{-# LANGUAGE CPP #-} {-# LANGUAGE Rank2Types #-} {-# LANGUAGE DefaultSignatures #-} {-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE FlexibleContexts #-} {-# LANGUAGE MultiParamTypeClasses #-} #ifdef TRUSTWORTHY {-# LANGUAGE Trustworthy #-} -- template-haskell #endif #ifndef MIN_VERSION_template_haskell #define MIN_VERSION_template_haskell(x,y,z) 1 #endif ------------------------------------------------------------------------------- -- | -- Module : Control.Lens.Plated -- Copyright : (C) 2012-13 Edward Kmett -- License : BSD-style (see the file LICENSE) -- Maintainer : Edward Kmett <ekmett@gmail.com> -- Stability : provisional -- Portability : Rank2Types -- -- The name \"plate\" stems originally from \"boilerplate\", which was the term -- used by the \"Scrap Your Boilerplate\" papers, and later inherited by Neil -- Mitchell's \"Uniplate\". -- -- <http://community.haskell.org/~ndm/uniplate/> -- -- The combinators in here are designed to be compatible with and subsume the -- @uniplate@ API with the notion of a 'Traversal' replacing -- a 'Data.Data.Lens.uniplate' or 'Data.Data.Lens.biplate'. -- -- By implementing these combinators in terms of 'plate' instead of -- 'Data.Data.Lens.uniplate' additional type safety is gained, as the user is -- no longer responsible for maintaining invariants such as the number of -- children they received. -- -- Note: The @Biplate@ is /deliberately/ excluded from the API here, with the -- intention that you replace them with either explicit traversals, or by using the -- @On@ variants of the combinators below with 'Data.Data.Lens.biplate' from -- @Data.Data.Lens@. As a design, it forced the user into too many situations where -- they had to choose between correctness and ease of use, and it was brittle in the -- face of competing imports. -- -- The sensible use of these combinators makes some simple assumptions. Notably, any -- of the @On@ combinators are expecting a 'Traversal', 'Setter' or 'Fold' -- to play the role of the 'Data.Data.Lens.biplate' combinator, and so when the -- types of the contents and the container match, they should be the 'id' 'Traversal', -- 'Setter' or 'Fold'. -- -- It is often beneficial to use the combinators in this module with the combinators -- from @Data.Data.Lens@ or @GHC.Generics.Lens@ to make it easier to automatically -- derive definitions for 'plate', or to derive custom traversals. ------------------------------------------------------------------------------- module Control.Lens.Plated ( -- * Uniplate Plated(..) -- * Uniplate Combinators , children , rewrite, rewriteOf, rewriteOn, rewriteOnOf , rewriteM, rewriteMOf, rewriteMOn, rewriteMOnOf , universe, universeOf, universeOn, universeOnOf , transform, transformOf, transformOn, transformOnOf , transformM, transformMOf, transformMOn, transformMOnOf , contexts, contextsOf, contextsOn, contextsOnOf , holes, holesOn, holesOnOf , para, paraOf , (...) -- * Compos -- $compos , composOpFold -- * Parts , parts ) where import Control.Applicative import Control.Lens.Fold import Control.Lens.Getter import Control.Lens.Indexed import Control.Lens.Internal.Context import Control.Lens.Type import Control.Lens.Setter import Control.Lens.Traversal import qualified Language.Haskell.TH as TH import Data.Data import Data.Data.Lens import Data.Monoid import Data.Tree #ifdef HLINT {-# ANN module "HLint: ignore Reduce duplication" #-} #endif -- | A 'Plated' type is one where we know how to extract its immediate self-similar children. -- -- /Example 1/: -- -- @ -- import Control.Applicative -- import Control.Lens -- import Control.Lens.Plated -- import Data.Data -- import Data.Data.Lens ('Data.Data.Lens.uniplate') -- @ -- -- @ -- data Expr -- = Val 'Int' -- | Neg Expr -- | Add Expr Expr -- deriving ('Eq','Ord','Show','Read','Data','Typeable') -- @ -- -- @ -- instance 'Plated' Expr where -- 'plate' f (Neg e) = Neg '<$>' f e -- 'plate' f (Add a b) = Add '<$>' f a '<*>' f b -- 'plate' _ a = 'pure' a -- @ -- -- /or/ -- -- @ -- instance 'Plated' Expr where -- 'plate' = 'Data.Data.Lens.uniplate' -- @ -- -- /Example 2/: -- -- @ -- import Control.Applicative -- import Control.Lens -- import Control.Lens.Plated -- import Data.Data -- import Data.Data.Lens ('Data.Data.Lens.uniplate') -- @ -- -- @ -- data Tree a -- = Bin (Tree a) (Tree a) -- | Tip a -- deriving ('Eq','Ord','Show','Read','Data','Typeable') -- @ -- -- @ -- instance 'Plated' (Tree a) where -- 'plate' f (Bin l r) = Bin '<$>' f l '<*>' f r -- 'plate' _ t = 'pure' t -- @ -- -- /or/ -- -- @ -- instance 'Data' a => 'Plated' (Tree a) where -- 'plate' = 'uniplate' -- @ -- -- Note the big distinction between these two implementations. -- -- The former will only treat children directly in this tree as descendents, -- the latter will treat trees contained in the values under the tips also -- as descendants! -- -- When in doubt, pick a 'Traversal' and just use the various @...Of@ combinators -- rather than pollute 'Plated' with orphan instances! -- -- If you want to find something unplated and non-recursive with 'Data.Data.Lens.biplate' -- use the @...OnOf@ variant with 'ignored', though those usecases are much better served -- in most cases by using the existing 'Lens' combinators! e.g. -- -- @ -- 'toListOf' 'biplate' ≡ 'universeOnOf' 'biplate' 'ignored' -- @ -- -- This same ability to explicitly pass the 'Traversal' in question is why there is no -- analogue to uniplate's @Biplate@. -- -- Moreover, since we can allow custom traversals, we implement reasonable defaults for -- polymorphic data types, that only 'Control.Traversable.traverse' into themselves, and /not/ their -- polymorphic arguments. class Plated a where -- | 'Traversal' of the immediate children of this structure. -- -- If you're using GHC 7.2 or newer and your type has a 'Data' instance, -- 'plate' will default to 'uniplate' and you can choose to not override -- it with your own definition. plate :: Traversal' a a #ifndef HLINT default plate :: Data a => Traversal' a a plate = uniplate #endif instance Plated [a] where plate f (x:xs) = (x:) <$> f xs plate _ [] = pure [] instance Plated (Tree a) where plate f (Node a as) = Node a <$> traverse f as {- Default uniplate instances -} instance Plated TH.Exp instance Plated TH.Dec instance Plated TH.Con instance Plated TH.Type #if !(MIN_VERSION_template_haskell(2,8,0)) instance Plated TH.Kind -- in 2.8 Kind is an alias for Type #endif instance Plated TH.Stmt instance Plated TH.Pat infixr 9 ... -- | Compose through a plate (...) :: (Applicative f, Plated c) => LensLike f s t c c -> Over p f c c a b -> Over p f s t a b l ... m = l . plate . m {-# INLINE (...) #-} ------------------------------------------------------------------------------- -- Children ------------------------------------------------------------------------------- -- | Extract the immediate descendants of a 'Plated' container. -- -- @ -- 'children' ≡ 'toListOf' 'plate' -- @ children :: Plated a => a -> [a] children = toListOf plate {-# INLINE children #-} ------------------------------------------------------------------------------- -- Rewriting ------------------------------------------------------------------------------- -- | Rewrite by applying a rule everywhere you can. Ensures that the rule cannot -- be applied anywhere in the result: -- -- @ -- propRewrite r x = 'all' ('Data.Just.isNothing' '.' r) ('universe' ('rewrite' r x)) -- @ -- -- Usually 'transform' is more appropriate, but 'rewrite' can give better -- compositionality. Given two single transformations @f@ and @g@, you can -- construct @\a -> f a `mplus` g a@ which performs both rewrites until a fixed point. rewrite :: Plated a => (a -> Maybe a) -> a -> a rewrite = rewriteOf plate {-# INLINE rewrite #-} -- | Rewrite by applying a rule everywhere you can. Ensures that the rule cannot -- be applied anywhere in the result: -- -- @ -- propRewriteOf l r x = 'all' ('Data.Just.isNothing' '.' r) ('universeOf' l ('rewriteOf' l r x)) -- @ -- -- Usually 'transformOf' is more appropriate, but 'rewriteOf' can give better -- compositionality. Given two single transformations @f@ and @g@, you can -- construct @\a -> f a `mplus` g a@ which performs both rewrites until a fixed point. -- -- @ -- 'rewriteOf' :: 'Control.Lens.Iso.Iso'' a a -> (a -> 'Maybe' a) -> a -> a -- 'rewriteOf' :: 'Lens'' a a -> (a -> 'Maybe' a) -> a -> a -- 'rewriteOf' :: 'Traversal'' a a -> (a -> 'Maybe' a) -> a -> a -- 'rewriteOf' :: 'Setter'' a a -> (a -> 'Maybe' a) -> a -> a -- @ rewriteOf :: ASetter' a a -> (a -> Maybe a) -> a -> a rewriteOf l f = go where go = transformOf l (\x -> maybe x go (f x)) {-# INLINE rewriteOf #-} -- | Rewrite recursively over part of a larger structure. -- -- @ -- 'rewriteOn' :: 'Plated' a => 'Control.Lens.Iso.Iso'' s a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOn' :: 'Plated' a => 'Lens'' s a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOn' :: 'Plated' a => 'Traversal'' s a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOn' :: 'Plated' a => 'ASetter'' s a -> (a -> 'Maybe' a) -> s -> s -- @ rewriteOn :: Plated a => ASetter s t a a -> (a -> Maybe a) -> s -> t rewriteOn b = over b . rewrite {-# INLINE rewriteOn #-} -- | Rewrite recursively over part of a larger structure using a specified 'Setter'. -- -- @ -- 'rewriteOnOf' :: 'Plated' a => 'Control.Lens.Iso.Iso'' s a -> 'Control.Lens.Iso.Iso'' a a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOnOf' :: 'Plated' a => 'Lens'' s a -> 'Lens'' a a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOnOf' :: 'Plated' a => 'Traversal'' s a -> 'Traversal'' a a -> (a -> 'Maybe' a) -> s -> s -- 'rewriteOnOf' :: 'Plated' a => 'Setter'' s a -> 'Setter'' a a -> (a -> 'Maybe' a) -> s -> s -- @ rewriteOnOf :: ASetter s t a a -> ASetter' a a -> (a -> Maybe a) -> s -> t rewriteOnOf b l = over b . rewriteOf l {-# INLINE rewriteOnOf #-} -- | Rewrite by applying a monadic rule everywhere you can. Ensures that the rule cannot -- be applied anywhere in the result. rewriteM :: (Monad m, Plated a) => (a -> m (Maybe a)) -> a -> m a rewriteM = rewriteMOf plate {-# INLINE rewriteM #-} -- | Rewrite by applying a monadic rule everywhere you recursing with a user-specified 'Traversal'. -- Ensures that the rule cannot be applied anywhere in the result. rewriteMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> a -> m a rewriteMOf l f = go where go = transformMOf l (\x -> f x >>= maybe (return x) go) {-# INLINE rewriteMOf #-} -- | Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified 'Traversal'. -- Ensures that the rule cannot be applied anywhere in the result. rewriteMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m (Maybe a)) -> s -> m t rewriteMOn b = mapMOf b . rewriteM {-# INLINE rewriteMOn #-} -- | Rewrite by applying a monadic rule everywhere inside of a structure located by a user-specified 'Traversal', -- using a user-specified 'Traversal' for recursion. Ensures that the rule cannot be applied anywhere in the result. rewriteMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m (Maybe a)) -> s -> m t rewriteMOnOf b l = mapMOf b . rewriteMOf l {-# INLINE rewriteMOnOf #-} ------------------------------------------------------------------------------- -- Universe ------------------------------------------------------------------------------- -- | Retrieve all of the transitive descendants of a 'Plated' container, including itself. universe :: Plated a => a -> [a] universe = universeOf plate {-# INLINE universe #-} -- | Given a 'Fold' that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself. -- -- @ -- 'universeOf' :: 'Fold' a a -> a -> [a] -- @ universeOf :: Getting [a] a a -> a -> [a] universeOf l = go where go a = a : foldMapOf l go a {-# INLINE universeOf #-} -- | Given a 'Fold' that knows how to find 'Plated' parts of a container retrieve them and all of their descendants, recursively. universeOn :: Plated a => Getting [a] s a -> s -> [a] universeOn b = universeOnOf b plate {-# INLINE universeOn #-} -- | Given a 'Fold' that knows how to locate immediate children, retrieve all of the transitive descendants of a node, including itself that lie -- in a region indicated by another 'Fold'. -- -- @ -- 'toListOf' l ≡ 'universeOnOf' l 'ignored' -- @ universeOnOf :: Getting [a] s a -> Getting [a] a a -> s -> [a] universeOnOf b = foldMapOf b . universeOf {-# INLINE universeOnOf #-} ------------------------------------------------------------------------------- -- Transformation ------------------------------------------------------------------------------- -- | Transform every element in the tree, in a bottom-up manner. -- -- For example, replacing negative literals with literals: -- -- @ -- negLits = 'transform' $ \\x -> case x of -- Neg (Lit i) -> Lit ('negate' i) -- _ -> x -- @ transform :: Plated a => (a -> a) -> a -> a transform = transformOf plate {-# INLINE transform #-} -- | Transform every element in the tree in a bottom-up manner over a region indicated by a 'Setter'. -- -- @ -- 'transformOn' :: 'Plated' a => 'Traversal'' s a -> (a -> a) -> s -> s -- 'transformOn' :: 'Plated' a => 'Setter'' s a -> (a -> a) -> s -> s -- @ transformOn :: Plated a => ASetter s t a a -> (a -> a) -> s -> t transformOn b = over b . transform {-# INLINE transformOn #-} -- | Transform every element by recursively applying a given 'Setter' in a bottom-up manner. -- -- @ -- 'transformOf' :: 'Traversal'' a a -> (a -> a) -> a -> a -- 'transformOf' :: 'Setter'' a a -> (a -> a) -> a -> a -- @ transformOf :: ASetter' a a -> (a -> a) -> a -> a transformOf l f = go where go = f . over l go {-# INLINE transformOf #-} -- | Transform every element in a region indicated by a 'Setter' by recursively applying another 'Setter' -- in a bottom-up manner. -- -- @ -- 'transformOnOf' :: 'Setter'' s a -> 'Traversal'' a a -> (a -> a) -> s -> s -- 'transformOnOf' :: 'Setter'' s a -> 'Setter'' a a -> (a -> a) -> s -> s -- @ transformOnOf :: ASetter s t a a -> ASetter' a a -> (a -> a) -> s -> t transformOnOf b l = over b . transformOf l {-# INLINE transformOnOf #-} -- | Transform every element in the tree, in a bottom-up manner, monadically. transformM :: (Monad m, Plated a) => (a -> m a) -> a -> m a transformM = transformMOf plate {-# INLINE transformM #-} -- | Transform every element in the tree in a region indicated by a supplied 'Traversal', in a bottom-up manner, monadically. -- -- @ -- 'transformMOn' :: ('Monad' m, 'Plated' a) => 'Traversal'' s a -> (a -> m a) -> s -> m s -- @ transformMOn :: (Monad m, Plated a) => LensLike (WrappedMonad m) s t a a -> (a -> m a) -> s -> m t transformMOn b = mapMOf b . transformM {-# INLINE transformMOn #-} -- | Transform every element in a tree using a user supplied 'Traversal' in a bottom-up manner with a monadic effect. -- -- @ -- 'transformMOf' :: 'Monad' m => 'Traversal'' a a -> (a -> m a) -> a -> m a -- @ transformMOf :: Monad m => LensLike' (WrappedMonad m) a a -> (a -> m a) -> a -> m a transformMOf l f = go where go t = mapMOf l go t >>= f {-# INLINE transformMOf #-} -- | Transform every element in a tree that lies in a region indicated by a supplied 'Traversal', walking with a user supplied 'Traversal' in -- a bottom-up manner with a monadic effect. -- -- @ -- 'transformMOnOf' :: 'Monad' m => 'Traversal'' s a -> 'Traversal'' a a -> (a -> m a) -> s -> m s -- @ transformMOnOf :: Monad m => LensLike (WrappedMonad m) s t a a -> LensLike' (WrappedMonad m) a a -> (a -> m a) -> s -> m t transformMOnOf b l = mapMOf b . transformMOf l {-# INLINE transformMOnOf #-} ------------------------------------------------------------------------------- -- Holes and Contexts ------------------------------------------------------------------------------- -- | Return a list of all of the editable contexts for every location in the structure, recursively. -- -- @ -- propUniverse x = 'universe' x '==' 'map' 'Control.Comonad.Store.Class.pos' ('contexts' x) -- propId x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w <- 'contexts' x] -- @ -- -- @ -- 'contexts' ≡ 'contextsOf' 'plate' -- @ contexts :: Plated a => a -> [Context a a a] contexts = contextsOf plate {-# INLINE contexts #-} -- | Return a list of all of the editable contexts for every location in the structure, recursively, using a user-specified 'Traversal' to walk each layer. -- -- @ -- propUniverse l x = 'universeOf' l x '==' 'map' 'Control.Comonad.Store.Class.pos' ('contextsOf' l x) -- propId l x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w <- 'contextsOf' l x] -- @ -- -- @ -- 'contextsOf' :: 'Traversal'' a a -> a -> ['Context' a a a] -- @ contextsOf :: ATraversal' a a -> a -> [Context a a a] contextsOf l x = sell x : f (map context (holesOf l x)) where f xs = do Context ctx child <- xs Context cont y <- contextsOf l child return $ Context (ctx . cont) y {-# INLINE contextsOf #-} -- | Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied 'Traversal', recursively using 'plate'. -- -- @ -- 'contextsOn' b ≡ 'contextsOnOf' b 'plate' -- @ -- -- @ -- 'contextsOn' :: 'Plated' a => 'Traversal'' s a -> s -> ['Context' a a s] -- @ contextsOn :: Plated a => ATraversal s t a a -> s -> [Context a a t] contextsOn b = contextsOnOf b plate {-# INLINE contextsOn #-} -- | Return a list of all of the editable contexts for every location in the structure in an areas indicated by a user supplied 'Traversal', recursively using -- another user-supplied 'Traversal' to walk each layer. -- -- @ -- 'contextsOnOf' :: 'Traversal'' s a -> 'Traversal'' a a -> s -> ['Context' a a s] -- @ contextsOnOf :: ATraversal s t a a -> ATraversal' a a -> s -> [Context a a t] contextsOnOf b l = f . map context . holesOf b where f xs = do Context ctx child <- xs Context cont y <- contextsOf l child return $ Context (ctx . cont) y {-# INLINE contextsOnOf #-} -- | The one-level version of 'context'. This extracts a list of the immediate children as editable contexts. -- -- Given a context you can use 'Control.Comonad.Store.Class.pos' to see the values, 'Control.Comonad.Store.Class.peek' at what the structure would be like with an edited result, or simply 'Control.Lens.Internal.Context.extract' the original structure. -- -- @ -- propChildren x = 'children' l x '==' 'map' 'Control.Comonad.Store.Class.pos' ('holes' l x) -- propId x = 'all' ('==' x) ['Control.Lens.Internal.Context.extract' w | w <- 'holes' l x] -- @ -- -- @ -- 'holes' = 'holesOf' 'plate' -- @ holes :: Plated a => a -> [Pretext (->) a a a] holes = holesOf plate {-# INLINE holes #-} -- | An alias for 'holesOf', provided for consistency with the other combinators. -- -- @ -- 'holesOn' ≡ 'holesOf' -- @ -- -- @ -- 'holesOn' :: 'Iso'' s a -> s -> ['Pretext' (->) a a s] -- 'holesOn' :: 'Lens'' s a -> s -> ['Pretext' (->) a a s] -- 'holesOn' :: 'Traversal'' s a -> s -> ['Pretext' (->) a a s] -- 'holesOn' :: 'IndexedLens'' i s a -> s -> ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s] -- 'holesOn' :: 'IndexedTraversal'' i s a -> s -> ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s] -- @ holesOn :: Conjoined p => Optical p (->) (Bazaar p a a) s t a a -> s -> [Pretext p a a t] holesOn = holesOf {-# INLINE holesOn #-} -- | Extract one level of 'holes' from a container in a region specified by one 'Traversal', using another. -- -- @ -- 'holesOnOf' b l ≡ 'holesOf' (b '.' l) -- @ -- -- @ -- 'holesOnOf' :: 'Iso'' s a -> 'Iso'' a a -> s -> ['Pretext' (->) a a s] -- 'holesOnOf' :: 'Lens'' s a -> 'Lens'' a a -> s -> ['Pretext' (->) a a s] -- 'holesOnOf' :: 'Traversal'' s a -> 'Traversal'' a a -> s -> ['Pretext' (->) a a s] -- 'holesOnOf' :: 'Lens'' s a -> 'IndexedLens'' i a a -> s -> ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s] -- 'holesOnOf' :: 'Traversal'' s a -> 'IndexedTraversal'' i a a -> s -> ['Pretext' ('Control.Lens.Internal.Indexed.Indexed' i) a a s] -- @ holesOnOf :: Conjoined p => LensLike (Bazaar p r r) s t a b -> Optical p (->) (Bazaar p r r) a b r r -> s -> [Pretext p r r t] holesOnOf b l = holesOf (b . l) {-# INLINE holesOnOf #-} ------------------------------------------------------------------------------- -- Paramorphisms ------------------------------------------------------------------------------- -- | Perform a fold-like computation on each value, technically a paramorphism. -- -- @ -- 'paraOf' :: 'Fold' a a -> (a -> [r] -> r) -> a -> r -- @ paraOf :: Getting (Endo [a]) a a -> (a -> [r] -> r) -> a -> r paraOf l f = go where go a = f a (go <$> toListOf l a) {-# INLINE paraOf #-} -- | Perform a fold-like computation on each value, technically a paramorphism. -- -- @ -- 'para' ≡ 'paraOf' 'plate' -- @ para :: Plated a => (a -> [r] -> r) -> a -> r para = paraOf plate {-# INLINE para #-} ------------------------------------------------------------------------------- -- Compos ------------------------------------------------------------------------------- -- $compos -- -- Provided for compatibility with Björn Bringert's @compos@ library. -- -- Note: Other operations from compos that were inherited by @uniplate@ are /not/ included -- to avoid having even more redundant names for the same operators. For comparison: -- -- @ -- 'composOpMonoid' ≡ 'foldMapOf' 'plate' -- 'composOpMPlus' f ≡ 'msumOf' ('plate' '.' 'to' f) -- 'composOp' ≡ 'descend' ≡ 'over' 'plate' -- 'composOpM' ≡ 'descendM' ≡ 'mapMOf' 'plate' -- 'composOpM_' ≡ 'descendM_' ≡ 'mapMOf_' 'plate' -- @ -- | Fold the immediate children of a 'Plated' container. -- -- @ -- 'composOpFold' z c f = 'foldrOf' 'plate' (c '.' f) z -- @ composOpFold :: Plated a => b -> (b -> b -> b) -> (a -> b) -> a -> b composOpFold z c f = foldrOf plate (c . f) z {-# INLINE composOpFold #-} ------------------------------------------------------------------------------- -- Parts ------------------------------------------------------------------------------- -- | The original @uniplate@ combinator, implemented in terms of 'Plated' as a 'Lens'. -- -- @ -- 'parts' ≡ 'partsOf' 'plate' -- @ -- -- The resulting 'Lens' is safer to use as it ignores 'over-application' and deals gracefully with under-application, -- but it is only a proper 'Lens' if you don't change the list 'length'! parts :: Plated a => Lens' a [a] parts = partsOf plate {-# INLINE parts #-}