i32); BaseType; [for<'a> fn(&'a i32) -> i32, i32] }; // -> "T is i32"
+    let _: u32 = spec! { x.higher_order_spec_method(|v: &u32| *v, 1u32); BaseType; [for<'a> fn(&'a u32) -> u32, u32] }; // -> "T is generic"
+}
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/lifetimes.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/lifetimes.rs
similarity index 96%
rename from spec-trait-impl/crates/spec-trait-bin/src/lifetimes.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/lifetimes.rs
index 30143da..a6f429e 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/lifetimes.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/lifetimes.rs
@@ -27,7 +27,7 @@ impl<T> LifetimesTrait<T> for BaseType {
 }
 
 pub fn run() {
-    println!("\n- Lifetimes Cases:");
+    println!("\n- Lifetimes Examples:");
 
     let x = BaseType;
 
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/examples/mod.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/mod.rs
new file mode 100644
index 0000000..bda4c07
--- /dev/null
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/mod.rs
@@ -0,0 +1,21 @@
+mod all;
+mod base;
+mod lifetimes;
+mod nested;
+mod order;
+mod sself;
+mod traits;
+mod types;
+mod higher;
+
+pub fn run() {
+    base::run();
+    types::run();
+    traits::run();
+    lifetimes::run();
+    nested::run();
+    sself::run();
+    higher::run();
+    order::run();
+    all::run();
+}
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/nested.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/nested.rs
similarity index 95%
rename from spec-trait-impl/crates/spec-trait-bin/src/nested.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/nested.rs
index f71b641..e6521bd 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/nested.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/nested.rs
@@ -27,7 +27,7 @@ impl<T, U> NestedTrait<T, U> for BaseType {
 }
 
 pub fn run() {
-    println!("\n- Nested Cases:");
+    println!("\n- Nested Examples:");
 
     let x = BaseType;
 
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/examples/order.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/order.rs
new file mode 100644
index 0000000..fad7c1c
--- /dev/null
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/order.rs
@@ -0,0 +1,29 @@
+use spec_trait_macro::{spec, when};
+
+pub fn run() {
+    println!("\n- Order Examples:");
+
+    let x = BaseType;
+
+    spec! { x.order_method(1u8); BaseType; [u8]  } // -> "T is u8"
+    spec! { x.order_method(1i8); BaseType; [i8] } // -> "Default"
+}
+
+struct BaseType;
+
+trait OrderTrait<T> {
+    fn order_method(&self, _x: T);
+}
+
+impl<T> OrderTrait<T> for BaseType {
+    fn order_method(&self, _x: T) {
+        println!("Default");
+    }
+}
+
+#[when(T = u8)]
+impl<T> OrderTrait<T> for BaseType {
+    fn order_method(&self, _x: T) {
+        println!("T is u8");
+    }
+}
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/sself.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/sself.rs
similarity index 98%
rename from spec-trait-impl/crates/spec-trait-bin/src/sself.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/sself.rs
index 8ac8484..89404d0 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/sself.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/sself.rs
@@ -60,7 +60,7 @@ impl<T, U, V> SelfTrait<T> for (U, V) {
 }
 
 pub fn run() {
-    println!("\n- Self Cases:");
+    println!("\n- Self Examples:");
 
     let x = BaseType1;
     spec! { x.self_method(42u8); BaseType1; [u8] } // -> "BaseType1: T is u8"
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/traits.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/traits.rs
similarity index 97%
rename from spec-trait-impl/crates/spec-trait-bin/src/traits.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/traits.rs
index 2495249..6719c33 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/traits.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/traits.rs
@@ -48,7 +48,7 @@ impl<T> TraitsTrait<T> for BaseType {
 }
 
 pub fn run() {
-    println!("\n- Traits Cases:");
+    println!("\n- Traits Examples:");
 
     let x = BaseType;
 
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/types.rs b/spec-trait-impl/crates/spec-trait-bin/src/examples/types.rs
similarity index 98%
rename from spec-trait-impl/crates/spec-trait-bin/src/types.rs
rename to spec-trait-impl/crates/spec-trait-bin/src/examples/types.rs
index ed1ec75..b314cb5 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/types.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/examples/types.rs
@@ -65,7 +65,7 @@ impl<T> TypesTrait<T> for BaseType {
 }
 
 pub fn run() {
-    println!("\n- Types Cases:");
+    println!("\n- Types Examples:");
 
     let x = BaseType;
 
diff --git a/spec-trait-impl/crates/spec-trait-bin/src/main.rs b/spec-trait-impl/crates/spec-trait-bin/src/main.rs
index 822490c..fb1c850 100644
--- a/spec-trait-impl/crates/spec-trait-bin/src/main.rs
+++ b/spec-trait-impl/crates/spec-trait-bin/src/main.rs
@@ -1,17 +1,5 @@
-mod all;
-mod base;
-mod lifetimes;
-mod nested;
-mod sself;
-mod traits;
-mod types;
+mod examples;
 
 fn main() {
-    base::run();
-    types::run();
-    traits::run();
-    lifetimes::run();
-    nested::run();
-    sself::run();
-    all::run();
+    examples::run();
 }
diff --git a/spec-trait-impl/crates/spec-trait-utils/src/specialize.rs b/spec-trait-impl/crates/spec-trait-utils/src/specialize.rs
index 356685b..ee21b73 100644
--- a/spec-trait-impl/crates/spec-trait-utils/src/specialize.rs
+++ b/spec-trait-impl/crates/spec-trait-utils/src/specialize.rs
@@ -336,6 +336,18 @@ mod tests {
         );
     }
 
+    #[test]
+    fn get_assignable_conditions_nested_types() {
+        let conditions = vec![
+            WhenCondition::Type("T".into(), "A".into()),
+            WhenCondition::Type("U".into(), "for <'a> fn(&'a T) -> T".into()),
+        ];
+
+        let res = get_assignable_conditions(&conditions, "<T, U>");
+
+        assert_eq!(res.len(), 2);
+    }
+
     #[test]
     fn get_generic_types_from_conditions_ordering_and_filtering() {
         let conditions = vec![
diff --git a/spec-trait-impl/crates/spec-trait-utils/src/types.rs b/spec-trait-impl/crates/spec-trait-utils/src/types.rs
index 52e01a5..1276b9f 100644
--- a/spec-trait-impl/crates/spec-trait-utils/src/types.rs
+++ b/spec-trait-impl/crates/spec-trait-utils/src/types.rs
@@ -164,7 +164,7 @@ fn can_assign(
                     || to_string(&array1.len) == to_string(&array2.len))
         }
 
-        // fn(T) -> U
+        // `fn(T) -> U`, `for<'a> fn(&'a T) -> U`
         (Type::BareFn(fn1), Type::BareFn(fn2)) => {
             let unsafety_compatible = matches!(
                 (&fn1.unsafety, &fn2.unsafety),
@@ -177,6 +177,26 @@ fn can_assign(
                 _ => false,
             };
 
+            // extend generics with the generics from the fn: `for<'a> fn(&'a T) -> U`
+            let all_new_lifetimes = fn1
+                .lifetimes
+                .as_ref()
+                .map(|bl| &bl.lifetimes)
+                .iter()
+                .chain(fn2.lifetimes.as_ref().map(|bl| &bl.lifetimes).iter())
+                .flat_map(|lts| {
+                    lts.iter().filter_map(|gp| {
+                        if let GenericParam::Lifetime(lt) = gp {
+                            Some((lt.lifetime.to_string(), None))
+                        } else {
+                            None
+                        }
+                    })
+                })
+                .collect::<GenericsMap>();
+
+            generics.lifetimes.extend(all_new_lifetimes);
+
             fn1.inputs.len() == fn2.inputs.len()
                 && unsafety_compatible
                 && abi_compatible
@@ -289,11 +309,12 @@ fn check_and_assign_type_generic(
         .cloned()
         .is_some_and(|assigned| {
             assigned.clone().is_none_or(|assigned| {
-                can_assign(
-                    &str_to_type_name(concrete_type),
-                    &str_to_type_name(&assigned),
-                    generics,
-                )
+                declared_type == assigned
+                    || can_assign(
+                        &str_to_type_name(concrete_type),
+                        &str_to_type_name(&assigned),
+                        generics,
+                    )
             })
         })
     {
@@ -961,6 +982,48 @@ mod tests {
         assert!(!can_assign(&t1, &t2, &mut g));
     }
 
+    #[test]
+    fn compare_types_generic_fn() {
+        let mut g = ConstrainedGenerics::default();
+
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        assert!(can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a _) -> _");
+        assert!(can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        g.types.insert("T".to_string(), None);
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a T) -> i32");
+        assert!(can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        g.types.insert("T".to_string(), None);
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a u8) -> T");
+        assert!(can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        g.types.insert("T".to_string(), None);
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a T) -> T");
+        assert!(!can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a i32) -> i32");
+        assert!(!can_assign(&t1, &t2, &mut g));
+
+        g = ConstrainedGenerics::default();
+        let t1 = str_to_type_name("for<'a> fn(&'a u8) -> i32");
+        let t2 = str_to_type_name("for<'a> fn(&'a u8) -> u8");
+        assert!(!can_assign(&t1, &t2, &mut g));
+    }
+
     #[test]
     fn compare_types_nested() {
         let mut g = ConstrainedGenerics::default();