Hi Will,
I can tell I'm talking to a kindred spirit - we oughta be able to describe
all this stuff in plain, simple, clear English. It's a great challenge for
a prose writer.
On Mon, Mar 2, 2009 at 9:21 AM, Will Ness
Maybe antilog or prelog or future trace or the like. In any case, I think that's useful for explaining lazy evaluation, but it's not directly implicated by monad semantics. IOW monad semantics and evaluation strategy are (mostly) orthogonal.
I don't follow. Monad semantics in general is to chain together its action- functions (:: a -> M b). IO monad's semantics is that it promises to perform the recorded requests, if called upon. Not only is it directly implicated by its semantics, it IS its semantics. It is what IO-bind is. Other monad's binds will mean something else.
Right, but this is //Haskell// monad semantics. It's an artifact of lazy evaluation. Referring back to the mathematical definition of monad, there's no evaluation process or promise, only denotation.
To recapture, the only difference IO monad has, is that it refers EXPLICITLY to a compiler, and its runtime execution operations. But from inside Haskell it's just anther monad (I've said that already haven't I? :) ).
Mmm, I wouldn't say explicitly. Again, this is because of lazy evaluation, not because of the nature of monads. They just put stuff in order, regardless of evaluation strategy.
That's why I propose to call these bind-chainable functions action functions, not just actions, and actual I/O acivities to call just that, activity. Also notice I write I/O there where it belongs to the actual world action (... the terminology really MUST be refined here!). I think anything else is confusing.
Agreed, that's the key distinction.
I'm open for another suggestion for how to name these "action-functions", but it's time the definite name is finalized; it's very confusing to see these IO- action-functions referred to, in all these tutorials, as performing real world I/O actions. They don't, of course.
Alas, this is where taste enters into it. You can come up with the perfect set of names and somebody won't like it. ;) My own preference is to dispense with the action/function idiom and just say that IO //terms// are essentially unbound (but typed) variables, that will be bound to values when interpreted at runtime. So I wouldn't even call "getChar" an action; I'd just say it's a term denoting an IO Char value to be provided later. In contrast with a constant term like '3'.
Better to avoid "evaluation" altogether (that seems to be your another idea from that log, is it?).
Yep. Hate evaluation. ;)
I think the KEY is to always keep a clear separation of what is inside the pure Haskell world, and what is executed by its run-time, as an imperative program iving inside the real volatile world (capable of calling back into Haskell).
Yeah, I don't recall many tutorials zeroing in on this. I think it's very helpful.
And when inside the pure Haskell world, IO monad is ABSOLUTELY in NO RESPECT no different than any other. The operational log metaphor help keep this part of its semantics clear, from the other part - the fact that its operational log will actually get executed by run-time.
Correction: special name for IO "functions" (actually "IO terms" would be better). Why? They are just fuctions, of type (Monad m => a -> m b). What I'm saying, they are of special type, chainable by the M monad, so it seems logical to have a special name for such M-chainable functions, e.g. "M-action functions" (whatever the M).
Technically they cannot be functions - there's no "same input, same output" (at least not for input operations).
Yes there is. There's the whole point I'm driving at. We are not performing a computation with our code. We describe the computation that will be performed. Our values are functions. The usage of actual input is deferred to the runtime system.
What's the domain of "getChar"? We can't mess with the mathematical definition of function, so we really can't use it for IO stuff (or any non-deterministic value, e.g. random). To quibble yet more: there's no computation involved in IO, strictly speaking, since it's analog. A Turing machine (as he originally described it) can't do IO.
It's just like Show functions that (will) add their output onto a hidden parameter, the string-being-built (when called). Same here, with the log-being- built. Assentially, we're dealing here with the delayed application of carried functions, that's all.
Here's again a simple outline of how an IO monad might look like, inside Haskell. It helped clarify things for me (dealing with output only, but still):
________________________________ data IO a = IORec -> (a,IORec) -- building the record of I/O activities to be performed
instance Monad IO where return a rec = (a,rec) -- return :: a -> IO a (m »= g) rec = uncurry g $ m rec -- g :: a -> IO b
putStrLn :: a -> IO () putStrLn a rec = ((),rec ++ [("putStrLn", a)]) ================================
No referential transparency. That's the problem.
Everything is referentially transparent. There are no side effects in Haskell. You know that. :) You wrote as much yourself (assuming you're the author of that blog). _______________________________________ IO value describes the computation that WILL BE performed OUTSIDE of Haskell. =======================================
That is a statement that is easy to understand, and is not at all confusing. I think.
But also logically inconsistent: how can an expression "inside" of Haskell refer to something outside of Haskell? More specifically, Haskell expressions can only denote values in the Haskell semantic universe. IO processes (not computations) lie outside of that universe, so Haskell cannot say anything about them. But the //result// of an IO process is a value within the semantic universe, so it can be referenced.
This was a big problem for me; I find terms like "action", "computation", "function" completely misleading for IO terms/values. Why? A function of type (a -> M b) is a function that returns a value, (:: M b), tagged with some monadic hidden data. In case of IO, it is a promise to perform some actual I/O that's passed around, hidden. But the M-action function itself is just a regular Haskell function. It can be defined elsewhere, anywhere.
But the "promise to perform" is a matter of evaluation semantics, not denotational semantics. Denotationally these things cannot be functions.
But they are. They describe future computation to be performed outside of
Haskell. Their values - inside Haskell - are one and the same - it's (:: IO a) entities. Which encapsulate the record, the _sceleton_of_future_computation_to_be_performed, which is ONE and only. It's just that it has holes in it, where the actual values will go into. It's like back into Prolog with its yet-unassigned variables. Or to any imperative language with set-once.
The whole future/promise thing comes from lazy evaluation. With strict evaluation, there would be no such promise; expressions would be evaluated (reduced) on the spot, so there would be no log of promised execution. Language semantics (denotational) and evaluation strategy (operational?) are orthogonal. Evaluation strategy doesn't change the meaning (denotation) of the program, but it does affect its execution profile - memory consumption, etc. - so programmers have to think about it. Except of course it does change the behavior of the program where IO is concerned. In a lazy language you can write IO expressions that will never get evaluate/performed, but not so in a strict language. But behavior and meaning are different things. Take another example: the strict application operator '$!'. It doesn't change the denotation of a program but it does change its behavior, by which I mean the interpretational process. Such operators don't denote, really; they're more like meta-syntax or pragmas than Haskell syntax.
Denotationally, all a monad does is ensure sequencing, which is necessary to properly order the (non-deterministic) IO values.
No it does more than that. It ascribes actual meaning to what its M-action- functions mean, and it defines what it means for them to be combined in a chain. They are of course kept in sequence, in that chain.
Ok, then for the IO monad all it does is ensure sequencing. The behavior of getChar comes from its implementation, not from the monad it is wrapped in. Remember GHC's implementation of IO as a state transformer is not the only possible implementation.
With lazy eval this gets translated into the building of a "future log" etc.
Right, only better not to use "eval" - ever. Haskell has expressions which get reduced; values belong to its runtime system. They are OUTSIDE of Haskell world.
We do not "evaluate" anything. It would be an imperative. :)
We're probably stuck with it, practically speaking, but where extra clarity is needed I suggest "reduction" instead of "evaluation", from the lambda calculus.
Thanks,-gregg
Thank you, for a great and enlightening discussion.
Same here!