Implement 'Let Arguments Go First'

[brendanzab]

It would be nice to improve the bidirectional type checking algorithm to also pull information from the arguments. This could also help us eventually implement implicit arguments (see #8). A nice approach for doing this was given in the paper Let Arguments Go First. In the introduction the authors state (emphasis added):

We believe that, similarly to standard bi-directional type checking, bi-directional type checking with an application mode can be applied to a wide range of type systems. Our work shows two particular and non-trivial applications. Other potential areas of applications are other type systems with subtyping, static overloading, implicit parameters or dependent types.

In section 3 (the Hindley-Milner example) of the paper they show the application context pulling type information from the arguments in order to fill in the 'hidden type arguments' via the subtyping rules. Perhaps we could do something similar!

Resources

• Let Arguments Go First (paper) (slides)