Version 1 (modified by dreixel, 3 years ago) (diff)

Initial import from my TeX notes

Syntax for explicit type and kind application

As a replacement for lexically-scoped type variables (and pattern signatures), we want to have explicit type (and kind) application, like in the following example:

case x of
  p@(C @a y z) -> ....

On the right-hand side we would have the type variable a in scope. Note how the use of @ is (in this case) unproblematic, since we can use the fact that constructors always start with an uppercase letter to distinguish whether the @ refers to an "as pattern" or to a type application. This cannot be used to pattern-match on specific types: the only thing that we can match on are variables.

How many arguments, and their order

When we have multiple variables, we can use as many as we need, and also use underscores:

f (C @_ @b x ) = ...

If the user gave a type signature for the binding, it is very easy to see which type patterns relate to which variables in the signature. In the absence of a signature, though, there are two possible choices:

  • Reject matching on type variables altogether.
  • Take the inferred signature, look at the introduced variables

syntactically from left to right, and use that order. This approach does not require tracking which bindings were given type signatures or not.

A problem with taking the inferred signature is that it is tied to many assumptions, including that of principal types.

Parsing matters


Consider a problematic example:

f :: Int -> forall a. a
f n @a = ....

In this case it is really ambiguous what the pattern means. For these cases we have the following workaround:

f :: Int -> forall a. a
(f n) @a = ....

This approach should work in general, and hopefully only few programs will actually need to use it.

Syntax for promoted datatypes

It also introduces the need to disambiguate between a datatype and its promoted kind. Consider the example:

data X = X

f :: forall (a : k). ....
... = ... f @'Nat @Nat ...

Since now it is not clear from the context anymore if we are expecting a kind or a type (since we use |@| both for kind and type application), we need to be able to disambiguate between datatypes and their corresponding promoted kinds.

More examples

Impredicative instantiation

Cons @(forall a. a -> a) should mean the constructor of type (forall a. a -> a) -> [forall a. a -> a] -> [forall a. a -> a].

Type/kind instantiation in classes

With the new kind-polymorphic Typeable class, we can recover the old kind-specific classes by saying, for instance:

type Typeable1 = Typeable @(* -> *)