I think what you’re trying to do is simply not supported by Java generics. The simpler case of public class Foo<T> { public T<String> bar() { return null; } } also does not compile using javac. Since Java does not know at compile-time what T is, it can’t guarantee that T<String> is at all meaningful. … Read more
Some terminology: The kind * is sometimes called ground. You can think of it as 0th order. Any kind of the form * -> * -> … -> * with at least one arrow is first-order. A higher-order kind is one that has a “nested arrow on the left”, e.g., (* -> *) -> *. … Read more
You touch so many interesting points in your question, so I am afraid this is going to be a long answer 🙂 Kind of (->) The kind of (->) is * -> * -> *, if we disregard the boxity GHC inserts. But there is no circularity going on, the ->s in the kind of … Read more
The terminology type and kind does not scale well. Type theorists since Bertrand Russell have used a hierarchy of “types.” One version of this has that Integer : Type 0, Type 0 : Type 1, Type 1 : Type 2, …, Type n : Type (n+1), …. In dependently typed languages like Coq and Agda, … Read more
Template-template parameters? template <template <typename> class m> struct Monad { template <typename a> static m<a> mreturn(const a&); template <typename a, typename b> static m<b> mbind(const m<a>&, m<b>(*)(const a&)); }; template <typename a> struct Maybe { bool isNothing; a value; }; template <> struct Monad<Maybe> { template <typename a> static Maybe<a> mreturn(const a& v) { Maybe<a> … Read more
Long story short, right now you (I?) have to provide a specific U: template <template <class> class HKT, class T, class U = T> concept HKTWithTemplateMemberFunctionF { return requires(HKT<T> h) { // HKT<T> is a type, h is an object h.F(std::declval<U>()) -> HKT<U>; } } since the compiler cannot prove for all types U that … Read more
So the kind of a type is its simple type. For instance Int has kind * which means it’s a base type and can be instantiated by values. By some loose definition of higher-kinded type (and I’m not sure where F# draws the line, so let’s just include it) polymorphic containers are a great example … Read more
Let me make up for starting some of this confusion by pitching in with some disambiguation. I like to use the analogy to the value level to explain this, as people tend to be more familiar with it. A type constructor is a type that you can apply to type arguments to “construct” a type. … Read more