NOTE: effect type system

This note will not be very complete, but might become a series.

1. Effect as interface

The first case, use maybe to implement raise effect.

fun raise-maybe( action : () -> <raise|e> a ) : e maybe<a>
  with handler
    return(x)      Just(x)   // normal return: wrap in Just
    ctl raise(msg) Nothing   // exception: return Nothing directly
  action()

<raise|e> ensure it's able to handle the effect other than raise
maybe became the underlying implementation of effect raise
return(x) lift the x : a into this monoid
ctl should be something like abort in delimited continuation, but the type is ensured, rather than depends on context

2. Polymorphic effect

fun map : (xs : list<a>, f : (a) -> e b) -> e list<b>
  match xs
    Cons(x,xx) -> Cons( f(x), map(xx,f) )
    Nil        -> Nil

3. Current question

How about

fun foo() : <state<int>,state<int>,state<int>> int

How to implement concurrency