`mfix` not working as expected - haskell

I expected the following code to first prompt start:, then wait for a user response, before echoing the previous user response back, and awaiting a new one:
import System.IO (hFlush, stdout)
import Control.Monad.Fix (mfix)
f :: [String] -> IO [String]
f = mapM $ \x -> putStr x >> putStr ": " >> hFlush stdout >> getLine
g x = f ("start":x)
main = mfix g
But it gives the error thread blocked indefinitely in an MVar operation after the first line is entered.
Why is this and how can I fix it (excuse the pun)?

The reason why this can't work is that in mfix f runs any effect in f exactly once. This follows from the tightening rule
mfix (\x -> a >>= \y -> f x y) = a >>= \y -> mfix (\x -> f x y)
in particular
mfix (\x -> a >> f x) = a >> mfix f
for any correct instance of MonadFix. So the fixed point is only computed for the pure (lazily computed) value inside the monadic action, not for the effects. In your case using mfix asks for printing/reading characters just once in such a way that the input is equal to the output, which is impossible. This isn't a proper use case for mfix. You'd use mfix with IO for example to construct a cyclic data structure in IO like in these examples.
In your case you should use iterateM_ or something similar rather than mfix. see also iterate + forever = iterateM? Repeating an action with feedback.

Unfortunately, mfix in the IO monad doesn't really work to produce lists piecemeal like that. This is because most actions in the IO monad are very strict: they don't produce any part of their result until the whole action has been performed. In particular, mapM in IO will not return any part of its result list until it has gone through all of its input list, which leaves mfix with no hope of tying the knot in the right way here.
In general, mfix in IO really only works if the tied-back value isn't looked at strictly until after the whole mfix action is completed. This still has some possible uses, like initializing a data structure with cycles of mutable cells using only newIORef.

Related

How to avoid the IO monad when solving arithmetic problems in SBV

I am trying to solve arithmetic problems with SBV.
For example
solution :: SymbolicT IO ()
solution = do
[x, y] <- sFloats ["x", "y"]
constrain $ x + y .<= 2
Main> s1 = sat solution
Main> s2 = isSatisfiable solution
Main> s1
Satisfiable. Model:
x = -1.2030502e-17 :: Float
z = -2.2888208e-37 :: Float
Main> :t s1
s1 :: IO SatResult
Main> s2
True
Main> :t s2
s2 :: IO Bool
While I can do useful things, it is easier for me to work with the pure value (SatResult or Bool) and not with the IO monad.
According to the documentation
sat :: Provable a => a -> IO SatResult
constrain :: SolverContext m => SBool -> m ()
sFloats :: [String] -> Symbolic [SFloat]
type Symbolic = SymbolicT IO
Given the type of functions I use, I understand why I always get to the IO monad.
But looking in the generalized versions of the functions for example sFloats.
sFloats :: MonadSymbolic m => [String] -> m [SFloat]
Depending on type of the function, I can work with a different monad than IO. This gives me hope that we will reach a more useful monad, the Identity monad for example.
Unfortunately looking at the examples always solves the problems within the IO monad, so I couldn't find any examples that would work for me.Besides that I don't have much experience working with monads.
Finally My question is:
Is there any way to avoid the IO monad when solving such a problem with SBV?
Thanks in advance
SBV calls out to the SMT solver of your choice (most likely z3, but others are available too), and presents the results back to you. This means that it performs IO under the hood, and thus you cannot be outside the IO monad. You can create custom monads using MonadSymbolic, but that will not get you out of the IO monad: Since the call to the SMT solver does IO you'll always be in IO.
(And I'd strongly caution against uses of unsafePerformIO as suggested in one of the comments. This is really a bad idea; and you can find lots more information on this elsewhere why you shouldn't do so.)
Note that this is no different than any other IO based computation in Haskell: You perform the IO "in-the-wrapper," but once you get your results, you can do whatever you'd like to do with them in a "pure" environment.
Here's a simple example:
import Data.SBV
import Data.SBV.Control
example :: IO ()
example = runSMT $ do
[x, y] <- sFloats ["x", "y"]
constrain $ x + y .<= 2
query $ do cs <- checkSat
case cs of
Unsat -> io $ putStrLn "Unsatisfiable"
Sat -> do xv <- getValue x
yv <- getValue y
let result = use xv yv
io $ putStrLn $ "Result: " ++ show result
_ -> error $ "Solver said: " ++ show cs
-- Use the results from the solver, in a purely functional way
use :: Float -> Float -> Float
use x y = x + y
Now you can say:
*Main> example
Result: -Infinity
The function example has type IO (), because it does involve calling out to the solver and getting the results. However, once you extract those results (via calls to getValue), you can pass them to the function use which has a very simple purely functional type. So, you keep the "wrapper" in the monad, but actual processing, use-of-the values, etc., remain in the pure world.
Alternatively, you can also extract the values and continue from there:
import Data.SBV
import Data.SBV.Control
example :: IO (Maybe (Float, Float))
example = runSMT $ do
[x, y] <- sFloats ["x", "y"]
constrain $ x + y .<= 2
query $ do cs <- checkSat
case cs of
Unsat -> pure Nothing
Sat -> do xv <- getValue x
yv <- getValue y
pure $ Just (xv, yv)
_ -> error $ "Solver said: " ++ show cs
Now you can say:
*Main> Just (a, b) <- example
*Main> a
-Infinity
*Main> b
4.0302105e-21
Long story short: Don't avoid the IO monad. It's there for a very good reason. Get into it, get your results out, and then the rest of your program can remain purely functional, or whatever other monad you might find yourself in.
Note that none of this is really SBV specific. This is the usual Haskell paradigm of how to use functions with side-effects. (For instance, anytime you use readFile to read the contents of a file to process it further.) Do not try to "get rid of the IO." Instead, simply work with it.
Depending on type of the function, I can work with a different monad than IO.
Not meaningfully different, in the sense you'd hope. Every instance of this class is going to be some transformed version of IO. Sorry!
Time to make a plan that involves understanding and working with IO.

Lazy evaluation of IO actions

I'm trying to write code in source -> transform -> sink style, for example:
let (|>) = flip ($)
repeat 1 |> take 5 |> sum |> print
But would like to do that using IO. I have this impression that my source can be an infinite list of IO actions, and each one gets evaluated once it is needed downstream. Something like this:
-- prints the number of lines entered before "quit" is entered
[getLine..] >>= takeWhile (/= "quit") >>= length >>= print
I think this is possible with the streaming libraries, but can it be done along the lines of what I'm proposing?
Using the repeatM, takeWhile and length_ functions from the streaming library:
import Streaming
import qualified Streaming.Prelude as S
count :: IO ()
count = do r <- S.length_ . S.takeWhile (/= "quit") . S.repeatM $ getLine
print r
This seems to be in that spirit:
let (|>) = flip ($)
let (.>) = flip (.)
getContents >>= lines .> takeWhile (/= "quit") .> length .> print
The issue here is that Monad is not the right abstraction for this, and attempting to do something like this results in a situation where referential transparency is broken.
Firstly, we can do a lazy IO read like so:
module Main where
import System.IO.Unsafe (unsafePerformIO)
import Control.Monad(forM_)
lazyIOSequence :: [IO a] -> IO [a]
lazyIOSequence = pure . go where
go :: [IO a] -> [a]
go (l:ls) = (unsafePerformIO l):(go ls)
main :: IO ()
main = do
l <- lazyIOSequence (repeat getLine)
forM_ l putStrLn
This when run will perform cat. It will read lines and output them. Everything works fine.
But consider changing the main function to this:
main :: IO ()
main = do
l <- lazyIOSequence (map (putStrLn . show) [1..])
putStrLn "Hello World"
This outputs Hello World only, as we didn't need to evaluate any of l. But now consider replacing the last line like the following:
main :: IO ()
main = do
x <- lazyIOSequence (map (putStrLn . show) [1..])
seq (head x) putStrLn "Hello World"
Same program, but the output is now:
1
Hello World
This is bad, we've changed the results of a program just by evaluating a value. This is not supposed to happen in Haskell, when you evaluate something it should just evaluate it, not change the outside world.
So if you restrict your IO actions to something like reading from a file nothing else is reading from, then you might be able to sensibly lazily evaluate things, because when you read from it in relation to all the other IO actions your program is taking doesn't matter. But you don't want to allow this for IO in general, because skipping actions or performing them in a different order can matter (and above, certainly does). Even in the reading a file lazily case, if something else in your program writes to the file, then whether you evaluate that list before or after the write action will affect the output of your program, which again, breaks referential transparency (because evaluation order shouldn't matter).
So for a restricted subset of IO actions, you can sensibly define Functor, Applicative and Monad on a stream type to work in a lazy way, but doing so in the IO Monad in general is a minefield and often just plain incorrect. Instead you want a specialised streaming type, and indeed Conduit defines Functor, Applicative and Monad on a lot of it's types so you can still use all your favourite functions.

Idiomatic Haskell syntax without do-blocks or accumulating parentheses?

I'm fairly new to Haskell and have been trying to find a way to pass multiple IO-tainted values to a function to deal with a C library. Most people seem to use the <- operator inside a do block, like this:
g x y = x ++ y
interactiveConcat1 = do {x <- getLine;
y <- getLine;
putStrLn (g x y);
return ()}
This makes me feel like I'm doing C, except emacs can't auto-indent. I tried to write this in a more Lispy style:
interactiveConcat2 = getLine >>= (\x ->
getLine >>= (\y ->
putStrLn (g x y) >>
return () ))
That looks like a mess, and has a string of closed parentheses you have to count at the end (except again, emacs can reliably assist with this task in Lisp, but not in Haskell). Yet another way is to say
import Control.Applicative
interactiveConcat3 = return g <*> getLine <*> getLine >>= putStrLn
which looks pretty neat but isn't part of the base language.
Is there any less laborious notation for peeling values out of the IO taint boxes? Perhaps there is a cleaner way using a lift* or fmap? I hope it isn't too subjective to ask what is considered "idiomatic"?
Also, any tips for making emacs cooperate better than (Haskell Ind) mode would be greatly appreciated. Thanks!
John
Edit: I stumbled across https://wiki.haskell.org/Do_notation_considered_harmful and realized that the nested parentheses in the lambda chain I wrote is not necessary. However it seems the community (and ghc implementors) have embraced the Applicative-inspired style using , <*>, etc, which seems to make the code easier to read in spite of the headaches with figuring out operator precedence.
Note: This post is written in literate Haskell. You can save it as Main.lhs and try it in your GHCi.
A short remark first: you can get rid of the semicolons and the braces in do. Also, putStrLn has type IO (), so you don't need return ():
interactiveConcat1 = do
x <- getLine
y <- getLine
putStrLn $ g x y
We're going to work with IO, so importing Control.Applicative or Control.Monad will come in handy:
> module Main where
> import Control.Applicative
> -- Repeat your definition for completeness
> g :: [a] -> [a] -> [a]
> g = (++)
You're looking for something like this:
> interactiveConcat :: IO ()
> interactiveConcat = magic g getLine getLine >>= putStrLn
What type does magic need? It returns a IO String, takes a function that returns an String and takes usual Strings, and takes two IO Strings:
magic :: (String -> String -> String) -> IO String -> IO String -> IO String
We can probably generalize this type to
> magic :: (a -> b -> c) -> IO a -> IO b -> IO c
A quick hoogle search reveals that there are already two functions with almost that type: liftA2 from Control.Applicative and liftM2 from Control.Monad. They're defined for every Applicative and – in case of liftM2 – Monad. Since IO is an instance of both, you can choose either one:
> magic = liftA2
If you use GHC 7.10 or higher, you can also use <$> and <*> without import and write interactiveConcat as
interactiveConcat = g <$> getLine <*> getLine >>= putStrLn
For completeness, lets add a main so that we can easily check this functionality via runhaskell Main.lhs:
> main :: IO ()
> main = interactiveConcat
A simple check shows that it works as intended:
$ echo "Hello\nWorld" | runhaskell Main.lhs
HelloWorld
References
Applicative in the Typeclassopedia
The section "Some useful monadic functions" of LYAH's chapter "For a Few Monads More".
You can use liftA2 (or liftM2 from Control.Monad):
import Control.Applicative (liftA2)
liftA2 g getLine getLine >>= putStrLn

What's the meaning of IO actions within pure functions?

I thought that in principle Haskell's type system would forbid calls to impure functions (i.e. f :: a -> IO b) from pure ones, but today I realized that by calling them with return they compile just fine. In this example:
h :: Maybe ()
h = do
return $ putStrLn "???"
return ()
h works in the Maybe monad, but it's a pure function nevertheless. Compiling and running it simply returns Just () as one would expect, without actually doing any I/O. I think Haskell's laziness puts the things together (i.e. putStrLn's return value is not used - and can't since its value constructors are hidden and I can't pattern match against it), but why is this code legal? Are there any other reasons that makes this allowed?
As a bonus, related question: in general, is it possible to forbid at all the execution of actions of a monad from within other ones, and how?
IO actions are first-class values like any other; that's what makes Haskell's IO so expressive, allowing you to build higher-order control structures (like mapM_) from scratch. Laziness isn't relevant here,1 it's just that you're not actually executing the action. You're just constructing the value Just (putStrLn "???"), then throwing it away.
putStrLn "???" existing doesn't cause a line to be printed to the screen. By itself, putStrLn "???" is just a description of some IO that could be done to cause a line to be printed to the screen. The only execution that happens is executing main, which you constructed from other IO actions, or whatever actions you type into GHCi. For more information, see the introduction to IO.
Indeed, it's perfectly conceivable that you might want to juggle about IO actions inside Maybe; imagine a function String -> Maybe (IO ()), which checks the string for validity, and if it's valid, returns an IO action to print some information derived from the string. This is possible precisely because of Haskell's first-class IO actions.
But a monad has no ability to execute the actions of another monad unless you give it that ability.
1 Indeed, h = putStrLn "???" `seq` return () doesn't cause any IO to be performed either, even though it forces the evaluation of putStrLn "???".
Let's desugar!
h = do return (putStrLn "???"); return ()
-- rewrite (do foo; bar) as (foo >> do bar)
h = return (putStrLn "???") >> do return ()
-- redundant do
h = return (putStrLn "???") >> return ()
-- return for Maybe = Just
h = Just (putStrLn "???") >> Just ()
-- replace (foo >> bar) with its definition, (foo >>= (\_ -> bar))
h = Just (putStrLn "???") >>= (\_ -> Just ())
Now, what happens when you evaluate h?* Well, for Maybe,
(Just x) >>= f = f x
Nothing >>= f = Nothing
So we pattern match the first case
f x
-- x = (putStrLn "???"), f = (\_ -> Just ())
(\_ -> Just ()) (putStrLn "???")
-- apply the argument and ignore it
Just ()
Notice how we never had to perform putStrLn "???" in order to evaluate this expression.
*n.b. It is somewhat unclear at which point "desugaring" stops and "evaluation" begins. It depends on your compiler's inlining decisions. Pure computations could be evaluated entirely at compile time.

Haskell monadic IO

compute fp = do
text <- readFile fp
let (a,b) = sth text
let x = data b
--g <- x
putStr $ print_matrix $ fst $ head $ x
It works when i get only first element but i want do this for all element on the list of pair.
When i write g<- x i got Couldn't match expected type `IO t0'
with actual type [([[Integer]], [[Integer]])]
You're inside the IO Monad here, so any time you write a "bind" arrow <-, the thing on the right side has to be an IO operation. So the short answer is, you don't want to use <- on the value x.
Now, it looks like you want to call print_matrix for each element of a list rather than a single element. In that case I think Macke is on the right track, but I would use mapM_ instead:
mapM_ (putStr . print_matrix . fst) x
should do the trick.
The reason is that you are explicitly saying you want to putStr each element, one at a time, but you don't care about the result of putStr itself.
It sounds like mapM might fit your bill: Monad a => (b -> a c) -> [b] -> a [c]
It's used to apply a monadic function to a list, and get a list back, in the monad

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