(Whether readers would consider the post [or indeed this post] an act of trollery was mooted and mentioned several times in the original post - my thoughts at the end. I am writing this because I would have expected somebody to have said this by now. If it has been said then my sincere apologies. Meta issues, flames, etc., to me and not the list of course.) Pure versus Impure I suspect introducing C into this discussion may not help clarify the fundamental issue. As anyone with experience of programming in Haskell appreciates, there is a big difference between (e.g.) these two functions for taking the sum of two integers: plus :: Int -> Int -> Int plusIO :: Int -> Int -> IO Int The choice is a profound one and will affect their construction as well as the contexts they can be used and so forth. Haskell supports both styles of programming and allows them to be safely and freely intermixed with the type system guaranteeing to keep them properly separated. The type system and static semantics are critical to the Haskell approach to IO and 'purity'. I can't see how it can be meaningfully pushed into the background in any discussion or comparative discussion of these issues. In Short If the programming context in question doesn't provide any equivalent formal separation in its type system of plus-like functions and plusIO-like computations, that programmers use in practice to guide the construction of their programs, then how can the said programming context be considered equivalent to Haskell's treatment of pure functions and effects-generating computations. You just need to consider your own Haskell programming activity and how the type system keeps calculations and I/O actions separate to see this point. I doubt if any extra theory (or theology!) will add much insight. That T word Again (or not) Let's keep this forward-looking. With the email piling in as I write this, please consider whether this continuation of this discussion is likely to be helpful to the general readers of this list or whether it will confuse or discourage them, before adding to it. A Happy New Year to you, Chris From: haskell-cafe-bounces@haskell.org [mailto:haskell-cafe-bounces@haskell.org] On Behalf Of Steve Horne Sent: 28 December 2011 17:40 To: Haskell Cafe Mailing List Subject: [Haskell-cafe] On the purity of Haskell This is just my view on whether Haskell is pure, being offered up for criticism. I haven't seen this view explicitly articulated anywhere before, but it does seem to be implicit in a lot of explanations - in particular the description of Monads in SBCs "Tackling the Awkward Squad". I'm entirely focused on the IO monad here, but aware that it's just one concrete case of an abstraction. Warning - it may look like trolling at various points. Please keep going to the end before making a judgement. To make the context explicit, there are two apparently conflicting viewpoints on Haskell... 1. The whole point of the IO monad is to support programming with side-effecting actions - ie impurity. 2. The IO monad is just a monad - a generic type (IO actions), a couple of operators (primarily return and bind) and some rules - within a pure functional language. You can't create impurity by taking a subset of a pure language. My view is that both of these are correct, each from a particular point of view. Furthermore, by essentially the same arguments, C is also both an impure language and a pure one. See what I mean about the trolling thing? I'm actually quite serious about this, though - and by the end I think Haskell advocates will generally approve. First assertion... Haskell is a pure functional language, but only from the compile-time point of view. The compiler manipulates and composes IO actions (among other things). The final resulting IO actions are finally swallowed by unsafePerformIO or returned from main. However, Haskell is an impure side-effecting language from the run-time point of view - when the composed actions are executed. Impurity doesn't magically spring from the ether - it results from the translation by the compiler of IO actions to executable code and the execution of that code. In this sense, IO actions are directly equivalent to the AST nodes in a C compiler. A C compiler can be written in a purely functional way - in principle it's just a pure function that accepts a string (source code) and returns another string (executable code). I'm fudging issues like separate compilation and #include, but all of these can be resolved in principle in a pure functional way. Everything a C compiler does at compile time is therefore, in principle, purely functional. In fact, in the implementation of Haskell compilers, IO actions almost certainly *are* ASTs. Obviously there's some interesting aspects to that such as all the partially evaluated and unevaluated functions. But even a partially evaluated function has a representation within a compiler that can be considered an AST node, and even AST nodes within a C compiler may represent partially evaluated functions. Even the return and bind operators are there within the C compiler in a sense, similar to the do notation in Haskell. Values are converted into actions. Actions are sequenced. Though the more primitive form isn't directly available to the programmer, it could easily be explicitly present within the compiler. What about variables? What about referential transparency? Well, to a compiler writer (and equally for this argument) an identifier is not the same thing as the variable it references. One way to model the situation is that for every function in a C program, all explicit parameters are implicitly within the IO monad. There is one implicit parameter too - a kind of IORef to the whole system memory. Identifiers have values which identify where the variable is within the big implicit IORef. So all the manipulation of identifiers and their reference-like values is purely functional. Actual handling of variables stored within the big implicit IORef is deferred until run-time. So once you accept that there's an implicit big IORef parameter to every function, by the usual definition of referential transparency, C is as transparent as Haskell. The compile-time result of each function is completely determined by its (implicit and explicit) parameters - it's just that that result is typically a way to look up the run-time result within the big IORef later. What's different about Haskell relative to C therefore... 1. The style of the "AST" is different. It still amounts to the same thing in this argument, but the fact that most AST nodes are simply partially-evaluated functions has significant practical consequences, especially with laziness mixed in too. There's a deep connection between the compile-time and run-time models (contrast C++ templates). 2. The IO monad is explicit in Haskell - side-effects are only permitted (even at run-time) where the programmer has explicitly opted to allow them. 3. IORefs are explicit in Haskell - instead of always having one you can have none, one or many. This is relevant to an alternative definition of referential transparency. Politicians aren't considered transparent when they bury the relevant in a mass of the irrelevant, and even pure functions can be considered to lack transparency in that sense. Haskell allows (and encourages) you to focus in on the relevant - to reference an IORef Bool or an IORef Int rather than dealing with an IORef Everything. That last sentence of the third point is my most recent eureka - not so long ago I posted a "Haskell is just using misleading definitions - it's no more transparent than C" rant, possibly on Stack Overflow. Wrong again :-( So - what do you think?