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The "proving theorems" stuff is definitely overstated. People always toss that term around, and it's true in principle, but in practice hardly anyone ever uses correctness proofs in real world code.

But to flip it around and make a less grandiose version of the same point: the majority of bugs are to do with state. (I don't actually know if that has been "proved" but it's definitely what I find in practice!) Pure FP gets rid of a whole swathe of potential bugs at one stroke. Of course it makes programming harder in some other respects, as often it can be hard to figure out a pure function that's as efficient as the obvious imperative algorithm, or even to figure out how do a state-y thing in FP in the first place.

I agree with this mostly. You can get rid of state in OO programs, and that often involves a bit of functional programming. Struct/values in C# help a lot in keeping the performance up (well, if GC is a problem, you can also inline your closures to prevent boxing...lots of crazy things like that). Essential (rather than accidental) state is impossible to eliminate in any case.

Yes, I think just trying to use an FP style where possible is a great approach.

> And how often does that occur in practice for most of the programs people write?

Very frequently. The simple theorems that equational reasoning supports are very convenient for refactoring and optimizing code. Understanding components in isolation is useful for testing, isolating bugs, and refactoring of subprograms independently from their contexts. Since I do testing and refactoring frequently, I make good use of what FP offers.

Sure, this isn't equivalent to full 'correctness' proofs. The lightweight equational reasoning FP offers for expressions and behavior doesn't prove you have 'correct' expressions or behavior. But it doesn't take theorems of correctness to be useful.

> that is true of statically typed OO also

Not really. Statically typed OO doesn't prove nearly as much about the behavior. This is mostly due to potential for aliasing of stateful sub-components. If you have capability secure OO, like E language or NewSpeak or Joe-E, that can help a lot, but the potential for hidden communication via aliased components still hinders a lot of useful equational reasoning.

> only way to get encapsulated state in Haskell is World -> World

That's simply untrue. Encapsulated state in Haskell can be modeled by a variety of types. One is `Machine i o = i → (o, Machine i o)`. Such machines can be composed, each component machine having its own internal, encapsulated state.

> OOP also is not very new, being formed from the culmination have patterns used in the 70s, and is about the same vintage as FP.

I'd say pure FP is a lot younger. The idioms for purely functional expression of IO simply didn't exist in the 70s. E.g. even in the mid 80s, you had languages like Miranda with impure 'readFile :: FileName → Bytes'. The Clean programming language using uniqueness types for IO was a new thing in the mid 80s. The modern use of monads harkens to Wadler in the mid 90s. I tend to think of `pure FP` as more a mid-90s paradigm. It really is a different paradigm - a different way of thinking about and constructing programs - than the ad-hoc impure FP of Lisp and OCaml.

> Very frequently. The simple theorems that equational reasoning supports are very convenient for refactoring and optimizing code.

I was generalizing across all programmers. Of course individual cases may vary, and it really depends on the code that you write!

> Not really. Statically typed OO doesn't prove nearly as much about the behavior. This is mostly due to potential for aliasing of stateful sub-components.

Haskell simply avoids aliasing with value semantics, and even then you can add it back and get the same problems.

> That's simply untrue. Encapsulated state in Haskell can be modeled by a variety of types. One is `Machine i o = i → (o, Machine i o)`. Such machines can be composed, each component machine having its own internal, encapsulated state.

I'm not disagreeing. My point is that you have to bury the state in something else, which is then exposed via a signature (well, in Haskell which supports this, of course).

> I'd say pure FP is a lot younger.

We could debate a lot on what pure FP is, what pure OO is, and who climbed the ladder faster. But the fact that paradigms developed around the same time is probably due to the programming field maturing in that time frame.

> generalizing across all programmers

I think the relevant question is whether functional programmers, not all programmers, regularly leverage the lightweight equational reasoning, refactoring, and context-independent behavior that is available with purely functional programming. I believe most do.

> avoids aliasing with value semantics, and even then you can add it back and get the same problems (...) you have to bury the state in something else, which is then exposed via a signature

In a programming model without side-effects, it is necessarily the case that all 'effects' are modeled in the call-return behavior. The type signature, too, for a strongly typed language. And I agree that, upon modeling state or aliasing, we get to deal with not just the feature but all of its associated problems.

OTOH, the problems of state and aliasing don't implicitly leak into every subprogram. The precise control over effects can be very convenient.

You couch that control in pessimistic terms like "pollute all function signatures it buried through". But in practice I've never had difficulty anticipating where I'll need to model effectful behavior, nor with extending the set of effects as needed. Oleg's recent development of freer monads with more extensible effects [1] is compelling in its potential to remove remaining drudge-work.

[1] http://okmij.org/ftp/Haskell/extensible/more.pdf

> We could debate a lot on what pure FP is, what pure OO is (...) paradigms developed around the same time

Pure FP (programming with mathematical functions, no side-effects) and impure FP (i.e. first-class procedural programming) are essentially different paradigms. They require different patterns of thinking, reasoning about, and constructing programs. Despite the ongoing battle over the "functional programming" branding, it isn't wise to conflate the two paradigms. It was impure FP that developed around the same time as OOP. Pure FP is about twenty years younger, more or less.

(The mention of 'pure OO' seems an irrelevant distraction. Do you believe pure OO vs. impure OO, however you distinguish them, require significantly different design and development patterns and are thus distinct paradigms?)

> I think the relevant question is whether functional programmers, not all programmers, regularly leverage the lightweight equational reasoning, refactoring, and context-independent behavior that is available with purely functional programming. I believe most do.

This begs the question of who is a functional programmer, and how typical are they? I know a few FP programmers who are able to stay in the abstract world for a long time, thinking symbolically, equationally, and don't need petty things like concrete examples (most of the members of WGFP, for example). Then there is the rest of us!

> In a programming model without side-effects, it is necessarily the case that all 'effects' are modeled in the call-return behavior. The type signature, too, for a strongly typed language.

You can always default to World -> World in a pure language, and ya...technically you don't have side effects anymore, but for all practical purposes you do! For this to be useful at all, you have to keep your effects fine grained, and for functions that call other functions (like a general ForEach), effects have to be parametric as well, or you wind up polluting everything (or worse, being unable to express something).

Pure FP culminates from a bunch of experience in the 70s (I'm not talking about Lisp), which happens to be where OO came from as well. Pure OO doesn't really make sense...OO can't be pure but rather organic.

Methinks you misunderstand the programming experience of FP. A nice property of 'equational reasoning' is that, as a universal property of code, I don't have to think about it. It just becomes a law of code - conservation of meaning. Abstraction, splicing, refactoring, and reuse happens easily and fluidly because I don't need to think about whether those actions are safe or correct. It isn't about hand-wavy abstract worlds at all, but rather concrete manipulation of source code. Concrete examples are also very common and useful with pure FP, e.g. use of REPLs is common.

A pure `World→World` effects model is NOT a practical equivalent to introducing side-effects. Unlike with side-effects, it's trivial to constrain a subprogram from access to the whole World, e.g. use divide and conquer tactics to hide parts of the world, or limit a subprogram to a constrained subset of monadic commands that an interpreter uses to access and update the world in limited ways.

No experience from the 70s left academics or industry prepared to support purely functional IO models. It should go without saying that you can't have a complete programming paradigm without an effective story for IO. Miranda, an attempt at a purely functional language of the mid 80s, made a valiant attempt at pure IO, and failed. Even early Haskell, up through the early 90s lacked an effective, coherent story for IO. I find your repeated assertions that pure FP was somehow a child of the 70s to be very dubious.

REPLs don't help out with refactoring, splicing, or even abstraction, at least with the current tool chain we have.

IF you add a World->World effect to your function, it is the equivalent to saying it has unconstrained side effects, is it not? It is the practical equivalent, even if its implementation can pair off the world as needed.

Hindley Milner, Landin, ISWIM, APL, list comprehensions, etc...are all children of the 70s. The IO problem wasn't solved until Wadler in early 90s, but then again we didn't get type parameters in OO languages before then either.

Wat? It's equational reasoning that lets us manipulate concrete code easily. REPLs are just proof that functional programmers like working concrete examples, too.

A World->World function is unconstrained in its effects upon the given world, modulo substructural types. But it is not a "side effect". Among other important differences, your program can't describe an infinite loop with observable effects on that World.

I don't consider type safety, list comprehensions, etc. to be essential for pure FP. Immutable values, first class functions, and explicit effects models on the call-return path (instead of side effects) are the critical ingredients. Comparing the essential IO problem to "type parameters" (which aren't even a problem for a rich ecosystem of dynamically typed OO) seems disingenuous.

Side effect free functional programming was taught using Lisp in the 60s.

See "Pure Lisp", a style and subset, where no side-effects has been used.

I wasn't able to find much on this via search. The papers I found date to 96. Do you know how 60s Pure Lisp handled IO?

> And how often does that occur in practice for most of the programs people write? Even the most hardcore Haskell programmer isn't going around proving theorems about their modules beyond what the type system can provide for free (and that is true of statically typed OO also).

"What the type system can provide for free" isn't static. Part of working in that kind of language is structuring your code such that important properties end up being proved by the type system.

It rarely rises to the level of a "theorem", but "is this piece of code equivalent to this other piece of code?" is what I'd venture to suggest programmers spend most of their day asking, and Haskell-like languages make that easier to answer.

> "is this piece of code equivalent to this other piece of code?" is what I'd venture to suggest programmers spend most of their day asking, and Haskell-like languages make that easier to answer.

It is a boring question to ask, and one that doesn't come up much in my work. Does this mean Haskell-like languages are not appropriate for my domain?

It means your domain is alien to mine, and I can't tell you what is or isn't appropriate.

For me programming is about automating some business process or at least something you already know how to do, so it's a case of: 1) transcribe the doing into plain code 2) factor out patterns/redundancy in the code. (In practice this is interleaved, and 2) results in building up a language for expressing the domain in code which in turn simplifies 1) - indeed, when adding new functionality it's often a case of first transforming the current code into a representation that makes the new functionality simple). 2) is where the vast majority of the work lies and what takes up the time. Just as good writing is good editing, good coding is good refactoring. At least in my domain.

I do research working on new experiences, like live programming environments. Nothing is really known, there is no spec, everything is a design prototype, code is disposable in a fail-fast kind of way. So I'm pretty extreme, I can see where other domains are very different.

As a weaker form of going around and proving stuff: people do care a lot about properties. We just check them via QuickCheck, instead of formally proving them.

And we organize our programs such as to get nice properties.

If you ask me what's the opposite of "proving", I'd say it's "testing". You call that "weaker"? It's the weakest form of validation I know of.

It may be weak, but by hell it's practical. Tons of tooling, tons of engineers who understand it, and with a pragmatic approach, eliminates many bugs and regressions.

And automatically testing lots and lots of examples gets you closer in spirit to proving than example-based vanilla unit testing.

Any sort of thinking about what the code does or does not do is essentially proving theorems about it, is it not? It seems to me one does that all the time when debugging.

I don't think about coding that way. To me debugging is more like a Sherlock Holmes investigation rather than a formal theorem proving process. I guess we maybe work on different kinds of programs.

You're still, at some point, simulating the steps of some abstract machine in your head to understand what the debugger is telling you.

The simplest case is replacing an expression with its value, given an environment of lexical bindings that are apprent from the source program. Not much investigation necessary. That's FP.

For OO code, you just need to keep track of a lot more context: the state of the receiver of the currently executing method, its heirarchy of parent classes, the runtime class of each object because late binding is pervasive. Of course you can write code that doesn't use any OO features, but the languages clearly aren't designed for it. See: any number of "functional C++" articles.

And, of course, you can get the same kind of highly dynamic behavior in FP languages by explicitly using open recursion, higher-order state and hiding everything behind existentials. But very few codebases do that because the vast, vast majority of the time just one of these features is enough to solve a problem.

OO context is internalized linguistically, via lots of metaphors. Those metaphors can lie, of course, but your brain can apply abstractions to the state of the machine to deal with its complexity, for better or worse. Ideal FP debugging, which I don't think exists in practice, relies on ultimate truth with equational reasoning realized through techniques like referential transparency. In the ideal case, you just reason about the equation and there are no hidden surprises, fuzzy metaphorical reasoning is minimized. In practice, there is still plenty of metaphorical reasoning going on for any non-trivial program as even explicit state necessarily becomes implicit as it increases in quantity (our brains can't handle seeing everything even if it is technically all in front of us).

OO thinking optimizes for the less ideal cases that are far more common. Ideal FP has this ideal mathematical view of the world that rarely pans out in practice, while less ideal FP just resorts to OO-style metaphors and abstraction in practice. For the kinds of experiences I work on (heavily reactive, lots of state, complex interactions), this works well for me, and we are developing techniques to make it less painful (live programming). "Worse is better", as RPG would say.

It sounds like we agree that lexically scoped immutable values are easier to understand, either precisely or with fuzzy metaphors. I'm not sure what "ideal" FP is or how it might have a certain "mathematical view of the world". The features I mentioned are just a subset of semantics that every high-level language programmer already knows, but are pointlessly hobbled in popular languages.

Why should expressing something basic like a tagged union require a detour through the quirks of a particular object system? Ditto for polymorphism, modularity, etc, etc. Clearly we disagree on how useful objects really are in practice, fine. Why not add these domain-specific features on top of a core language with simple semantics? It worked fine for lisps. Luckily, after a couple of decades of "everything is an object!" nonsense, that seems to be where newer languages (Rust, Swift) are headed.

You mean CLOS? This is exactly the context RPG coined "worse is better".

Languages are not so much a collection of features but mindsets. So polymorphism, dynamic dispatch, subtyping, etc...do not define OOP so much as they are leveraged by those languages to enable reasoning with names and metaphors. Calling them just domain specific features misses the point like talking about some dish only as the sum of its ingredients.

Tagged unions and GADTs are quite different in expressiveness and modularity, I still remember the mega case matches used in scalac. Should one function really be given so much functionality when a layered design with several virtual method implementations would be much more amenable to change and modular reasoning? Well, I guess it's a matter of how you view code.

  Languages are not so much a collection of features ...

If you want to define objects precisely, even just to have a language spec, they are absolutely made up of sums, products, recursive types, etc. Whatever useful metaphors one might have to work with objects doesn't change what they actually are. If you give the programmer access to these building blocks, you get ML.

  Calling them just domain specific ...

I meant that the particular way they're combined to get OOP is domain-specific.

Again, I'm just asking: why mess with the basics? Why require encoding simple, universal concepts in terms of an ad-hoc object system? You can still have an object system on top, if you find that helps with the really complicated cases, but why encode the parts of your code that are simple in terms of much more complicated, derived concepts?

Debugging is a time to stop thinking and start looking.

Thinking is probably what got you the bug in the first place, so to kill it a different angle is usually preferable.

In practice, this means sending in test data to see what happens and/or stepping through the code to see where it diverges from what we think it does.