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 ` |

`|` |
`Insert of ` |

`|` |
`Keep of ` |

`|` |
`Change of ` |

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

module Define:

`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