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
r, if different patches result in different states, we say that the state diverges.
- We always return the optimal patch on prefixes of
ron 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
The kind of changes which is used to share printing and styling across implementation