[pron]

I understand. I just said that classifying non-linear transfer of control (whether exceptions or proper continuation) as an effect at all is quite arbitrary, and is just a common usage in the PFP world.

Of course, substructural types are also a language concept (that does indeed interact badly with non-local jumps), which is why I said it was a nitpick about the use of the word "effect".

[catnaroek]

> I just said that classifying non-linear transfer of control (whether exceptions or proper continuation) as an effect at all is quite arbitrary, and is just a common usage in the PFP world.

What exactly makes it arbitrary? It's pretty sensible, even if you don't have substructural types.

> Of course, substructural types are also a language concept (that does indeed interact badly with non-local jumps)

Control effects and substructural types don't interact “badly”. They just require care if you want them together. If you desugar control effects into delimited continuations (that is, normal higher-order functions), it becomes clear as daylight how to correctly handle their interaction with substructural types.

[pron]

> What exactly makes it arbitrary?

The word effect in the PFP world denotes anything that a language-level function does which may affect other functions and is not an argument or a return parameter. That definition is not valid outside of PFP/LC, because it defines as effects as things that are indistinguishable from non-effects in other models of computation. E.g. it calls assignments to certain memory cells "effects" while assignments to other memory cells non-effects.

Again, my (very minor) point is that the word "effect" as you use it simply denotes a PFP linguistic concept rather than an essential computational thing. The only reason I mention it is that the word "effect" has a connotation of something that's real and measurable beyond the language. That's true for IO and time (computational complexity, which, interestingly, is not generally considered an effect in PFP), but not true for jumps (or continuations) and mutation.

> delimited continuations (that is, normal higher-order functions)

Again, you are assuming PFP nomenclature. Delimited continuations do not require language-level functions at all, and higher-order functions can be defined in terms of delimited continuations just as the opposite is true. Delimited continuations are no more higher-order functions than higher-order functions (or monads, rather) are delimited continuations. PFP is not the only way to look at abstractions and not the only fundamental nomenclature.

[tel]

Purity can be defined very nicely against the arrows in a compositional semantics of a language and then effects follow as reasons for impurity.

This is absolutely just a choice. It all ends up depending upon how you define equality of arrows. You could probably even get weirder notions of purity if you relax equality to a higher-dimensional one.

So, it's of course arbitrary in the sense that you can just pick whatever semantics you like and then ask whether or not purity makes much sense there. You point out that "passage of time" is an impurity often ignored and this is, of course, true since we're talking (implicitly) about "Haskell purity" which is built off something like an arm-wavey Bi-CCC value semantics.

A much more foundational difference of opinion about purity arises from whether or not you allow termination.

I'd be interested to see a semantics where setting mutable stores is sufficiently ignored by the choice of equality as to be considered a non-effect. I'm not sure what it would look like, though.

[pron]

> A much more foundational difference of opinion about purity arises from whether or not you allow termination.

Termination or non-termination? One of the (many) things that annoy me about PFP is the special treatment of non-termination, which is nothing more than unbounded complexity. In particular, I once read a paper by D.A. Turner about Total Functional Programming that neglected to mention that every program ever created in the universe could be turned into a total function by adding 2^64 (or a high enough counter) to every recursive loop without changing an iota of its semantics, therefore termination cannot offer a shred of added valuable information about program behavior. Defining non-termination as an effect -- as in F* or Koka (is that a Microsoft thing?) -- but an hour's-computation as pure is just baffling to me.

> I'd be interested to see a semantics where setting mutable stores is sufficiently ignored by the choice of equality as to be considered a non-effect. I'm not sure what it would look like, though.

I think both transactions and monotonic data (CRDTs), where mutations are idempotent, are a step in that direction.

[tel]

Non-termination, my bad!

And of course that's true! Trivially so, though, in that we could do the same by picking the counter to be 10 instead of 2^1000, since we don't appear to care about changing the meaning of the program.

If we do, then we have to consider whether we want our equality to distinguish terminating and non-terminating programs. If it does distinguish, then non-terminating ones are impure.

Now, what I think you're really asking for is a blurry edge where we consider equality module "reasonable finite observation" in which something different might arise.

But in this case you need partial information so we're headed right at CRDTs, propagators, LVars, and all that jazz. I'm not for a single second going to state that there aren't interesting semanticses out there.

Although I will say that CRDTs have really nice value semantics with partial information. I think it's a lot nicer than the operational/combining model.

[pron]

> If we do, then we have to consider whether we want our equality to distinguish terminating and non-terminating programs.

But this is what bugs me. As someone working on algorithms (and does not care as much about semantics and abstractions), the algorithm's correctness is only slightly more important than its complexity. While there are (pragmatic) reasons to care about proving partial correctness more than total correctness (or prioritizing safety over liveness in algorithmists' terms), it seems funny to me to almost completely sweep complexity -- the mother of all effects, and the one at the very core of computation -- under the rug. Speaking about total functions does us no favors: there is zero difference between a program that never terminates, and one that terminates one nanosecond "after" the end of the physical universe. Semantic proof of termination, then, cannot give us any more useful information than no such proof. Just restricting our computational model from TM to total-FP doesn't restrict it in any useful way at all! Moreover, in practical terms, there is also almost no difference (for nearly all programs) between a program that never terminates and one that terminates after a year.

Again, I fully understand that there are pragmatic reasons to do that (concentrate on safety rather than liveness), but pretending that there is a theoretical justification to ignore complexity -- possibly the most important concept in computation -- in the name of "mathematics" (rather than pragmatism) just boggles my mind. The entire notion of purity is the leakiest of all abstractions (hyperbole; there are other abstractions just as leaky or possibly leakier). But we've swayed waaaay off course of this discussion (entirely my fault), and I'm just venting :)

[catnaroek]

I don't agree with pron overall, but he does have a point. Termination and algorithmic complexity do matter, and the techniques Haskell programmers advocate for reasoning about programs have a tendency to sweep theese concerns under the rug. This is in part why I've switched to Standard ML, in spite of its annoyances: No purity, higher kinds, first-class existentials or polymorphic recursion. And no mature library ecosystem. But I get a sane cost model for calculating the time complexity of algorithms. And, when I need laziness, I can carefully control how much laziness I want. Doing the converse in Haskell is much harder, and you get no help whatsoever from the type system.

As an example, consider the humble cons list type constructor. Looks like the free monoid, right? Well, wrong. The free monoid is a type constructor of finite sequences, and Haskell lists are potentially infinite. But even if we consider only finite lists, as in Standard ML or Scheme, the problem remains that, while list concatenation is associative, it's much less efficient when used left-associatively than when used right-associatively. The entire point to identifying a monoid structure is that it gives you the freedom to reassociate the binary operation however you want. If using this “freedom” will utterly destroy your program's performance, then you probably won't want to use this freedom much - or at least I know I wouldn't. So, personally, I wouldn't provide a Monoid instance for cons lists. Instead, I would provide a Monoid instance for catenable lists. [0]

By the way, this observation was made by Stepanov long ago: “That is the fundamental point: algorithms are defined on algebraic structures.” [1] This is the part Haskellers acknowledge. Stepanov then continues: “It took me another couple of years to realize that you have to extend the notion of structure by adding complexity requirements to regular axioms.” [1]

Of course, none of this justifies pron's suspicion of linguistic models of computation.

[0] http://www.westpoint.edu/eecs/SiteAssets/SitePages/Faculty%2...

[1] http://stlport.org/resources/StepanovUSA.html

[pron]

> Of course, none of this justifies pron's suspicion of linguistic models of computation.

Of course. :)

But my view stems from the following belief that finally brings us back to your original point and my original response: there can be no (classical) mathematical justification to what you call linguistic models of computation because computation is not (classical) math, as it does not preserve equality under substitution. The implication I draw from this is not quite the one you may attribute to me such as an overall suspicion, complete rejection or dismissal of those models, but the recognition that their entire justification is not mathematical but pragmatic, and that means that the very same (practical) reasons that might make us adopt the (leaky) abstraction of those models, might lead us to adopt (or even prefer) other models that are justified by pragmatism alone -- such as empirical results showing a certain "affinity" to human cognition -- even if they don't try to abstract computation as classical math.

[catnaroek]

> because computation is not (classical) math

Of course, computation is more foundational. It's mathematics that's just applied computation.

> as it does not preserve equality under substitution

You just need to stop using broken models.

> but the recognition that their entire justification is not mathematical but pragmatic

I don't see a distinction. To me, nothing is more pragmatic to use than a reliable mathematical model.

> the (leaky) abstraction of those models

Other than the finiteness of real computers, what else is leaky? Mind you, abstracting over the finiteness of the computer is an idea that even... uh... “less mathematically gifted” languages (such as Java) acknowledge as good.

> such as empirical results showing a certain "affinity" to human cognition

Experience shows that humans are incapable of understanding computation at all. But computation is here to stay, so the best we can do is rise to the challenge. Denying the nature of computation is denying reality itself.