I made a function similar to numpy's array. It converts lists to arrays, lists of lists to 2d arrays, etc.
It works like this:
ghci> arrFromNestedLists ["hello", "world"] :: Array (Int, (Int, ())) Char
array ((0,(0,())),(1,(4,()))) [((0,(0,())),'h'),((0,(1,())),'e'),((0,(2,())),'l'),((0,(3,())),'l'),((0,(4,())),'o'),((1,(0,())),'w'),((1,(1,())),'o'),((1,(2,())),'r'),((1,(3,())),'l'),((1,(4,())),'d')]
(Int, (Int, ())) and not (Int, Int) because I don't know of a programatic way to increase the length of a tuple. (side question: is there such way?)
The coding of it was awkward and I had to do a "workaround" (passing around dummy arguments to functions) for it to work. I wonder if there's a better way.
So here's the code, interrupted with details of the ugly workarounds:
{-# LANGUAGE FlexibleInstances, ScopedTypeVariables, TypeFamilies #-}
type family ListOfIndex i a
type instance ListOfIndex () a = a
type instance ListOfIndex (Int, i) a = [ListOfIndex i a]
class Ix i => ArrConv i where
acBounds :: a -> ListOfIndex i a -> (i, i)
acFlatten :: i -> ListOfIndex i a -> [a]
acBounds "should" be :: ListOfIndex i a -> (i, i). And similarly for acFlatten. Each is given a dummy variable (undefined is always the value given) because otherwise I couldn't get it to compile :(
arrFromNestedLists :: forall i a. ArrConv i => ListOfIndex i a -> Array i a
arrFromNestedLists lst =
listArray
(acBounds (undefined :: a) lst)
(acFlatten (undefined :: i) lst)
Above is the dummy undefined argument passing at work. It tells the GHC which instance of ListOfIndex to use.
instance ArrConv () where
acBounds _ = const ((), ())
acFlatten _ = (: [])
The below function should have been the acBounds function in an instance of ArrConv, and is declared outside only because I need to use ScopedTypeVariables and I don't know how I can do it in a function in an instance definition..
acSucBounds
:: forall a i. ArrConv i
=> a -> [ListOfIndex i a] -> ((Int, i), (Int, i))
acSucBounds _ lst =
((0, inStart), (length lst - 1, inEnd))
where
(inStart, inEnd) = acBounds (undefined :: a) (head lst)
instance ArrConv i => ArrConv (Int, i) where
acBounds = acSucBounds
acFlatten _ = concatMap (acFlatten (undefined :: i))
The reason that the extra arguments to acBounds and acFlatten are necessary is that the types a and i cannot be recovered from ListOfIndex i a -> (i, i) and ListOfIndex i a -> [a] respectively. One workaround is to combine the two methods into one method acArgs of type ListOfIndex i a -> ((i, i), a). Now the only problem is to use it in the instance of (Int, i) in a way which prevents the typechecker from generalizing its type too much causing the same problem as before (for example, we cannot simply use fst . acArgs).
{-# LANGUAGE TypeFamilies, FlexibleInstances #-}
import Data.Array
type family ListOfIndex i a
type instance ListOfIndex () a = a
type instance ListOfIndex (Int, i) a = [ListOfIndex i a]
class Ix i => ArrConv i where
acArgs :: ListOfIndex i a -> ((i, i), [a])
instance ArrConv () where
acArgs x = (((), ()), [x])
instance ArrConv i => ArrConv (Int, i) where
acArgs lst =
(((0, inStart), (length lst - 1, inEnd)), args >>= snd)
where
args = map acArgs lst
(inStart, inEnd) = fst (head args)
arrFromNestedLists :: ArrConv i => ListOfIndex i a -> Array i a
arrFromNestedLists = uncurry listArray . acArgs