Deriving Dependently-Typed OOP from First Principles

https://arxiv.org/abs/2403.06707

by matt_d • 2 years ago

172 18 2 years ago

arxiv.org

grafs50• 2 years ago

Interesting, I wondered what it would even mean to derive a programming paradigm.

kikimora• 2 years ago

Very interesting. I’m on page 3 and already got a big AHA moment about OOP and FP duality.

_ZeD_• 2 years ago

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

_glass• 2 years ago

For me best described in, and also as a topic mentioned in the paper about the visitor pattern connection, "A Little Java, A Few Patterns". This book writes really impractical Java, but in such a Scheme way, that you really can understand the deep connections between functional and object-oriented programming.

liquid_bluing• 2 years ago

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.“

bruce343434• 2 years ago

I think the best example of this is the strategy pattern. In that way, strategy classes are really just a wrapper around a function and its persistent, mutable internal data/state.

abecedarius• 2 years ago

Whenever there's another interminable thread about, like, what is OO really and how thoroughly does it suck? I wish everyone knew this short paper as background.

Teaser: the first OO language was Church's lambda calculus.

trealira2• 2 years ago

This reminds me of this article: "The visitor pattern is essentially the same thing as Church Encoding" [0], although I think this comment [1] and this one [2] on HN explain it better. The article is written in Haskell, but it's basically saying that, because object-oriented programming languages lacked sum types, the visitor pattern makes the transform from

  (a | b | c) -> T

  (a -> T, b -> T, c -> T) -> T

where (a | b | c) is a sum type saying "it can be either a of type a, type b, or type c", and (a -> T, b-> T, c -> T) is a stand-in for a record of functions (i.e. the v-table of an instance of a visitor class).

[0] https://www.haskellforall.com/2021/01/the-visitor-pattern-is...

[1] https://news.ycombinator.com/item?id=26034790

[2] https://news.ycombinator.com/item?id=26024600

elbear• 2 years ago

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...

agumonkey• 2 years ago

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.

svieira• 2 years ago

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

msoad• 2 years ago

You can play around with the language itself here

https://polarity-lang.github.io/oopsla24/#ChurchEncodingCoda...

abeppu• 2 years ago

Maybe I'm just missing something, but I'm not on board with the definitions they take in the introduction.

the essence of object-oriented programming is programming against interfaces, which correspond to the type theoretic concept of codata and copattern matching

They then use the classic codata example of a Stream, with a head and a tail. The Stream they declare looks a lot more like the version of that concept in functional languages than the version of it in an OO one, but clearly it exists in both paradigms.

https://www.cs.cmu.edu/~15150/resources/libraries/stream.pdf https://hackage.haskell.org/package/Stream-0.4.7.2/docs/Data... https://docs.oracle.com/en/java/javase/21/docs/api/java.base...

Tainnor• 2 years ago

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).

Twisol• 2 years ago

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).

peterbb_net• 2 years ago

Nice paper on an interesting topic. I’ve not had a chance to read the paper thoroughly, but the judgmental equality ended up weaker than I anticipated. I’d hope we’d end up with alpha-equivalent codefs being judgmentally equal.

Which makes me wonder what the next steps for a proof assistant based on this is. Will the de-/refunctionalization play an active role in the proof assistant as well, thus solving it as described in section 4.1?

Deriving Dependently-Typed OOP from First Principles

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