# Module Diffing

    module Diffing: sig .. end

Parametric diffing

This module implements diffing over lists of arbitrary content. It is parameterized by

- The content of the two lists
- The equality witness when an element is kept
- The diffing witness when an element is changed

Diffing is extended to maintain state depending on the computed changes while walking through the two lists.

The underlying algorithm is a modified Wagner-Fischer algorithm (see <https://en.wikipedia.org/wiki/Wagner%E2%80%93Fischer_algorithm>).

We provide the following guarantee: Given two lists `l` and `r`, if different patches result in different states, we say that the state diverges.

- We always return the optimal patch on prefixes of `l` and `r` on which state does not diverge.
- Otherwise, we return a correct but non-optimal patch where subpatches with no divergent states are optimal for the given initial state.

More precisely, the optimality of Wagner-Fischer depends on the property that the edit-distance between a k-prefix of the left input and a l-prefix of the right input d(k,l) satisfies

d(k,l) = min ( del_cost + d(k-1,l), insert_cost + d(k,l-1), change_cost + d(k-1,l-1) )

Under this hypothesis, it is optimal to choose greedily the state of the minimal patch transforming the left k-prefix into the right l-prefix as a representative of the states of all possible patches transforming the left k-prefix into the right l-prefix.

If this property is not satisfied, we can still choose greedily a representative state. However, the computed patch is no more guaranteed to be globally optimal. Nevertheless, it is still a correct patch, which is even optimal among all explored patches.

    module type Defs = sig .. end

The core types of a diffing implementation

    type change_kind =

`|` | `Deletion`
`|` | `Insertion`
`|` | `Modification`
`|` | `Preservation`

The kind of changes which is used to share printing and styling across implementation

    val prefix : Format.formatter -> int * change_kind -> unit

    val style : change_kind -> Misc.Color.style list

    type ('left, 'right, 'eq, 'diff) change =

`|` | `Delete of `'left``
`|` | `Insert of `'right``
`|` | `Keep of `'left * 'right * 'eq``
`|` | `Change of `'left * 'right * 'diff``

    val classify : ('a, 'b, 'c, 'd) change -> change_kind

    module Define: functor (D : Defs) -> sig .. end

`Define(Defs)` creates the diffing types from the types defined in `Defs` and the functors that need to be instantatied with the diffing algorithm parameters