.TH "Diffing" 3o 2023-09-20 OCamldoc "OCaml library"
.SH NAME
Diffing \- Parametric diffing
.SH Module
Module   Diffing
.SH Documentation
.sp
Module
.BI "Diffing"
 : 
.B sig end

.sp
Parametric diffing
.sp
This module implements diffing over lists of arbitrary content\&.
It is parameterized by
.sp
\-The content of the two lists
.sp
\-The equality witness when an element is kept
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\-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\&.
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The underlying algorithm is a modified Wagner\-Fischer algorithm
(see <https://en\&.wikipedia\&.org/wiki/Wagner%E2%80%93Fischer_algorithm>)\&.
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We provide the following guarantee:
Given two lists 
.ft B
l
.ft R
and 
.ft B
r
.ft R
, if different patches result in different
states, we say that the state diverges\&.
.sp
\-We always return the optimal patch on prefixes of 
.ft B
l
.ft R
and 
.ft B
r
.ft R
on which state does not diverge\&.
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\-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
.sp
d(k,l) = min (
del_cost + d(k\-1,l),
insert_cost + d(k,l\-1),
change_cost + d(k\-1,l\-1)
)
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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\&.
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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\&.

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.sp
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.I module type Defs = 
.B sig end

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The core types of a diffing implementation

.sp
.I type change_kind 
=
 | Deletion
 | Insertion
 | Modification
 | Preservation
 
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The kind of changes which is used to share printing and styling
across implementation

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

.I val style 
: 
.B change_kind -> Misc.Color.style list
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.sp
.I type 
.B ('left, 'right, 'eq, 'diff)
.I change 
=
 | Delete
.B of 
.B 'left
 | Insert
.B of 
.B 'right
 | Keep
.B of 
.B 'left * 'right * 'eq
 | Change
.B of 
.B 'left * 'right * 'diff
 
.sp

.sp

.I val classify 
: 
.B ('a, 'b, 'c, 'd) change -> change_kind
.sp

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

.sp

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

.sp