Deriving Dependently-Typed OOP from First Principles

Their definitions of OOP and FP are rather restrictive - it's basically FP = ADTs (data) and OOP = interfaces (codata). Many modern languages support both (e.g. Haskell has typeclasses, Java has records and sealed interfaces).

I think the key ingredient you're looking for is mutability. If you take advantage of the ability to implicitly modify state, your declared interfaces reduce in size because you don't need to model the threading of state through the interface. Since mutability means that your method signatures are less restrictive then they appear to be, it makes sense that this research (focusing on dependent types, and especially on dependently-typed proofs) would prefer a setting without implicit mutability. (Mutation is orthogonal to OOP vs. FP, anyway -- you can have pure OOP interfaces and also mutable FP interfaces.)

The Java stream interface also has a lot of methods that can technically be implemented in terms of other methods on the interface, but are present so that implementers can provide more efficient implementations depending on the capabilities of their model of streams. It makes sense that the present research would only consider the bare essentials of streams, and not things that could be layered on top at the cost of some optimization opportunities.

As a Java programmer, the essence of an OOP stream seems to be captured by the following interface:

    interface Stream<T> {
      T next();
    }

If we make mutation explicit, this evolves into:

    interface Stream<T> {
      Pair<T, Stream<T>> next();
    }

And then we can split this into two methods, providing each of the two components of the original `Pair`:

    interface Stream<T> {
      T head();
      Stream<T> tail();
    }

This is exactly what the paper shows on page 2, up to syntactic differences (like explicit type parameters to the methods).

The very old Qc Na koan is still relevant -- http://people.csail.mit.edu/gregs/ll1-discuss-archive-html/m...

One of the most mind-bending papers on this topic is William Cook’s On Understanding Data Abstraction, Revisited https://www.cs.utexas.edu/~wcook/Drafts/2009/essay.pdf “Object interfaces are essentially higher-order types, in the same sense that passing functions as values is higher-order. Any time an object is passed as a value, or returned as a value, the object-oriented program is passing functions as values and returning functions as values. The fact that the functions are collected into records and called methods is irrelevant. As a result, the typical object-oriented program makes far more use of higher-order values than many functional programs.“

Funny coincidence. A few days ago I was reading a blog post also about the Visitor pattern in Java, but in the context of recursion schemes (category theory):

http://logji.blogspot.com/2012/02/correcting-visitor-pattern...

That's what I get from studying FP and smalltalk. There are strong similar notions behind the paradigms. The dirt came from the industry.. they started to apply OO for large engineering projects and patterns became a fad.

The thing that really brought it home to me was the talk "Uniting Church and State: FP and OO Together" by Noel Welsh: https://www.youtube.com/watch?v=IO5MD62dQbI