arrays - Can't find a proper signature for a function using STUArray (neither can GHC) -

i built function finding determinant of matrix using st-monad , unboxed starrays (stuarray). type matrix following:

newtype matrix e = matrix (array int (uarray int e)) 

that is, immutable array containing immutable unboxed arrays containing elements. require me add predicate iarray uarray e functions dealing matrix, in turn requires flexiblecontexts. okay, done.

the function used calculate determinant has following signature:

detst :: (iarray uarray e, marray (stuarray s) e (st s),           num e, eq e, division e)    => array int (uarray int e) -> st s e 

i required add predicate marray (stuarray s) e (st s) since internally arrays converted mutable arrays (the outer boxed, inner unboxed).

this function can used so:

main =     let m@(matrix x) = matrix [ [1,-2,3,234]                               , [5,2,3,-3]                               , [7,18,3,40]                               , [2,9,71,0] ]         d = runst (detst x) :: int -- needed type check, ambiguous otherwise  print d 

works, fine. how ugly is! of course not want give away internals of of matrix (at least not further predicates attached functions make me to). define following function:

det :: matrix e -> e 

and can't.

i tried without proper signature:

det (matrix arr) = runst (detst arr) 

fails. fair enough, i'll put brain work: detst requires iarray uarray e, marray (stuarray s) e (st s), num e, eq e, division e, det, doesn't it?

det :: (iarray uarray e, marray (stuarray s) e (st s),           num e, eq e, division e) => matrix e -> e 

fails. don't see how. message ghc (7.4.2) gives me is:

could not deduce (marray (stuarray s) t (st s))   arising use of `detst' 

but exact term in predicates!

ghc suggests:

add (marray (stuarray s) t (st s)) context of   type expected context: st s t   or inferred type of      det :: (eq t, num t, iarray uarray t, division t) => matrix t -> t or add instance declaration (marray (stuarray s) t (st s)) 

okay. understanding have done first thing. there exist instance (marray ...) (otherwise, how have used in main?!).

i not sure wrong here. believe has "hidden" st state in s, , s of detst other s s in det be, don't know how write type this.

what proper definition of det - , why?!

the program without det compiles fine using flexiblecontexts, no warnings -wall. complete source code can found as gist here.

i managed work using trick described keegan mcallister in article:

{-# language flexiblecontexts, scopedtypevariables, rankntypes, gadts #-}  data evidence s e   evidence :: (marray (stuarray s) e (st s)) => evidence s e  data elemtype e = elemtype (forall s. evidence s e)  det :: forall e . (iarray uarray e, num e, eq e, division e)        => elemtype e -> matrix e -> e det (elemtype e) mat = runst (f e mat)       f :: evidence s e -> matrix e -> st s e     f evidence (matrix arr) = detst arr 

usage:

main :: io () main =     let m = matrix [ [1,-2,3,234]                    , [5,2,3,-3]                    , [7,18,3,40]                    , [2,9,71,0] ]     print $ det (elemtype evidence) (m :: matrix int) 

the problem stems lack of higher-rank constraints - runst has type (forall s. st s a) -> a, need constraint forall s . marray (stuarray s) e (st s), not supported ghc. trick allows convince type checker constraint holds. more in-depth discussion of problem available in article linked above.