Htykuut

I'm trying to create a Haskell function with a class to get this function to work with different numbers of arguments.

{-# Language FlexibleInstances #-}



class Titles a where

  titleTeX ::  String -> a



instance Titles String where

  titleTeX str = titleWithFrame 1 "%" "%" "%" [str]



instance  Titles (String -> String) where

  titleTeX str = (s -> titleWithFrame 1 "%" "%" "%" (s:[str]))



titleWithFrame::Int -> String -> String -> String -> [String] -> String

titleWithFrame nb beg end com lstr =

  cadr++cont++cadr

    where

          cadr = concat $ replicate nb (beg++rempl++end++"n")

          cont = concatMap (s -> beg++" "++s++" "++end++"n") lstr

          rempl = take long $ concat $ replicate long com

          long = (maximum $ map length lstr) + 2

When I try this function with ghci, I have the following results:

ghci> putStr $ titleTeX "Line 1"

%%%%%%%%%%

% Line 1 %

%%%%%%%%%%

ghci> putStr $ titleTeX "Line 1" "Line 2"

%%%%%%%%%%

% Line 1 %

% Line 2 %

%%%%%%%%%%

ghci> putStr $ titleTeX "Line 1" "Line 2" "Line 3"



<interactive>:4:10: error:

    • No instance for (Main.Titles ([Char] -> [Char] -> String))

        arising from a use of ‘titleTeX’

        (maybe you haven't applied a function to enough arguments?)

    • In the second argument of ‘($)’, namely

        ‘titleTeX "Line 1" "Line 2" "Line 3"’

      In the expression: putStr $ titleTeX "Line 1" "Line 2" "Line 3"

      In an equation for ‘it’:

          it = putStr $ titleTeX "Line 1" "Line 2" "Line 3"

I don't understand where my error is and why my polyvariadic function doesn't work with more than 2 arguments.

Do you know where my error comes from? and How to make my function work with an arbitrary number of arguments?

The error occurs because you have exactly two instances of Titles in your program:

instance Titles String

instance Titles (String -> String)

These let you call titleTeX with one and two arguments respectively, but three arguments would require

instance Titles (String -> String -> String)

which doesn't exist. Or as ghc puts it:

• No instance for (Main.Titles ([Char] -> [Char] -> String))

    arising from a use of ‘titleTeX’

([Char] is the same as String.)

It's as if you'd defined a function

foo :: [Int] -> Int

foo [x] = ...

foo [x, y] = ...

but foo [x, y, z] is an error.

To make this work for any number of arguments, we need to use recursion. As with list functions (where you'd typically have a base case foo = ... and a recursive case foo (x : xs) = ... that calls foo xs somewhere), we need to define a Titles instance in terms of other instances:

instance Titles String

instance (Titles a) => Titles (String -> a)

The tricky bit is that I don't see a way to implement a titleTeX that fits the above declarations.

I had to make other changes to your code to make it work:

{-# Language FlexibleInstances #-}



titleTeX :: (Titles a) => String -> a

titleTeX str = titleTeXAccum [str]

titleTeX isn't a method anymore. It's just a convenience front-end for the actual titleTeXAccum method.

In principle we could have omitted the String parameter and defined titleTeX :: (Titles a) => a as titleTeX = titleTexAccum , but then titleTex :: String would crash at runtime (because we end up calling maximum on an empty list).

class Titles a where

  titleTeXAccum :: [String] -> a

Our method now takes a list of strings that it (somehow) turns into a value of type a.

instance Titles String where

  titleTeXAccum acc = titleWithFrame 1 "%" "%" "%" (reverse acc)

The implementation for String is easy: We just call titleWithFrame. We also pass reverse acc because the order of elements in the accumulator is backwards (see below).

instance (Titles a) => Titles (String -> a) where

  titleTeXAccum acc str = titleTeXAccum (str : acc)

This is the crucial part: The general titleTeXAccum method forwards to another titleTeXAccum method (of a different type / different Titles instance). It adds str to the accumulator. We could have written acc ++ [str] to add the new element at the end, but that's inefficient: Calling titleTeXAccum with N elements would take O(N^2) time (due to repeated list traversals in ++). Using : and only calling reverse once at the end reduces this to O(N).

It works if you use the function you presented, titleTeX, and not some other function you have yet to show, titleLaTeX.