Files
mercury/library/edit_seq.m
2020-04-04 08:24:22 +11:00

595 lines
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Mathematica

%---------------------------------------------------------------------------%
% vim: ft=mercury ts=4 sw=4 et
%---------------------------------------------------------------------------%
% Copyright (C) 2019 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%---------------------------------------------------------------------------%
%
% File: edit_seq.m.
% Stability: medium.
%
% This module finds an edit sequence, which means that given two sequences
% of items, it finds the shortest sequence of edit operations (deletes,
% inserts and/or replaces) that will transform the first sequence
% into the second.
%
% The code is a naive implementation of the Wagner-Fischer algorithm,
% which is documented on its own wikipedia page.
%
% Given two lists of length M and N, its time complexity is O(MN),
% so it is suitable for use only on reasonably short lists.
%
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
:- module edit_seq.
:- interface.
:- import_module list.
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
% Given two item sequences A and B, the edit sequence is the sequence
% of edit operations that transforms sequence A into sequence B.
%
% Item numbers start at 1. The item numbers in edit operations reflect
% the *original* position of the relevant item, i.e. they are not affected
% by any edit operations that take place before that position.
%
:- type edit_seq(T) == list(edit(T)).
:- type edit(T)
---> delete(int)
% Delete item #N in sequence A.
; insert(int, T)
% Insert the given item from sequence B
% after item #N in sequence A.
; replace(int, T).
% Replace item #N in sequence A with the given item
% from sequence B.
:- type edit_params
---> edit_params(
% The cost of delete, insert and replace operations
% respectively. Only the *relative* values of the costs matter;
% if these are fixed, their *absolute* values are irrelevant
% (unless they are so high that they cause arithmetic
% overflows).
cost_of_delete :: int,
cost_of_insert :: int,
cost_of_replace :: int
).
% find_shortest_edit_seq(Params, SeqA, SeqB, Edits):
%
% Compute Edits as the cheapest sequence of edit operations
% that will transform SeqA into SeqB, where the cost of each kind of
% edit operation is specified by Params.
%
:- pred find_shortest_edit_seq(edit_params::in, list(T)::in, list(T)::in,
edit_seq(T)::out) is det.
%---------------------------------------------------------------------------%
% A diff_seq represents a unified diff with unlimited context,
% such as the output of "diff -u --context=MAXINT".
%
% Each line (or in general, one item) in it can be an item from SeqA
% that is left unchanged, an item from SeqA that is to be deleted, or
% an item (from SeqB) that is to be inserted.
:- type diff_seq(T) == list(diff(T)).
:- type diff(T)
---> unchanged(T)
; deleted(T)
; inserted(T).
% Given an edit sequence computed by find_shortest_edit_seq, return
% the unified diff representing that edit sequence.
%
% The main difference between the edit sequence and the diff sequence
% is that given several consecutive replace edits, a naive representation
% of those edit operations would output interleaved pairs of items
% to be deleted and inserted, while the diff sequence would output
% *all* of the items to be deleted by those replace operations *before*
% printing the insertions of their replacements.
%
:- pred find_diff_seq(list(T)::in, edit_seq(T)::in, diff_seq(T)::out) is det.
%---------------------------------------------------------------------------%
% This type and its fields are documented below.
:- type change_hunk(T)
---> change_hunk(
ch_seq_a_start :: int,
ch_seq_a_length :: int,
ch_seq_b_start :: int,
ch_seq_b_length :: int,
ch_diff :: diff_seq(T)
).
% find_change_hunks(ContextSize, DiffSeq, ChangeHunks):
%
% A diff_seq may contain long sequences of unchanged items, which are
% often not of interest. This predicate computes from a diff sequence
% a list of its *change hunks*, which are its interesting parts,
% the parts that contain insertions and/or deletions.
%
% A change hunk looks like this, using the syntax of "diff -u".
% The ContextSize of this example is 3.
%
% @@ -25,6 +25,7 @@
% Roosevelt
% Taft
% Wilson
% +Pershing
% Harding
% Coolidge
% Hoover
%
% This change hunk shows the insertion of one line containing "Pershing"
% into a list of US presidents. The "-25,6" part of the header shows that
% the part of the original sequence (sequence A) covered by this change
% hunk contains six lines, starting at line 25. The "+25,7" part shows that
% the part of the updated sequence (sequence B) contains seven lines,
% starting at line at 25 in that sequence as well. The first four fields
% of the change_hunk type contain these two pairs of numbers.
%
% A change hunk consists of three parts, of which the first and/or last
% may be empty.
%
% - The first part is a sequence of up to ContextSize unchanged items
% (the initial context).
% - The second part is a sequence of unchanged, insertion or deletion
% items that
% * starts with an insertion or deletion item,
% * ends with an insertion or deletion item, and
% * contains at most 2 * ContextSize consecutive unchanged items.
% The start and end item may be the same, as in the example above.
% - The third part is a sequence of up to ContextSize unchanged items
% (the trailing context).
%
% The idea is to surround regions of changes with ContextSize unchanged
% items to provide context (hence the name ContextSize). The first and
% third parts will always contain *exactly* ContextSize unchanged items,
% unless the changed region occurs so close to the start or to the end
% of the item sequence that there are fewer than ContextSize unchanged
% items there.
%
% The reason why there may be up to 2 * ContextSize consecutive unchanged
% items in the middle of a change hunk is that if the limit were any lower,
% then some of those unchanged items would end up *both* in the trailing
% context of one change hunk and the initial context of the next change
% hunk.
%
% To make sense, ContextSize must be least one. This predicate throws
% an exception if ContextSize is zero or negative.
%
:- pred find_change_hunks(int::in, diff_seq(T)::in,
list(change_hunk(T))::out) is det.
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
:- implementation.
:- import_module cord.
:- import_module int.
:- import_module map.
:- import_module require.
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
find_shortest_edit_seq(Params, SeqA, SeqB, Edits) :-
% The Wagner-Fischer algorithm. One difference from the algorithm's
% wikipedia page is that we iterate over the table in row major order,
% not column major. Since the algorithm is symmetric about the table's
% diagonal, this should not matter. The other difference is that we don't
% just compute the edit *distance*; we compute the edit *sequence* as well.
%
% Note that the complexity of this algorithm is O(MN) where
% M and N are the lengths of SeqA and SeqB.
list.length(SeqA, LenA),
list.length(SeqB, LenB),
some [!Table] (
init_table(!:Table),
add_entry(0, 0, entry(cord.init, 0), !Table),
init_row_zero_inserts(Params, 1, SeqB, cord.init, !Table),
init_col_zero_deletes(Params, 1, SeqA, cord.init, !Table),
process_rows(Params, 1, SeqA, SeqB, !Table),
lookup_entry(!.Table, LenA, LenB, CornerEntry),
Edits = cord.list(CornerEntry ^ e_edits)
).
:- pred init_row_zero_inserts(edit_params::in, int::in, list(T)::in,
cord(edit(T))::in, dynprog_table(T)::in, dynprog_table(T)::out) is det.
init_row_zero_inserts(_Params, _ColNum, [], _CurEdits, !Table).
init_row_zero_inserts(Params, ColNum, [HeadSeqB | TailSeqB], PrevEdits,
!Table) :-
CurEdits = cord.snoc(PrevEdits, insert(1, HeadSeqB)),
Entry = entry(CurEdits, ColNum * Params ^ cost_of_insert),
add_entry(0, ColNum, Entry, !Table),
init_row_zero_inserts(Params, ColNum + 1, TailSeqB, CurEdits, !Table).
:- pred init_col_zero_deletes(edit_params::in, int::in, list(T)::in,
cord(edit(T))::in, dynprog_table(T)::in, dynprog_table(T)::out) is det.
init_col_zero_deletes(_Params, _RowNum, [], _CurEdits, !Table).
init_col_zero_deletes(Params, RowNum, [_HeadSeqA | TailSeqA],
PrevEdits, !Table) :-
CurEdits = cord.snoc(PrevEdits, delete(RowNum)),
Entry = entry(CurEdits, RowNum * Params ^ cost_of_delete),
add_entry(RowNum, 0, Entry, !Table),
init_col_zero_deletes(Params, RowNum + 1, TailSeqA, CurEdits, !Table).
:- pred process_rows(edit_params::in, int::in, list(T)::in, list(T)::in,
dynprog_table(T)::in, dynprog_table(T)::out) is det.
process_rows(_Params, _RowNum, [], _SeqB, !Table).
process_rows(Params, RowNum, [HeadSeqA | TailSeqA], SeqB, !Table) :-
% We need only the current row and the one before it.
delete_row(RowNum - 2, !Table),
process_columns(Params, RowNum, HeadSeqA, 1, SeqB, !Table),
process_rows(Params, RowNum + 1, TailSeqA, SeqB, !Table).
:- pred process_columns(edit_params::in, int::in, T::in, int::in, list(T)::in,
dynprog_table(T)::in, dynprog_table(T)::out) is det.
process_columns(_Params, _RowNum, _RowA, _ColNum, [], !Table).
process_columns(Params, RowNum, RowA, ColNum, [HeadSeqB | TailSeqB], !Table) :-
process_entry(Params, RowNum, RowA, ColNum, HeadSeqB, !Table),
process_columns(Params, RowNum, RowA, ColNum + 1, TailSeqB, !Table).
:- pred process_entry(edit_params::in, int::in, T::in, int::in, T::in,
dynprog_table(T)::in, dynprog_table(T)::out) is det.
process_entry(Params, RowNum, A, ColNum, B, !Table) :-
( if A = B then
lookup_entry(!.Table, RowNum - 1, ColNum - 1, Entry)
else
lookup_entry(!.Table, RowNum - 1, ColNum, EntryUp),
lookup_entry(!.Table, RowNum, ColNum - 1, EntryLeft),
lookup_entry(!.Table, RowNum - 1, ColNum - 1, EntryDiag),
EntryUp = entry(EditsUp, CostUp0),
EntryLeft = entry(EditsLeft, CostLeft0),
EntryDiag = entry(EditsDiag, CostDiag0),
CostUp = CostUp0 + Params ^ cost_of_delete,
CostLeft = CostLeft0 + Params ^ cost_of_insert,
CostDiag = CostDiag0 + Params ^ cost_of_replace,
% The order of the tests here can be important when the parameters
% favour delete/insert pairs over replace operations.
%
% By preferring insert here, we create delete(R)/insert(R, ...) pairs.
% If we preferred delete here, we would create insert(R, ...)/delete(R)
% pairs, which find_diff_cord would not be able to handle.
% (In the left and up predecessors, we would have just an insert
% or a delete; the choice between insert and delete exists only
% on the *second* operation of the pair.)
( if CostLeft =< CostUp, CostLeft =< CostDiag then
% We can transform SeqA[1 .. RowNum] into SeqB[1 .. ColNum-1]
% in CostLeft0 steps.
% We can thus transfrom SeqA[1 .. RowNum] into SeqB[1 .. ColNum]
% in CostLeft0 + ConstInsert steps by inserting B after #RowNum
% in SeqA.
Edits = cord.snoc(EditsLeft, insert(RowNum, B)),
Entry = entry(Edits, CostLeft)
else if CostUp =< CostLeft, CostUp =< CostDiag then
% We can transform SeqA[1 .. RowNum-1] into SeqB[1 .. ColNum]
% in CostUp0 steps.
% We can thus transform SeqA[1 .. RowNum] into SeqB[1 .. ColNum]
% in CostUp0 + CostDelete steps by deleting item #RowNum from SeqA.
Edits = cord.snoc(EditsUp, delete(RowNum)),
Entry = entry(Edits, CostUp)
else
% We can transfrom SeqA[1 .. RowNum-1] into SeqB[1 .. ColNum-1]
% in CostDiag0 steps.
% We can thus transfrom SeqA[1 .. RowNum] into SeqB[1 .. ColNum]
% in CostDiag0 + CostReplace steps by replacing item #RowNum
% in SeqA by B.
Edits = cord.snoc(EditsDiag, replace(RowNum, B)),
Entry = entry(Edits, CostDiag)
)
),
add_entry(RowNum, ColNum, Entry, !Table).
%---------------------------------------------------------------------------%
%
% The dynamic programming table.
%
% The row numbers #R must fall into the range [0, LenA].
% The column numbers #C must fall into the range [0, LenB].
%
% The entry at row #R, column #C contains both the shortest sequence of
% edit operations required to transform the first #R items of SeqA
% into the first #C items of SeqB, and the cost of that sequence according to
% the parameters, which give the cost of each basic edit operation.
%
:- type dynprog_table(T) == map(int, map(int, dynprog_entry(T))).
:- type dynprog_entry(T)
---> entry(
e_edits :: cord(edit(T)),
e_cost :: int
).
:- pred init_table(dynprog_table(T)::out) is det.
init_table(Table) :-
map.init(Table).
:- pred lookup_entry(dynprog_table(T)::in, int::in, int::in,
dynprog_entry(T)::out) is det.
lookup_entry(Table, RowNum, ColNum, Entry) :-
map.lookup(Table, RowNum, Row),
map.lookup(Row, ColNum, Entry).
:- pred add_entry(int::in, int::in, dynprog_entry(T)::in,
dynprog_table(T)::in, dynprog_table(T)::out) is det.
add_entry(RowNum, ColNum, Entry, !Table) :-
( if map.search(!.Table, RowNum, Row0) then
map.det_insert(ColNum, Entry, Row0, Row),
map.det_update(RowNum, Row, !Table)
else
Row = map.singleton(ColNum, Entry),
map.det_insert(RowNum, Row, !Table)
).
:- pred delete_row(int::in,
dynprog_table(T)::in, dynprog_table(T)::out) is det.
delete_row(RowNum, !Table) :-
map.delete(RowNum, !Table).
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
find_diff_seq(SeqA, Edits, DiffSeq) :-
Deletes0 = cord.init,
Inserts0 = cord.init,
DiffCord0 = cord.init,
find_diff_cord(1, SeqA, Edits, Deletes0, Inserts0, DiffCord0, DiffCord),
DiffSeq = cord.list(DiffCord).
:- type diff_cord(T) == cord(diff(T)).
:- pred find_diff_cord(int::in, list(T)::in,
edit_seq(T)::in, diff_cord(T)::in, diff_cord(T)::in,
diff_cord(T)::in, diff_cord(T)::out) is det.
find_diff_cord(CurA, SeqA, [Edit | Edits], !.Deletes, !.Inserts, !Diffs) :-
(
Edit = delete(A),
uncons(SeqA, HeadA, TailA),
( if A = CurA then
!:Deletes = cord.snoc(!.Deletes, deleted(HeadA)),
find_diff_cord(CurA + 1, TailA, Edits,
!.Deletes, !.Inserts, !Diffs)
else
flush_deletes_inserts(!Deletes, !Inserts, !Diffs),
!:Diffs = cord.snoc(!.Diffs, unchanged(HeadA)),
find_diff_cord(CurA + 1, TailA, [Edit | Edits],
!.Deletes, !.Inserts, !Diffs)
)
;
Edit = insert(A, Item),
% The insert(A, Item) operation means inserting Item *after* item A
% in SeqA. We implement this as inserting Item before item A+1
% *if* there is an item A+1, and before the end of the list otherwise.
( if A+1 = CurA then
!:Inserts = cord.snoc(!.Inserts, inserted(Item)),
find_diff_cord(CurA, SeqA, Edits,
!.Deletes, !.Inserts, !Diffs)
else
(
SeqA = [],
!:Inserts = cord.snoc(!.Inserts, inserted(Item)),
find_diff_cord(CurA, SeqA, Edits,
!.Deletes, !.Inserts, !Diffs)
;
SeqA = [HeadA | TailA],
flush_deletes_inserts(!Deletes, !Inserts, !Diffs),
!:Diffs = cord.snoc(!.Diffs, unchanged(HeadA)),
find_diff_cord(CurA + 1, TailA, [Edit | Edits],
!.Deletes, !.Inserts, !Diffs)
)
)
;
Edit = replace(A, Item),
uncons(SeqA, HeadA, TailA),
( if CurA = A then
!:Deletes = cord.snoc(!.Deletes, deleted(HeadA)),
!:Inserts = cord.snoc(!.Inserts, inserted(Item)),
find_diff_cord(CurA + 1, TailA, Edits,
!.Deletes, !.Inserts, !Diffs)
else
flush_deletes_inserts(!Deletes, !Inserts, !Diffs),
!:Diffs = cord.snoc(!.Diffs, unchanged(HeadA)),
find_diff_cord(CurA + 1, TailA, [Edit | Edits],
!.Deletes, !.Inserts, !Diffs)
)
).
find_diff_cord(_, SeqA, [], !.Deletes, !.Inserts, !Diffs) :-
flush_deletes_inserts(!.Deletes, _, !.Inserts, _, !Diffs),
LeftOvers = list.map(func(I) = unchanged(I), SeqA),
!:Diffs = !.Diffs ++ cord.from_list(LeftOvers).
:- pred uncons(list(T)::in, T::out, list(T)::out) is det.
uncons([], _, _) :-
unexpected($pred, "empty list").
uncons([Head | Tail], Head, Tail).
:- pred flush_deletes_inserts(
diff_cord(T)::in, diff_cord(T)::out,
diff_cord(T)::in, diff_cord(T)::out,
diff_cord(T)::in, diff_cord(T)::out) is det.
flush_deletes_inserts(!Deletes, !Inserts, !Diffs) :-
!:Diffs = !.Diffs ++ !.Deletes ++ !.Inserts,
!:Deletes = cord.init,
!:Inserts = cord.init.
%---------------------------------------------------------------------------%
%---------------------------------------------------------------------------%
find_change_hunks(ContextSize, Diffs, CHunks) :-
( if ContextSize > 0 then
find_change_hunks_loop(ContextSize, Diffs, 1, 1, [], RevCHunks),
list.reverse(RevCHunks, CHunks)
else
unexpected($pred,
"A context size must be strictly positive to make sense.")
).
:- pred find_change_hunks_loop(int::in, diff_seq(T)::in, int::in, int::in,
list(change_hunk(T))::in, list(change_hunk(T))::out) is det.
find_change_hunks_loop(ContextSize, Diffs, InitPosA, InitPosB, !RevCHunks) :-
scan_initial_unchanged_diffs(Diffs, AfterInitUnchangedsDiffs,
[], RevUnchangedDiffs, 0, NumUnchangedDiffs),
scan_change_hunk_diffs(ContextSize, AfterInitUnchangedsDiffs,
LeftOverDiffs, [], RevChangeTrailContextDiffs,
0, NumCHunkDeleted, 0, NumCHunkInserted,
0, NumCHunkUnchanged, 0, _),
(
RevChangeTrailContextDiffs = []
% Diffs does not contain any change hunk.
;
RevChangeTrailContextDiffs = [_ | _],
list.reverse(RevChangeTrailContextDiffs, ChangeTrailContextDiffs),
% ChangeTrailContextDiffs contains the trailing context,
% but the initial context is in RevUnchangedDiffs.
list.take_upto(ContextSize, RevUnchangedDiffs, RevInitContextDiffs),
list.reverse(RevInitContextDiffs, InitContextDiffs),
list.length(InitContextDiffs, NumInitContextDiffs),
CHunkDiffs = InitContextDiffs ++ ChangeTrailContextDiffs,
NumSkippedUnchangedDiffs = NumUnchangedDiffs - NumInitContextDiffs,
StartA = InitPosA + NumSkippedUnchangedDiffs,
StartB = InitPosB + NumSkippedUnchangedDiffs,
LenA = NumInitContextDiffs + NumCHunkUnchanged + NumCHunkDeleted,
LenB = NumInitContextDiffs + NumCHunkUnchanged + NumCHunkInserted,
CHunk = change_hunk(StartA, LenA, StartB, LenB, CHunkDiffs),
!:RevCHunks = [CHunk | !.RevCHunks],
NextPosA = StartA + LenA,
NextPosB = StartB + LenB,
find_change_hunks_loop(ContextSize, LeftOverDiffs,
NextPosA, NextPosB, !RevCHunks)
).
:- pred scan_initial_unchanged_diffs(list(diff(T))::in, list(diff(T))::out,
list(diff(T))::in, list(diff(T))::out, int::in, int::out) is det.
scan_initial_unchanged_diffs(Diffs, LeftOverDiffs,
!RevUnchangedDiffs, !NumUnchanged) :-
(
Diffs = [],
LeftOverDiffs = []
;
Diffs = [HeadDiff | TailDiffs],
(
HeadDiff = unchanged(_),
!:RevUnchangedDiffs = [HeadDiff | !.RevUnchangedDiffs],
!:NumUnchanged = !.NumUnchanged + 1,
scan_initial_unchanged_diffs(TailDiffs, LeftOverDiffs,
!RevUnchangedDiffs, !NumUnchanged)
;
( HeadDiff = deleted(_)
; HeadDiff = inserted(_)
),
LeftOverDiffs = Diffs
)
).
:- pred scan_change_hunk_diffs(int::in, list(diff(T))::in, list(diff(T))::out,
list(diff(T))::in, list(diff(T))::out,
int::in, int::out, int::in, int::out,
int::in, int::out, int::in, int::out) is det.
scan_change_hunk_diffs(ContextSize, Diffs, LeftOverDiffs, !RevCHunkDiffs,
!NumDeleted, !NumInserted, !NumUnchanged, !NumContigUnchanged) :-
(
Diffs = [],
LeftOverDiffs = []
;
Diffs = [HeadDiff | TailDiffs],
(
HeadDiff = unchanged(_),
( if ContextSize =< !.NumContigUnchanged then
( if
scan_joined_context(ContextSize, Diffs, AfterContextDiffs,
!RevCHunkDiffs, !NumUnchanged)
then
!:NumContigUnchanged = 0,
scan_change_hunk_diffs(ContextSize, AfterContextDiffs,
LeftOverDiffs,
!RevCHunkDiffs, !NumDeleted, !NumInserted,
!NumUnchanged, !NumContigUnchanged)
else
LeftOverDiffs = Diffs
)
else
!:RevCHunkDiffs = [HeadDiff | !.RevCHunkDiffs],
!:NumUnchanged = !.NumUnchanged + 1,
!:NumContigUnchanged = !.NumContigUnchanged + 1,
scan_change_hunk_diffs(ContextSize, TailDiffs, LeftOverDiffs,
!RevCHunkDiffs, !NumDeleted, !NumInserted,
!NumUnchanged, !NumContigUnchanged)
)
;
HeadDiff = deleted(_),
!:RevCHunkDiffs = [HeadDiff | !.RevCHunkDiffs],
!:NumDeleted = !.NumDeleted + 1,
!:NumContigUnchanged = 0,
scan_change_hunk_diffs(ContextSize, TailDiffs, LeftOverDiffs,
!RevCHunkDiffs, !NumDeleted, !NumInserted,
!NumUnchanged, !NumContigUnchanged)
;
HeadDiff = inserted(_),
!:RevCHunkDiffs = [HeadDiff | !.RevCHunkDiffs],
!:NumInserted = !.NumInserted + 1,
!:NumContigUnchanged = 0,
scan_change_hunk_diffs(ContextSize, TailDiffs, LeftOverDiffs,
!RevCHunkDiffs, !NumDeleted, !NumInserted,
!NumUnchanged, !NumContigUnchanged)
)
).
% Our caller calls us when it finds ContextLines consecutive unchanged
% lines. Our caller wants to extend its change hunk *if and only if*
% this is followed by (a) ContextLines or fewer consecutive unchanged
% lines, and then (b) a deletion or insertion. We succeed iff this
% is the case. We return the unchanged lines by adding them to
% !RevUnchangedDiffs, counting them in !NumUnchanged. We leave the
% changed items in LeftOverDiffs.
%
:- pred scan_joined_context(int::in, list(diff(T))::in, list(diff(T))::out,
list(diff(T))::in, list(diff(T))::out, int::in, int::out) is semidet.
scan_joined_context(MaxUnchanged, Diffs, LeftOverDiffs,
!RevUnchangedDiffs, !NumUnchanged) :-
Diffs = [HeadDiff | TailDiffs],
(
HeadDiff = unchanged(_),
MaxUnchanged > 0,
!:RevUnchangedDiffs = [HeadDiff | !.RevUnchangedDiffs],
!:NumUnchanged = !.NumUnchanged + 1,
scan_joined_context(MaxUnchanged - 1, TailDiffs, LeftOverDiffs,
!RevUnchangedDiffs, !NumUnchanged)
;
( HeadDiff = deleted(_)
; HeadDiff = inserted(_)
),
LeftOverDiffs = Diffs
).
%---------------------------------------------------------------------------%
:- end_module edit_seq.
%---------------------------------------------------------------------------%