:- module(lists, [member/2, select/3, append/2, append/3, foldl/4, foldl/5, memberchk/2, reverse/2, length/2, maplist/2, maplist/3, maplist/4, maplist/5, maplist/6, maplist/7, maplist/8, maplist/9, same_length/2, nth0/3, sum_list/2, transpose/2, list_to_set/2, list_max/2, list_min/2, permutation/2]). /* Author: Mark Thom, Jan Wielemaker, and Richard O'Keefe Copyright (c) 2018-2021, Mark Thom Copyright (c) 2002-2020, University of Amsterdam VU University Amsterdam SWI-Prolog Solutions b.v. All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: 1. Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. 2. Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution. THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. */ :- use_module(library(error)). :- meta_predicate maplist(1, ?). :- meta_predicate maplist(2, ?, ?). :- meta_predicate maplist(3, ?, ?, ?). :- meta_predicate maplist(4, ?, ?, ?, ?). :- meta_predicate maplist(5, ?, ?, ?, ?, ?). :- meta_predicate maplist(6, ?, ?, ?, ?, ?, ?). :- meta_predicate maplist(7, ?, ?, ?, ?, ?, ?, ?). :- meta_predicate maplist(8, ?, ?, ?, ?, ?, ?, ?, ?). :- meta_predicate foldl(3, ?, ?, ?). :- meta_predicate foldl(4, ?, ?, ?, ?). length(Xs0, N) :- '$skip_max_list'(M, N, Xs0,Xs), !, ( Xs == [] -> N = M ; nonvar(Xs) -> var(N), Xs = [_|_], throw(error(resource_error(finite_memory),length/2)) ; nonvar(N) -> R is N-M, length_rundown(Xs, R) ; N == Xs -> throw(error(resource_error(finite_memory),length/2)) ; length_addendum(Xs, N, M) ). length(_, N) :- integer(N), !, domain_error(not_less_than_zero, N, length/2). length(_, N) :- type_error(integer, N, length/2). length_addendum([], N, N). length_addendum([_|Xs], N, M) :- M1 is M + 1, length_addendum(Xs, N, M1). length_rundown(Xs, 0) :- !, Xs = []. length_rundown([_|Xs], N) :- N1 is N-1, length_rundown(Xs, N1). member(X, [X|_]). member(X, [_|Xs]) :- member(X, Xs). select(X, [X|Xs], Xs). select(X, [Y|Xs], [Y|Ys]) :- select(X, Xs, Ys). append([], []). append([L0|Ls0], Ls) :- append(L0, Rest, Ls), append(Ls0, Rest). append([], R, R). append([X|L], R, [X|S]) :- append(L, R, S). memberchk(X, Xs) :- member(X, Xs), !. reverse(Xs, Ys) :- ( nonvar(Xs) -> reverse(Xs, Ys, [], Xs) ; reverse(Ys, Xs, [], Ys) ). reverse([], [], YsRev, YsRev). reverse([_|Xs], [Y1|Ys], YsPreludeRev, Xss) :- reverse(Xs, Ys, [Y1|YsPreludeRev], Xss). maplist(_, []). maplist(Cont1, [E1|E1s]) :- call(Cont1, E1), maplist(Cont1, E1s). maplist(_, [], []). maplist(Cont2, [E1|E1s], [E2|E2s]) :- call(Cont2, E1, E2), maplist(Cont2, E1s, E2s). maplist(_, [], [], []). maplist(Cont3, [E1|E1s], [E2|E2s], [E3|E3s]) :- call(Cont3, E1, E2, E3), maplist(Cont3, E1s, E2s, E3s). maplist(_, [], [], [], []). maplist(Cont, [E1|E1s], [E2|E2s], [E3|E3s], [E4|E4s]) :- call(Cont, E1, E2, E3, E4), maplist(Cont, E1s, E2s, E3s, E4s). maplist(_, [], [], [], [], []). maplist(Cont, [E1|E1s], [E2|E2s], [E3|E3s], [E4|E4s], [E5|E5s]) :- call(Cont, E1, E2, E3, E4, E5), maplist(Cont, E1s, E2s, E3s, E4s, E5s). maplist(_, [], [], [], [], [], []). maplist(Cont, [E1|E1s], [E2|E2s], [E3|E3s], [E4|E4s], [E5|E5s], [E6|E6s]) :- call(Cont, E1, E2, E3, E4, E5, E6), maplist(Cont, E1s, E2s, E3s, E4s, E5s, E6s). maplist(_, [], [], [], [], [], [], []). maplist(Cont, [E1|E1s], [E2|E2s], [E3|E3s], [E4|E4s], [E5|E5s], [E6|E6s], [E7|E7s]) :- call(Cont, E1, E2, E3, E4, E5, E6, E7), maplist(Cont, E1s, E2s, E3s, E4s, E5s, E6s, E7s). maplist(_, [], [], [], [], [], [], [], []). maplist(Cont, [E1|E1s], [E2|E2s], [E3|E3s], [E4|E4s], [E5|E5s], [E6|E6s], [E7|E7s], [E8|E8s]) :- call(Cont, E1, E2, E3, E4, E5, E6, E7, E8), maplist(Cont, E1s, E2s, E3s, E4s, E5s, E6s, E7s, E8s). sum_list(Ls, S) :- foldl(lists:sum_, Ls, 0, S). sum_(L, S0, S) :- S is S0 + L. same_length([], []). same_length([_|As], [_|Bs]) :- same_length(As, Bs). foldl(Goal_3, Ls, A0, A) :- foldl_(Ls, Goal_3, A0, A). foldl_([], _, A, A). foldl_([L|Ls], G_3, A0, A) :- call(G_3, L, A0, A1), foldl_(Ls, G_3, A1, A). foldl(Goal_4, Xs, Ys, A0, A) :- foldl_(Xs, Ys, Goal_4, A0, A). foldl_([], [], _, A, A). foldl_([X|Xs], [Y|Ys], G_4, A0, A) :- call(G_4, X, Y, A0, A1), foldl_(Xs, Ys, G_4, A1, A). transpose(Ls, Ts) :- lists_transpose(Ls, Ts). lists_transpose([], []). lists_transpose([L|Ls], Ts) :- maplist(lists:same_length(L), Ls), foldl(lists:transpose_, L, Ts, [L|Ls], _). transpose_(_, Fs, Lists0, Lists) :- maplist(lists:list_first_rest, Lists0, Fs, Lists). list_first_rest([L|Ls], L, Ls). list_to_set(Ls0, Ls) :- maplist(lists:with_var, Ls0, LVs0), keysort(LVs0, LVs), same_elements(LVs), pick_firsts(LVs0, Ls). pick_firsts([], []). pick_firsts([E-V|EVs], Fs0) :- ( V == visited -> Fs0 = Fs ; V = visited, Fs0 = [E|Fs] ), pick_firsts(EVs, Fs). with_var(E, E-_). same_elements([]). same_elements([EV|EVs]) :- foldl(lists:unify_same, EVs, EV, _). unify_same(E-V, Prev-Var, E-V) :- ( Prev == E -> Var = V ; true ). nth0(N, Es, E) :- can_be(integer, N), can_be(list, Es), ( integer(N) -> nth0_index(N, Es, E) ; nth0_search(N, Es, E) ). nth0_index(0, [E|_], E) :- !. nth0_index(N, [_|Es], E) :- N > 0, N1 is N - 1, nth0_index(N1, Es, E). nth0_search(N, Es, E) :- nth0_search(0, N, Es, E). nth0_search(N, N, [E|_], E). nth0_search(N0, N, [_|Es], E) :- N1 is N0 + 1, nth0_search(N1, N, Es, E). list_max([N|Ns], Max) :- foldl(lists:list_max_, Ns, N, Max). list_max_(N, Max0, Max) :- Max is max(N, Max0). list_min([N|Ns], Min) :- foldl(lists:list_min_, Ns, N, Min). list_min_(N, Min0, Min) :- Min is min(N, Min0). %! permutation(?Xs, ?Ys) is nondet. % % True when Xs is a permutation of Ys. This can solve for Ys given % Xs or Xs given Ys, or even enumerate Xs and Ys together. The % predicate permutation/2 is primarily intended to generate % permutations. Note that a list of length N has N! permutations, % and unbounded permutation generation becomes prohibitively % expensive, even for rather short lists (10! = 3,628,800). % % The example below illustrates that Xs and Ys being proper lists % is not a sufficient condition to use the above replacement. % % == % ?- permutation([1,2], [X,Y]). % X = 1, Y = 2 ; % X = 2, Y = 1 ; % false. % == % % @error type_error(list, Arg) if either argument is not a proper % or partial list. permutation(Xs, Ys) :- '$skip_max_list'(Xlen, _, Xs, XTail), '$skip_max_list'(Ylen, _, Ys, YTail), ( XTail == [], YTail == [] % both proper lists -> Xlen == Ylen ; var(XTail), YTail == [] % partial, proper -> length(Xs, Ylen) ; XTail == [], var(YTail) % proper, partial -> length(Ys, Xlen) ; var(XTail), var(YTail) % partial, partial -> length(Xs, Len), length(Ys, Len) ; must_be(list, Xs), % either is not a list must_be(list, Ys) ), perm(Xs, Ys). perm([], []). perm(List, [First|Perm]) :- select(First, List, Rest), perm(Rest, Perm).