module MapAlgebra 
	(
	 CoveragesOps (..)
	) 
	where

import Coverage

class (Coverages cov ) => CoveragesOps cov where
	-- operations
	single :: (b -> c) -> (cov a b ) -> (cov a c ) -- altera o contra-domaininio
	multiple :: (Eq a, Eq b) => ( [b] -> c ) -> [(cov a b )] -> (cov a b ) -> (cov a c ) -- altera o contra-dominio
	select :: (cov a b ) -> (a -> c -> Bool ) -> c -> (cov a b ) -- altera o dominio
	compose :: ( [b] -> b ) -> (cov a b ) ->  b
	spatial :: ( [b] -> b )  -> (cov a b ) -> (a -> c -> Bool ) ->  (cov c b ) -> (cov c b ) -- altera o contra-dominio
	
	-- axioms
	single g m =  new_cov (domain m) (g . (fun m) )  
	multiple fn mlist mref = new_cov (domain mref) (\x ->  fn (faux mlist x) )  
	compose fn m = (fn (values m))
	spatial fn m p mref = new_cov (domain mref) (\i -> compose fn (select  m p i) ) 
	select m p o = new_cov sel_dom (fun m) -- a Fun�o de mapeamento se mantem
		where
		sel_dom = [ e | e <- (domain m) , (p e o)] -- g �o novo dominio com restri�o do predicado
		
instance CoveragesOps Coverage where 


faux :: (Coverages cov, Eq a, Eq b) => [(cov a b )] -> a -> [b]
faux [] _ = []
faux (x:xs) e = faux' (evaluate x e)
	where
	faux' (Just v ) = v : (faux xs e)
	faux' (Nothing) =(faux xs e)