Data.Knot

Module for tying the knot on data structures that reference each other by some kind of keys. The tie function replaces all such references with the actual value, creating possibly recursive or cyclic data structures.

The module re-exports a part of the fixpoint package.

An example how to construct a structure with circular dependencies:

 data Person = Person { name :: String, loves :: [Person] }
 -- Define a variant of Person where the recursive type
 -- is given as a parameter, and injection/projection functions.
 instance Fixpoint Person where
   data Pre Person t = Loves { _name :: String, _loves :: [t] }
   inject ~(Loves n ps)    = Person n ps
   project ~(Person n ps)  = Loves n ps

 -- The easisest way to get 'Foldable' + 'Functor' is to implement
 -- 'Traversable' and then just use the default implementations.
 instance T.Traversable (Pre Person) where
     traverse f (Loves n ns) = Loves n <$> T.traverse f ns

 instance Functor (Pre Person) where
     fmap = T.fmapDefault
 instance F.Foldable (Pre Person) where
     foldMap = T.foldMapDefault

 -- Let's create a person with cicrular dependencies:
 alice :: Person
 alice = fromJust . Map.lookup "Alice" .
             tie' . Map.fromList . map (\l -> (_name l, l)) $ lst
   where
     lst = [ Loves "Alice" ["Bob", "cat"]
           , Loves "Bob"   ["Alice"]
           -- you may disagree, but the cat thinks of itself as Person
           , Loves "cat"   ["cat"]
           ]

Documentation

tie :: (Ord k, Foldable (Pre v), Fixpoint v) => RefMap k (Pre v) -> Either (TieError k) (Map k v)

Checks consistency by calling isConsistent and then and ties the knot using tie'.

tie' :: (Ord k, Fixpoint v) => RefMap k (Pre v) -> Map k v

Ties the knot without checking consistency. If the references are inconsistent, an exception is raised.

isConsistent

Arguments

:: (Ord k, Foldable v, Functor v)

=> RefMap k v

The loader to check.

-> Either (TieError k) (RefMap k v)

The loader argument or an error.

Check the loader for consistency, i.e. if all referenced keys have a corresponding value. Values need to implement Foldable that traverses over all referenced keys.

type RefMap k v = Map k (v k)

Represents a set of data v that reference each other using keys of type k.

data TieError k

Possible errors when tying the knot.

Constructors

MissingKey k k

A value with key k1 referenced non-existent key k2.

Instances

Eq k => Eq (TieError k)

(Eq (TieError k), Ord k) => Ord (TieError k)

Show k => Show (TieError k)

class Functor (Pre t) => Fixpoint t where

The class of data types representable by fixpoints.

Associated Types

data Pre t1 ($a)

Methods

project :: t -> Pre t t

Projection from the data type to its underlying functor.

inject :: Pre t t -> t

Injection from the underlying functor into the data type.

Instances

Functor (Pre [a]) => Fixpoint [a]

data family Pre t1 ($a)

inject :: Fixpoint t => Pre t t -> t

Injection from the underlying functor into the data type.

project :: Fixpoint t => t -> Pre t t

Projection from the data type to its underlying functor.