haskell - generating the first n terms of the continued fraction expansion of a number -


edit: @downvoters: @ least please tell me how can improve question? tried best can, , getting downvotes without comment not constructive in opinion.

im still new haskell, , exercises, i'm trying make function, returns first n terms of continued fraction expansion of x. first argument x can floting point or integral, second argument must int. code far, load without error:

continuedfraction x n | x < 0  = []                       | n < 1 = []                       | otherwise = [floor x] ++ (take n (continuedfraction (1 / (x - floor x)) (n-1) ) )

(i aware not elegant, simplest 1 able come @ point.)

as use function e.g. continuedfraction 3.1415 4 error message below. can point out error / explain message?

(i did try make type definition ideas above, without success too: continuedfraction :: (num x) => x -> int -> [integer])

the error message (when running without type definition):

*main> continuedfraction 3.1415 4  <interactive>:86:1:     not deduce (integral a0)       arising use of `continuedfraction'     context (integral t)       bound inferred type of :: integral t => [t]       @ <interactive>:86:1-26     type variable `a0' ambiguous     note: there several potential instances:       instance integral integer -- defined in `ghc.real'       instance integral int -- defined in `ghc.real'       instance integral word -- defined in `ghc.real'     in expression: continuedfraction 3.1415 4     in equation `it': = continuedfraction 3.1415 4  <interactive>:86:19:     not deduce (fractional a0) arising literal `3.1415'     context (integral t)       bound inferred type of :: integral t => [t]       @ <interactive>:86:1-26     type variable `a0' ambiguous     note: there several potential instances:       instance integral => fractional (ghc.real.ratio a)         -- defined in `ghc.real'       instance fractional double -- defined in `ghc.float'       instance fractional float -- defined in `ghc.float'     in first argument of `continuedfraction', namely `3.1415'     in expression: continuedfraction 3.1415 4     in equation `it': = continuedfraction 3.1415 4

advice

if beginner @ haskell there few rules should stick to:

  • if have function, make sure give type signature expresses intended input/output
  • if in doubt stick concrete types double on typeclasses fractional a
  • if function working intended remove type signature or use language extension -xscopedtypevariables , ghci explore signatures compiler infer feel typeclasses

answer

now let explore function - want generate continued fraction assume formula have written down generating correct. haskell powerful enough model infinite lists let use power , rid of second parameter , generate (possibly) infinite list.

continuedfraction :: double -> [int]

so see - expecting double input , result [int], i.e. list of integers, chose int simplicity - huge integer don't think algorithm neither stable nor efficient - , using double's guess real problem floating point arithmetics.

continued fraction x | x < 0     = []                      | otherwise = let = floor x                                        x' = 1/(x - fromintegral i)                                    in : continuedfraction x'

this simplest solution came with, problems had were

  • i :: int, x :: double in haskell cannot subtract things of different type, there no autoboxing/automatic coercion. control on things - compiler not smart enough infer 'obviously' wanted calculate (you see leads if use ms excel).

  • the solution problem explicit conversion fromintegral :: double -> int in case

  • for readability switched [a] ++ a : equivalent, less write , more performant, performance not of concern here

using function in ghci: ghci myfile.hs

> continuedfraction 3.1415 [3,.....] --infinite list > take 4 $ continuedfraction 3.1415 [3,7,14,1]

now can explore function!

how use advice

{-# language scopedtypevariables#-}  module so34830462  --continuedfraction :: double -> [int] continuedfraction :: double -> _ continuedfraction x | x < 0  = []                     | otherwise = let = floor x                                       x' = 1/ (x - fromintegral i)                                   in : continuedfraction  x'

ghci myfile.hs leads error

ghci, version 7.10.2: http://www.haskell.org/ghc/  :? [1 of 1] compiling so34830462       ( 34830462.hs, interpreted )  myfile.hs:6:32:     found hole ‘_’ type: [t]     [...]                continuedfraction :: integral t => double -> [t]     [...] failed, modules loaded: none.

it tells in short - "oh didn't specify correct type signature", ghc use type signature.

you can substitute type signature , same double parameter, exploring function bit bit.

if not sure start can omit type signature , call :t continuedfraction iside ghci session.


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