It incrementally covers normalization by evaluation, bidirectional typechecking, basic pattern unification, implicit insertion (which relies on unification), and then more sophisticated variants on pattern unification.
I'm more familiar with F#, so I got stuck at this line:
type ('a,'b) app += List_name : 'a list -> ('a,list_name) app
I understand that app is an extensible type and this line adds a union case called List_name to the type, but the signature of List_name confuses me. If I write (List_name x) is x a list or a function?
The variable "x" would be a list in this case. This the GADT (Generalized Abstract Data Types) syntax, where the type of the whole union can depend on the discriminated union case. Thus
List_name: 'a list -> ('a, list_name) app
reads: for any value "x" of type "'a list", "List_name x" constructs a value of type "('a, list_name) app". In this case, it is the the "list_name" tag part of the type which is dependent on the union case.
I wonder how much this is a problem in practice, aside from the type-checker taking too long.