Safe Haskell | Safe-Infered |
---|

Uniplate-style traversals.

Toy example: Consider our favourite data type

data Expr e = Kst Int | Var String | Add e e deriving (Eq,Show,Functor,Foldable,Traversable) instance ShowF Expr where showsPrecF = showsPrec

and write a function simplifying additions with zero:

simplifyAdd :: Mu Expr -> Mu Expr simplifyAdd = transform worker where worker expr = case expr of Fix (Add x (Fix (Kst 0))) -> x -- 0+x = x Fix (Add (Fix (Kst 0)) y) -> y -- x+0 = 0 _ -> expr

Unfortunately, all these `Fix`

wrappers are rather ugly; but they are straightforward to put in,
and in principle one could use Template Haskell quasi-quotation to generate patterns.

- children :: Foldable f => Mu f -> [Mu f]
- universe :: Foldable f => Mu f -> [Mu f]
- transform :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f
- transformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)
- topDownTransform :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f
- topDownTransformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)
- descend :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu f
- descendM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)
- rewrite :: Functor f => (Mu f -> Maybe (Mu f)) -> Mu f -> Mu f
- rewriteM :: (Traversable f, Monad m) => (Mu f -> m (Maybe (Mu f))) -> Mu f -> m (Mu f)
- restructure :: Functor f => (f (Mu g) -> g (Mu g)) -> Mu f -> Mu g
- restructureM :: (Traversable f, Monad m) => (f (Mu g) -> m (g (Mu g))) -> Mu f -> m (Mu g)
- context :: Traversable f => Mu f -> Attr f (Mu f -> Mu f)
- contextList :: Traversable f => Mu f -> [(Mu f, Mu f -> Mu f)]
- foldLeft :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> a
- foldLeftLazy :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> a
- foldRight :: Foldable f => (Mu f -> a -> a) -> a -> Mu f -> a

# Queries

universe :: Foldable f => Mu f -> [Mu f]Source

The list of all substructures. Together with list-comprehension syntax this is a powerful query tool. For example the following is how you get the list of all variable names in an expression:

variables expr = [ s | Fix (Var s) <- universe expr ]

# Traversals

transformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)Source

topDownTransform :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu fSource

Top-down transformation. This provided only for completeness;
usually, it is `transform`

what you want use instead.

topDownTransformM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)Source

descend :: Functor f => (Mu f -> Mu f) -> Mu f -> Mu fSource

Non-recursive top-down transformation. This is basically just `fmap`

.

descendM :: (Traversable f, Monad m) => (Mu f -> m (Mu f)) -> Mu f -> m (Mu f)Source

Similarly, this is basically just `mapM`

.

rewrite :: Functor f => (Mu f -> Maybe (Mu f)) -> Mu f -> Mu fSource

Bottom-up transformation until a normal form is reached.

# Structure change

restructure :: Functor f => (f (Mu g) -> g (Mu g)) -> Mu f -> Mu gSource

Bottom-up transformation (typically "shallow", that is, restricted to a single level)
which can change the structure functor (actually `transform`

is a special case of this).

restructureM :: (Traversable f, Monad m) => (f (Mu g) -> m (g (Mu g))) -> Mu f -> m (Mu g)Source

# Context

context :: Traversable f => Mu f -> Attr f (Mu f -> Mu f)Source

We *annotate* the nodes of the tree with functions which replace that
particular subtree.

contextList :: Traversable f => Mu f -> [(Mu f, Mu f -> Mu f)]Source

Flattened version of `context`

.

# Folds

foldLeft :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> aSource

(Strict) left fold. Since `Mu f`

is not a functor, but a data type, we cannot make
it an instance of the `Foldable`

type class.

foldLeftLazy :: Foldable f => (a -> Mu f -> a) -> a -> Mu f -> aSource