/* Level 1*/
:-use_module(library(clpr)).

/* Q1 */
positive([]).
positive([X|Xs]) :- X>0, positive(Xs).

/* Q2, see alternate implementation for reverse below */
rev(Xs,Rs) :- revhelper(Xs,[],Rs).
revhelper([],Rs,Rs).
revhelper([X|Xs],Ys,Rs) :- revhelper(Xs,[X|Ys],Rs).

/* Q3 */
mylast([X],X).
mylast([_|Xs],X) :- mylast(Xs,X).

/* Q4 */
mysum([],0).
mysum([X],X).
mysum([X|Xs],S) :- mysum(Xs,S1), {X+S1=S}.


/* Derivation trees, diagrams coming soon */

/* reverse as implemented in mini-exercises */
reverse([],[]).
reverse([X|Xs],Ys) :- reverse(Xs,Rs), append(Rs,[X],Ys).
append([],Ys,Ys).
append([X|Xs],Ys,[X|Zs]) :- append(Xs,Ys,Zs).

/* level 2 */

/* Q1 */

/* order of elements in second list is by last occurrence in first list */
remove_dupl([],[]).
remove_dupl([X|Xs],[X|Ys]) :- \+ member(X,Xs), remove_dupl(Xs,Ys).
remove_dupl([X|Xs],Ys) :- member(X,Xs), member(X,Ys), remove_dupl(Xs,Ys).

/* Q2 */
set_int([],_,[]).
set_int([X|Xs],Ys,[X|Zs]):- member(X,Ys),set_int(Xs,Ys,Zs).
set_int([X|Xs],Ys,Zs):- \+ member(X,Ys), set_int(Xs,Ys,Zs).

set_diff([],_,[]).
set_diff([X|Xs],Ys,Zs) :- member(X,Ys),set_diff(Xs,Ys,Zs).
set_diff([X|Xs],Ys,[X|Zs]) :- \+ member(X,Ys), set_diff(Xs,Ys,Zs).

/* Q3 */
take(0,_,[]).
take(N,[X|Xs],[X|Ys]) :- take(M,Xs,Ys), {M=N-1}.

/* Q4, should also check that S is a member of the original list */
my_max(_,[]).
my_max(S,[X|Xs]) :- {S > X}, mymax(A,Xs).
my_max(S,[X|Xs]) :- {S <= X}, mymax(X,Xs).