403 lines
10 KiB
Prolog
403 lines
10 KiB
Prolog
% This file has been included as an YAP library by Vitor Santos Costa, 1999
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%
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% This file includes code from Bob Welham, Lawrence Byrd, and R. A. O'Keefe.
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%
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:- module(lists,
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[
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append/3,
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append/2,
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delete/3,
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last/2,
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member/2,
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memberchk/2,
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nextto/3,
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nth/3,
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nth/4,
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nth0/3,
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nth0/4,
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nth1/3,
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nth1/4,
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permutation/2,
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prefix/2,
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remove_duplicates/2,
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reverse/2,
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same_length/2,
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select/3,
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selectchk/3,
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sublist/2,
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substitute/4,
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sum_list/2,
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sum_list/3,
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suffix/2,
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sumlist/2,
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list_concat/2,
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flatten/2,
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max_list/2,
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min_list/2,
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numlist/3,
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intersection/3
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]).
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:- use_module(library(error),
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[must_be/2]).
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%% append(+ListOfLists, ?List)
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%
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% Concatenate a list of lists. Is true if Lists is a list of
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% lists, and List is the concatenation of these lists.
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%
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% @param ListOfLists must be a list of -possibly- partial lists
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append(ListOfLists, List) :-
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% must_be(list, ListOfLists),
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append_(ListOfLists, List).
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append_([], []).
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append_([L|Ls], As) :-
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append(L, Ws, As),
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append_(Ls, Ws).
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% delete(List, Elem, Residue)
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% is true when List is a list, in which Elem may or may not occur, and
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% Residue is a copy of List with all elements identical to Elem deleted.
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delete([], _, []).
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delete([Head|List], Elem, Residue) :-
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Head == Elem, !,
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delete(List, Elem, Residue).
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delete([Head|List], Elem, [Head|Residue]) :-
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delete(List, Elem, Residue).
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% last(List, Last)
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% is true when List is a List and Last is identical to its last element.
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% This could be defined as last(L, X) :- append(_, [X], L).
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last([H|List], Last) :-
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last(List, H, Last).
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last([], Last, Last).
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last([H|List], _, Last) :-
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last(List, H, Last).
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% nextto(X, Y, List)
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% is true when X and Y appear side-by-side in List. It could be written as
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% nextto(X, Y, List) :- append(_, [X,Y,_], List).
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% It may be used to enumerate successive pairs from the list.
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nextto(X,Y, [X,Y|_]).
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nextto(X,Y, [_|List]) :-
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nextto(X,Y, List).
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% nth0(?N, +List, ?Elem) is true when Elem is the Nth member of List,
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% counting the first as element 0. (That is, throw away the first
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% N elements and unify Elem with the next.) It can only be used to
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% select a particular element given the list and index. For that
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% task it is more efficient than nmember.
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% nth(+N, +List, ?Elem) is the same as nth0, except that it counts from
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% 1, that is nth(1, [H|_], H).
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nth0(V, In, Element) :- var(V), !,
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generate_nth(0, V, In, Element).
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nth0(0, [Head|_], Head) :- !.
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nth0(N, [_|Tail], Elem) :-
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M is N-1,
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find_nth0(M, Tail, Elem).
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find_nth0(0, [Head|_], Head) :- !.
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find_nth0(N, [_|Tail], Elem) :-
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M is N-1,
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find_nth0(M, Tail, Elem).
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nth1(V, In, Element) :- var(V), !,
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generate_nth(1, V, In, Element).
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nth1(1, [Head|_], Head) :- !.
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nth1(N, [_|Tail], Elem) :-
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nonvar(N), !,
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M is N-1, % should be succ(M, N)
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find_nth(M, Tail, Elem).
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nth(V, In, Element) :- var(V), !,
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generate_nth(1, V, In, Element).
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nth(1, [Head|_], Head) :- !.
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nth(N, [_|Tail], Elem) :-
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nonvar(N), !,
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M is N-1, % should be succ(M, N)
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find_nth(M, Tail, Elem).
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find_nth(1, [Head|_], Head) :- !.
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find_nth(N, [_|Tail], Elem) :-
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M is N-1,
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find_nth(M, Tail, Elem).
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generate_nth(I, I, [Head|_], Head).
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generate_nth(I, IN, [_|List], El) :-
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I1 is I+1,
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generate_nth(I1, IN, List, El).
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% nth0(+N, ?List, ?Elem, ?Rest) unifies Elem with the Nth element of List,
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% counting from 0, and Rest with the other elements. It can be used
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% to select the Nth element of List (yielding Elem and Rest), or to
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% insert Elem before the Nth (counting from 1) element of Rest, when
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% it yields List, e.g. nth0(2, List, c, [a,b,d,e]) unifies List with
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% [a,b,c,d,e]. nth is the same except that it counts from 1. nth
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% can be used to insert Elem after the Nth element of Rest.
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nth0(V, In, Element, Tail) :- var(V), !,
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generate_nth(0, V, In, Element, Tail).
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nth0(0, [Head|Tail], Head, Tail) :- !.
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nth0(N, [Head|Tail], Elem, [Head|Rest]) :-
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M is N-1,
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nth0(M, Tail, Elem, Rest).
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find_nth0(0, [Head|Tail], Head, Tail) :- !.
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find_nth0(N, [Head|Tail], Elem, [Head|Rest]) :-
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M is N-1,
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find_nth0(M, Tail, Elem, Rest).
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nth1(V, In, Element, Tail) :- var(V), !,
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generate_nth(1, V, In, Element, Tail).
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nth1(1, [Head|Tail], Head, Tail) :- !.
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nth1(N, [Head|Tail], Elem, [Head|Rest]) :-
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M is N-1,
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nth1(M, Tail, Elem, Rest).
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nth(V, In, Element, Tail) :- var(V), !,
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generate_nth(1, V, In, Element, Tail).
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nth(1, [Head|Tail], Head, Tail) :- !.
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nth(N, [Head|Tail], Elem, [Head|Rest]) :-
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M is N-1,
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nth(M, Tail, Elem, Rest).
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find_nth(1, [Head|Tail], Head, Tail) :- !.
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find_nth(N, [Head|Tail], Elem, [Head|Rest]) :-
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M is N-1,
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find_nth(M, Tail, Elem, Rest).
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generate_nth(I, I, [Head|Tail], Head, Tail).
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generate_nth(I, IN, [E|List], El, [E|Tail]) :-
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I1 is I+1,
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generate_nth(I1, IN, List, El, Tail).
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% permutation(List, Perm)
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% is true when List and Perm are permutations of each other. Of course,
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% if you just want to test that, the best way is to keysort/2 the two
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% lists and see if the results are the same. Or you could use list_to_bag
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% (from BagUtl.Pl) to see if they convert to the same bag. The point of
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% perm is to generate permutations. The arguments may be either way round,
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% the only effect will be the order in which the permutations are tried.
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% Be careful: this is quite efficient, but the number of permutations of an
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% N-element list is N!, even for a 7-element list that is 5040.
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permutation([], []).
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permutation(List, [First|Perm]) :-
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select(First, List, Rest), % tries each List element in turn
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permutation(Rest, Perm).
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% prefix(Part, Whole) iff Part is a leading substring of Whole
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prefix([], _).
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prefix([Elem | Rest_of_part], [Elem | Rest_of_whole]) :-
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prefix(Rest_of_part, Rest_of_whole).
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% remove_duplicates(List, Pruned)
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% removes duplicated elements from List. Beware: if the List has
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% non-ground elements, the result may surprise you.
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remove_duplicates([], []).
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remove_duplicates([Elem|L], [Elem|NL]) :-
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delete(L, Elem, Temp),
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remove_duplicates(Temp, NL).
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% reverse(List, Reversed)
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% is true when List and Reversed are lists with the same elements
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% but in opposite orders. rev/2 is a synonym for reverse/2.
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reverse(List, Reversed) :-
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reverse(List, [], Reversed).
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reverse([], Reversed, Reversed).
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reverse([Head|Tail], Sofar, Reversed) :-
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reverse(Tail, [Head|Sofar], Reversed).
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% same_length(?List1, ?List2)
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% is true when List1 and List2 are both lists and have the same number
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% of elements. No relation between the values of their elements is
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% implied.
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% Modes same_length(-,+) and same_length(+,-) generate either list given
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% the other; mode same_length(-,-) generates two lists of the same length,
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% in which case the arguments will be bound to lists of length 0, 1, 2, ...
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same_length([], []).
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same_length([_|List1], [_|List2]) :-
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same_length(List1, List2).
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%% selectchk(+Elem, +List, -Rest) is semidet.
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%
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% Semi-deterministic removal of first element in List that unifies
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% Elem.
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selectchk(Elem, List, Rest) :-
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select(Elem, List, Rest0), !,
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Rest = Rest0.
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% select(?Element, ?Set, ?Residue)
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% is true when Set is a list, Element occurs in Set, and Residue is
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% everything in Set except Element (things stay in the same order).
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select(Element, [Element|Rest], Rest).
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select(Element, [Head|Tail], [Head|Rest]) :-
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select(Element, Tail, Rest).
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% sublist(Sublist, List)
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% is true when both append(_,Sublist,S) and append(S,_,List) hold.
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%% sublist(?Sub, +List) is nondet.
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%
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% True if all elements of Sub appear in List in the same order.
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sublist(L, L).
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sublist(Sub, [H|T]) :-
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'$sublist1'(T, H, Sub).
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'$sublist1'(Sub, _, Sub).
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'$sublist1'([H|T], _, Sub) :-
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'$sublist1'(T, H, Sub).
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'$sublist1'([H|T], X, [X|Sub]) :-
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'$sublist1'(T, H, Sub).
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% substitute(X, XList, Y, YList)
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% is true when XList and YList only differ in that the elements X in XList
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% are replaced by elements Y in the YList.
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substitute(X, XList, Y, YList) :-
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substitute2(XList, X, Y, YList).
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substitute2([], _, _, []).
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substitute2([X0|XList], X, Y, [Y|YList]) :-
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X == X0, !,
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substitute2(XList, X, Y, YList).
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substitute2([X0|XList], X, Y, [X0|YList]) :-
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substitute2(XList, X, Y, YList).
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% suffix(Suffix, List)
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% holds when append(_,Suffix,List) holds.
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suffix(Suffix, Suffix).
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suffix(Suffix, [_|List]) :-
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suffix(Suffix,List).
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% sumlist(Numbers, Total)
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% is true when Numbers is a list of integers, and Total is their sum.
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sumlist(Numbers, Total) :-
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sumlist(Numbers, 0, Total).
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sum_list(Numbers, SoFar, Total) :-
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sumlist(Numbers, SoFar, Total).
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sum_list(Numbers, Total) :-
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sumlist(Numbers, 0, Total).
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sumlist([], Total, Total).
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sumlist([Head|Tail], Sofar, Total) :-
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Next is Sofar+Head,
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sumlist(Tail, Next, Total).
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% list_concat(Lists, List)
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% is true when Lists is a list of lists, and List is the
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% concatenation of these lists.
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list_concat([], []).
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list_concat([H|T], L) :-
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list_concat(H, L, Li),
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list_concat(T, Li).
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list_concat([], L, L).
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list_concat([H|T], [H|Lf], Li) :-
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list_concat(T, Lf, Li).
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%
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% flatten a list
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%
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flatten(X,Y) :- flatten_list(X,Y,[]).
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flatten_list(V) --> {var(V)}, !, [V].
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flatten_list([]) --> !.
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flatten_list([H|T]) --> !, flatten_list(H),flatten_list(T).
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flatten_list(H) --> [H].
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max_list([H|L],Max) :-
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max_list(L,H,Max).
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max_list([],Max,Max).
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max_list([H|L],Max0,Max) :-
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(
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H > Max0
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->
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max_list(L,H,Max)
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;
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max_list(L,Max0,Max)
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).
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min_list([H|L],Max) :-
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min_list(L,H,Max).
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min_list([],Max,Max).
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min_list([H|L],Max0,Max) :-
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(
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H < Max0
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->
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min_list(L, H, Max)
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;
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min_list(L, Max0, Max)
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).
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%% numlist(+Low, +High, -List) is semidet.
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%
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% List is a list [Low, Low+1, ... High]. Fails if High < Low.%
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%
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% @error type_error(integer, Low)
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% @error type_error(integer, High)
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numlist(L, U, Ns) :-
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must_be(integer, L),
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must_be(integer, U),
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L =< U,
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numlist_(L, U, Ns).
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numlist_(U, U, OUT) :- !, OUT = [U].
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numlist_(L, U, [L|Ns]) :-
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succ(L, L2),
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numlist_(L2, U, Ns).
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% copied from SWI lists library.
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intersection([], _, []) :- !.
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intersection([X|T], L, Intersect) :-
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memberchk(X, L), !,
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Intersect = [X|R],
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intersection(T, L, R).
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intersection([_|T], L, R) :-
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intersection(T, L, R).
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