How to convert a generic type in Haskell into a String within a Monadic context

Question

In the MVE code below I have tried to create a function collect which is supposed to take a RegModule-monad as argument such as the scanChar and when this scanChar or other RegModule succeeds in scanning a char as seen in its case branch then the collect shall behave the same way, that is 'scan' the char as well, and increment the associated i as seen in scanChar. On top of the behavior of scanChar however it shall also return a string, hence the return type RegModule d (String, a), where string are all of the 'scanned' Chars within an input string. This shall however not only apply to the scanChar but more generally to other types of monadic-functions using RegModule, but as a start if it could be implemented to only take scanChar into account that will be fine.

The problem is that when I try to return a string I get a type inconsistency error since data d' that I try to use for the function is not explicitly of that time. I have tried with using show but this require that I change the type signature of the method collect, which I would like to avaoid. Any ideas about how to work around this without changing the type signature of any of the methods?

import qualified Data.Set as S
import Control.Monad
type CharSet = S.Set Char
data RE =
 RClass Bool CharSet
newtype RegModule d a =
 RegModule {runRegModule :: String -> Int -> d -> [(a, Int, d)]}
instance Monad (RegModule d) where
 return a = RegModule (\_s _i d -> return (a, 0, d))
 m >>= f =
 RegModule (\s i d -> do (a, j, d') <- runRegModule m s i d
 (b, j', d'') <- runRegModule (f a) s (i + j) d'
 return (b, j + j', d''))
instance Functor (RegModule d) where fmap = liftM
instance Applicative (RegModule d) where pure = return; (<*>) = ap
scanChar :: RegModule d Char
scanChar = RegModule (\s i d ->
 case drop i s of
 (c:cs) -> return (c, i+1, d)
 [] -> []
 )
regfail :: RegModule d a
regfail = RegModule (\_s _i d -> []
 )
regEX :: RE -> RegModule [String] ()
regEX (RClass b cs) = do
 next <- scanChar 
 if (S.member next cs)
 then return ()
 else regfail
fetchData :: RegModule d d
fetchData = RegModule (\_s _i d -> [(d, 0, d)])
collect :: RegModule d a -> RegModule d (String, a)
collect module = do
 a <- module
 consumed <- fetchData
 let consumedStr = (show consumed)
 return (consumedStr, a)
 
runRegModuleThrice :: RegModule d a -> String -> Int -> d -> [(a, Int, d)]
runRegModuleThrice matcher input startPos state =
 let (result1, pos1, newState1) = head $ runRegModule matcher input startPos state
 (result2, pos2, newState2) = head $ runRegModule matcher input pos1 newState1
 (result3, pos3, newState3) = head $ runRegModule matcher input pos2 newState2
 in [(result1, pos1, newState1), (result2, pos2, newState2), (result3, pos3, newState3)]

• leftaroundabout: "whatever this monad matches it shall match, likewise it shall consume the same as the monad, and modify the state of whatever the monad mondfies" / this is all quite nebulous. Please add smaller snippets with concrete description of what you want to work in which way.
• Piskator: @leftaroundabout I have tried to clarify. Hopefully it helped.
• n. m. could be an AI: If you want something like gather, look at how gather is implemented and do likewise. ReadP a hides a function that returns R a. gather takes this function and produces another one that returns R (String, a). Your type hides a function that returns something something [(a, Int, d)]. Can you build a function that returns something something [((String, a), Int, d)] out of it?
• n. m. could be an AI: But perhaps before doing that you want to explain what this RegModule type is all about, because I surely can neither gather not collect what it is supposed to do. Why does it have the type it has?
• Piskator: @n.m.willseey'allonReddit , yes,it was my idea as well to try to look it up in the source and do something similar. It did seem quite advanced for my current skill level, so I will however probablay have to do iterate over it selveral times, but so far what I tried is what you can see from my code above.

Answer 1

Your monad seems a little buggy. In the signature:

String -> Int -> d -> [(a, Int, d)]

the implementation of >>= suggests that the String is the full, constant input string, the first Int is an offset into that String, and the second Int is the number of characters read by the operation and not the new offset. In particular, when the computation on the LHS of >>= starts at offset i and returns a count of characters scanned j, the computation on the right hand side is run starting at offset i+j, not j.

However, your scanChar implementation doesn't appear to match this implementation, since it starts scanning at offset i and then returns the new offset i+1, instead of the number of characters read, which should just be 1.

The reason I bring all this up is that you probably want collect m to run m and then use the offset and number of characters scanned by m to directly extract the scanned substring and add it to the return value, something like:

collect :: RegModule d a -> RegModule d (String, a)
collect m = RegModule $ \s i d -> do
 (a, j, d') <- runRegModule m s i d
 pure ((take j (drop i s), a), j, d')

In order for this to work with your scanChar, the definition will need to be fixed:

scanChar :: RegModule d Char
scanChar = RegModule (\s i d ->
 case drop i s of
 (c:cs) -> return (c, 1, d) -- return "1" char scanned
 [] -> []
 )

• Piskator: A Buhr , thanks for your answer. I might not have the full understanding as to why the Monad is made the way it is but I shall try to respond anyway. So the original Monad is given as part of an assignment inbluding the signature, the return and the bind. I think the i+1 is actually correct as someone else pointed out to me here: stackoverflow.com/questions/76594962/… . I have just tested your code for just 1: ghci> runRegModuleTwice (collect scanChar) "aaa" 0 [] [(("a",'a'),1,[]),(("a",'a'),1,[]),(("a",'a'),1,[])]
• Piskator: If I run it with i+1 I get: ghci> runRegModuleTwice (collect scanChar) "aaa" 0 [] [(("a",'a'),1,[]),(("aa",'a'),2,[]),(("a",'a'),3,[])] which is slightly better, since there seems to be an accumulation in the captured data in the first and second iteration, although the captured elements it seemed reset back to just "a" at the last element of the list.
• Piskator: I am not sure I completely understand why you think that j should be 1 considering these 'prints' of the runRegModuleTwice, but I suspect that your might actually still be right, and perhaps that the flaw is actually in runRegModuleTwice which I implemented myself but which my reflect an underlying and perhaps incorrect conception of the whole code or approach to making a RegEx parser using monads. I need to think more about why you pure approach works without type errors, but I suspsect that what is collected in your code is the input string and not only the 'captured' Chars.
• Piskator: I tried to change collect a bit into: collect m = RegModule ( \s i d -> do (a, i', d') <- runRegModule m s i d; return ((take (i'-i) (drop i s), a), i', d')) this seems to produce ghci> runRegModuleTwice (collect scanChar) "abcd" 0 [] [(("a",'a'),1,[]),(("b",'b'),2,[]),(("c",'c'),3,[]),(("d",'d'),4,[])], which is what is expected for the scanChar I think, since it shows every char that was consumed. I am however still not certain that you are not correct in you assessment above. In the post I linked the comments mention something about history and monads.
• Piskator: And it does seem a bit wierd that any bind should take i+1 rather than 1, since the latter should indeed be the increment-ratio and not the new offset considering the way the bind is defined.