Data.Patch

For gory implementation details, please see Data.Patch.Internal

Patches

data Patch a

A patch is a collection of edits performed to a document, in this case a Vector. They are implemented as a list of Edit, and can be converted to and from raw lists of edits using toList and fromList respectively.

Patches form a group (a Monoid with inverses), where the inverse element can be computed with inverse and the group operation is composition of patches. Applying p1 <> p2 is the same as applying p1 then p2 (see apply). This composition operator may produce structurally different patches depending on associativity, however the patches are guaranteed to be equivalent in the sense that the resultant document will be the same when they are applied.

forAll (patchesFrom d) $ \a -> a <> mempty == a

forAll (patchesFrom d) $ \a -> mempty <> a == a

forAll (historyFrom d 3) $ \[a, b, c] -> apply (a <> (b <> c)) d == apply ((a <> b) <> c) d

The indices of the Edit s are all based on the original document, so:

>>> Vector.toList $ apply (fromList [Insert 0 'a', Insert 1 'b']) (Vector.fromList "123")
"a1b23"

>>> Vector.toList $ apply (fromList [Insert 0 'a', Insert 0 'b']) (Vector.fromList "123")
"ab123"

Note that the first Insert didn't introduce an offset for the second.

Instances

Eq a => Eq (Patch a)

(Eq a, Read a) => Read (Patch a)

Show a => Show (Patch a)

Eq a => Monoid (Patch a)

toList :: Patch a -> [Edit a]

Convert a patch to a list of edits.

fromList :: Eq a => [Edit a] -> Patch a

Convert a list of edits to a patch, making sure to eliminate conflicting edits and sorting by index.

unsafeFromList :: [Edit a] -> Patch a

Directly convert a list of edits to a patch, without sorting edits by index, and resolving contradictory edits. Use this function if you know that the input list is already a wellformed patch.

inverse :: Patch a -> Patch a

Compute the inverse of a patch, such that:

forAll (patchesFrom d) $ \p -> p <> inverse p == mempty

forAll (patchesFrom d) $ \p -> inverse p <> p == mempty

forAll (patchesFrom d) $ \p -> inverse (inverse p) == p

forAll (historyFrom d 2) $ \[p, q] -> inverse (p <> q) == inverse q <> inverse p

forAll (patchesFrom d) $ \p -> inverse mempty == mempty

Transformations and merges

transformWith :: Eq a => (a -> a -> a) -> Patch a -> Patch a -> (Patch a, Patch a)

Given two diverging patches p and q, transform m p q returns a pair of updated patches (p',q') such that q <> p' and p <> q' are equivalent patches that incorporate the changes of both p and q, up to merge conflicts, which are handled by the provided function m.

This is the standard transform function of Operational Transformation patch resolution techniques.

forAll (divergingPatchesFrom d) $ \(p,q) -> let (p', q') = transformWith ours p q in apply (p <> q') d == apply (q <> p') d

This function is commutative iff m is commutative.

forAll (divergingPatchesFrom d) $ \(p,q) -> let (p', q') = transformWith (*) p q; (q'', p'') = transformWith (*) q p in p' == p'' && q' == q''

Some example conflict strategies are provided below.

Conflict strategies

transform :: (Eq a, Monoid a) => Patch a -> Patch a -> (Patch a, Patch a)

A convenience version of transformWith which resolves conflicts using mappend.

ours :: a -> a -> a

Resolve a conflict by always using the left-hand side

theirs :: a -> a -> a

Resolve a conflict by always using the right-hand side

Documents

apply :: Patch a -> Vector a -> Vector a

Apply a patch to a document.

Technically, apply is a monoid morphism to the monoid of endomorphisms Vector a -> Vector a, and that's how we can derive the following two laws:

forAll (historyFrom d 2) $ \[a, b] -> apply b (apply a d) == apply (a <> b) d

apply mempty d == d

diff :: Eq a => Vector a -> Vector a -> Patch a

Compute the difference between two documents, using the Wagner-Fischer algorithm. O(mn) time and space.

apply (diff d e) d == e

apply (diff d e) d == apply (inverse (diff e d)) d

apply (diff a b <> diff b c) a == apply (diff a c) a

Edits

data Edit a

An Edit is a single alteration of the vector, either inserting, removing, or replacing an element.

Useful optics are provided below, for the index, the old element, and the new element.

Constructors

Insert Int a

Insert i x inserts the element x at position i.

Delete Int a

Delete i x deletes the element x from position i.

Replace Int a a

Replace i x x' replaces the element x at position i with x'.

Instances

Eq a => Eq (Edit a)

Read a => Read (Edit a)

Show a => Show (Edit a)

index :: Lens' (Edit a) Int

A lens for the index where an edit is to be performed.

nonEmpty d ==> forAll (editsTo d) $ \e -> set index v e ^. index == v

nonEmpty d ==> forAll (editsTo d) $ \e -> set index (e ^. index) e == e

nonEmpty d ==> forAll (editsTo d) $ \e -> set index v' (set index v e) == set index v' e

old :: Traversal' (Edit a) a

A traversal for the old element to be replaced/deleted. Empty in the case of an Insert.

new :: Traversal' (Edit a) a

A traversal for the new value to be inserted or replacing the old value. Empty in the case of a Delete.