How to multiply all elements of two lists with each other in Prolog

Question

I am thinking how to multiply all elements of two list with each other. Then I want to put all results in List3. For example,

List1 = [1,3,5].
List         


        

Answer 1

Use dcg! "Cross product"—shown here—is just one of many applications. Proceed like this:

:- meta_predicate xproduct(4,?,?,?).
xproduct(P_4,As) -->
   xproduct(P_4,As,As).

:- meta_predicate xproduct(4,?,?,?,?).
xproduct(P_4,As,Bs) -->
   xproduct_aux1(As,Bs,P_4).                % use 1st argument indexing for As

:- meta_predicate xproduct_aux1(?,?,4,?,?).
xproduct_aux1([]    ,_ , _ ) --> [].
xproduct_aux1([A|As],Bs,P_4) -->
   xproduct_aux2(Bs,[A|As],P_4).            % use 1st argument indexing for Bs

:- meta_predicate xproduct_aux2(?,?,4,?,?).
xproduct_aux2([],_,_) --> [].
xproduct_aux2([B|Bs],As,P_4) -->
   xproduct_(As,[B|Bs],P_4).

:- meta_predicate xproduct_(?,?,4,?,?).
xproduct_([],_,_) --> [].
xproduct_([A|As],Bs,P_4) -->
    xprod_(Bs,A,P_4),
    xproduct_(As,Bs,P_4).

:- meta_predicate xprod_(?,?,4,?,?).
xprod_([],_,_) --> [].
xprod_([B|Bs],A,P_4) -->
    call(P_4,A,B),
    xprod_(Bs,A,P_4).

Let's use clpfd and lambdas to run the query you provided in your question:

:- use_module([library(clpfd),library(lambda)]).

?- phrase(xproduct(\X^Y^[Z|Zs]^Zs^(Z #= X*Y),[1,3,5],[2,6,7]),Fs).
Fs = [2,6,7,6,18,21,10,30,35].

Above lambdas use difference-lists explicitly; with phrase//1 we can also use them implicitly!

?- phrase(xproduct(\X^Y^phrase(([Z],{Z #= X*Y})),[1,3,5],[2,6,7]),Fs).
Fs = [2,6,7,6,18,21,10,30,35].

clpfd enables us to do very general queries. Thanks to @PauloMoura for his suggestion! Look!

?- phrase(xproduct(\X^Y^phrase(([Z],{Z #= X*Y})),As,Bs),
          [2,6,7,6,18,21,10,30,35]),
   maplist(labeling([]),[As,Bs]).
  As = [-2,-6,-7,-6,-18,-21,-10,-30,-35], Bs = [-1]
; As = [ 2, 6, 7, 6, 18, 21, 10, 30, 35], Bs = [ 1]
; As = [-1,-3,-5],                        Bs = [-2,-6,-7]
; As = [ 1, 3, 5],                        Bs = [ 2, 6, 7]
; As = [-1],                              Bs = [-2,-6,-7,-6,-18,-21,-10,-30,-35]
; As = [ 1],                              Bs = [ 2, 6, 7, 6, 18, 21, 10, 30, 35]
; false.