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--------------------------------------------------------------------------- --- Library to support lightweight generic traversals --- through tree-structured data. See --- [here](http://www-ps.informatik.uni-kiel.de/~sebf/projects/traversal.html) --- for a description of the library. --- --- @author Sebastian Fischer --- @version January 2019 --------------------------------------------------------------------------- module Data.Traversal ( Traversable, noChildren, children, replaceChildren, mapChildren, family, childFamilies, mapFamily, mapChildFamilies, evalFamily, evalChildFamilies, fold, foldChildren, replaceChildrenIO, mapChildrenIO, mapFamilyIO, mapChildFamiliesIO, evalFamilyIO, evalChildFamiliesIO ) where --- A datatype is <code>Traversable</code> if it defines a function --- that can decompose a value into a list of children of the same type --- and recombine new children to a new value of the original type. --- type Traversable a b = a -> ([b], [b] -> a) --- Traversal function for constructors without children. --- noChildren :: Traversable _ _ noChildren x = ([], const x) --- Yields the children of a value. --- children :: Traversable a b -> a -> [b] children tr = fst . tr --- Replaces the children of a value. --- replaceChildren :: Traversable a b -> a -> [b] -> a replaceChildren tr = snd . tr --- Applies the given function to each child of a value. --- mapChildren :: Traversable a b -> (b -> b) -> a -> a mapChildren tr f x = replaceChildren tr x (map f (children tr x)) --- Computes a list of the given value, its children, those children, etc. --- family :: Traversable a a -> a -> [a] family tr x = familyFL tr x [] --- Computes a list of family members of the children of a value. --- The value and its children can have different types. --- childFamilies :: Traversable a b -> Traversable b b -> a -> [b] childFamilies tra trb x = childFamiliesFL tra trb x [] --- Applies the given function to each member of the family of a value. --- Proceeds bottom-up. --- mapFamily :: Traversable a a -> (a -> a) -> a -> a mapFamily tr f = f . mapChildFamilies tr tr f --- Applies the given function to each member of the families of the children --- of a value. The value and its children can have different types. --- Proceeds bottom-up. --- mapChildFamilies :: Traversable a b -> Traversable b b -> (b -> b) -> a -> a mapChildFamilies tra trb = mapChildren tra . mapFamily trb --- Applies the given function to each member of the family of a value --- as long as possible. On each member of the family of the result the given --- function will yield <code>Nothing</code>. --- Proceeds bottom-up. --- evalFamily :: Traversable a a -> (a -> Maybe a) -> a -> a evalFamily tr f = mapFamily tr g where g x = maybe x (mapFamily tr g) (f x) --- Applies the given function to each member of the families of the children --- of a value as long as possible. --- Similar to 'evalFamily'. --- evalChildFamilies :: Traversable a b -> Traversable b b -> (b -> Maybe b) -> a -> a evalChildFamilies tra trb = mapChildren tra . evalFamily trb --- Implements a traversal similar to a fold with possible default cases. --- fold :: Traversable a a -> (a -> [r] -> r) -> a -> r fold tr f = foldChildren tr tr f f --- Fold the children and combine the results. --- foldChildren :: Traversable a b -> Traversable b b -> (a -> [rb] -> ra) -> (b -> [rb] -> rb) -> a -> ra foldChildren tra trb f g a = f a (map (fold trb g) (children tra a)) --- IO version of replaceChildren --- replaceChildrenIO :: Traversable a b -> a -> IO [b] -> IO a replaceChildrenIO tr = liftIO . replaceChildren tr --- IO version of mapChildren --- mapChildrenIO :: Traversable a b -> (b -> IO b) -> a -> IO a mapChildrenIO tr f a = replaceChildrenIO tr a (mapIO f (children tr a)) --- IO version of mapFamily --- mapFamilyIO :: Traversable a a -> (a -> IO a) -> a -> IO a mapFamilyIO tr f a = mapChildFamiliesIO tr tr f a >>= f --- IO version of mapChildFamilies --- mapChildFamiliesIO :: Traversable a b -> Traversable b b -> (b -> IO b) -> a -> IO a mapChildFamiliesIO tra trb = mapChildrenIO tra . mapFamilyIO trb --- IO version of evalFamily --- evalFamilyIO :: Traversable a a -> (a -> IO (Maybe a)) -> a -> IO a evalFamilyIO tr f = mapFamilyIO tr g where g a = f a >>= maybe (return a) (mapFamilyIO tr g) --- IO version of evalChildFamilies --- evalChildFamiliesIO :: Traversable a b -> Traversable b b -> (b -> IO (Maybe b)) -> a -> IO a evalChildFamiliesIO tra trb = mapChildrenIO tra . evalFamilyIO trb -- implementation of 'family' with functional lists for efficiency reasons type FunList a = [a] -> [a] concatFL :: [FunList a] -> FunList a concatFL [] ys = ys concatFL (x:xs) ys = x (concatFL xs ys) familyFL :: Traversable a a -> a -> FunList a familyFL tr x xs = x : childFamiliesFL tr tr x xs childFamiliesFL :: Traversable a b -> Traversable b b -> a -> FunList b childFamiliesFL tra trb x xs = concatFL (map (familyFL trb) (children tra x)) xs liftIO :: (a -> b) -> IO a -> IO b liftIO f ioa = ioa >>= return . f |