% The possible suspects of the crimes are:

possible_suspect(fred).
possible_suspect(mary).
possible_suspect(jane).
possible_suspect(george).

% The facts about the crimes from the police log.

crime(robbery1, john, tuesday, park).
crime(assault1, mary, wednesday, park).
crime(robbery2, jim, wednesday, pub).
crime(assault2, robin, thursday, park).

% Tell prolog where the suspects were on
% different days.

was_at(fred, park, tuesday).
was_at(fred, pub, wednesday).
was_at(fred, pub, thursday).

was_at(george, pub, tuesday).
was_at(george, pub, wednesday).
was_at(george, home, thursday).

was_at(jane, home, tuesday).
was_at(jane, park, wednesday).
was_at(jane, park, thursday).

was_at(mary, pub, tuesday).
was_at(mary, park, wednesday).
was_at(mary, home, thursday).

% Tell prolog who is jealous of who

jealous_of(fred, john).
jealous_of(jane, mary).

% And who owes money to whom

owes_money_to(george, jim).
owes_money_to(mary, robin).

% A Person has a motive against a Victim if
% Person is jealous of Victim or
% Person owes money to Victim

motive_against(Person, Victim) :-
    jealous_of(Person, Victim);
    owes_money_to(Person, Victim).

% A Person is a prime suspect of a crime if
% Person is a possible suspect and the person
% was at the time and place of the crime and
% the person had a motive against the victim
% of the crime.

prime_suspect(Person, Crime) :-
    possible_suspect(Person),
    was_at(Person, Place, Day),
    crime(Crime, Victim, Day, Place),
    motive_against(Person, Victim).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QUERIES / RESPONSES FOR Q1
%
% 1 ?- prime_suspect(fred,robbery1).
% 
% Yes
% 2 ?- prime_suspect(george, assault2).
% 
% No
% 3 ?- prime_suspect(Prime_Suspect, robbery1).
% 
% Prime_Suspect = fred ;
% 
% No
% 4 ?- prime_suspect(Prime_Suspect, robbery2).
% 
% Prime_Suspect = george ;
% 
% No
% 5 ?- prime_suspect(Prime_Suspect, assault1).
% 
% Prime_Suspect = jane ;
% 
% No
% 6 ?- prime_suspect(Prime_Suspect, assault2).
% 
% No
% 7 ?- prime_suspect(fred, Crime).
% 
% Crime = robbery1 ;
% 
% No
% 8 ?- prime_suspect(george, Crime).
% 
% Crime = robbery2 ;
% 
% No
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%     Q2. MISC                                  %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1. Compute the last member of a nonempty list

last([X],X).
last([_|T],X) :-
    last(T,X).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2. Reverse a list

append([],L,L).
append([H|T],L2,[H|L3]) :-
    append(T,L2,L3).

reverse([],[]).
reverse([H|T],R) :-
    reverse(T,X),
    append(X,[H],R).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3. Remove one occurrence of X from list K

select(X,K,L) :-
    append(I,[X|J],K),
    append(I,J,L).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4. X and Y are different members of L

member(X,[X|_]).
member(X,[_|Yt]) :-
    member(X,Yt).

% X and Y are different members of L if
% X is a member of L and Y is a member of
% list K where K is list L with X removed.

different(X,Y,L) :-
    member(X,L),
    select(X,L,K),
    member(Y,K).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5. K and L are lists of the same length if
%    they are both empty after chopping their
%    heads off the same amount of times.

samelength([],[]).
samelength([_|K],[_|L]) :-
    samelength(K,L).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 6. K and L are lists of the same length and
%    contain the same elements.

same_elements([],[]).
same_elements([Kh|Kt],L) :-
    select(Kh,L,X),
    same_elements(Kt,X).

% List K is similar to list L if
% K and L are the same length and
% K and L contain the same elements

similar([],[]).
similar(K, L) :-
    samelength(K,L),
    same_elements(K,L).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% QUERIES / RESPONSES FOR Q2
%
% 2 ?- last([a,b,c,d],Last).
%
% Last = d ;%
%
% No
% 3 ?- reverse([a,b,c,d],Reversed).
%
% Reversed = [d, c, b, a] ;
%
% No
% 4 ?- select(a,[a,b,c,a],List).
%
% List = [b, c, a] ;
%
% List = [a, b, c] ;
%
% No
% 5 ?- different(X,Y,[1,2,3]).
%
% X = 1
% Y = 2 ;
%
% X = 1
% Y = 3 ;
%
% X = 2
% Y = 1 ;
%
% X = 2
% Y = 3 ;
%
% X = 3
% Y = 1 ;
%
% X = 3
% Y = 2 ;
%
% No
% 6 ?- samelength([a,b,c],L).
%
% L = [_G359, _G362, _G365] ;
%
% No
% 7 ?- samelength(L,[a,b,c]).
%
% L = [_G359, _G362, _G365] ;
%
% No
% 8 ?- similar([a,b,a],L).
%
% L = [a, b, a] ;
%
% L = [a, a, b] ;
%
% L = [b, a, a] ;
%
% L = [a, a, b] ;
%
% L = [b, a, a] ;
%
% L = [a, b, a] ;
%
% No
% 9 ?- similar(L,[a,b,a]).
%
% L = [a, b, a] ;
%
% L = [a, a, b] ;
%
% L = [b, a, a] ;
%
% L = [b, a, a] ;
%
% L = [a, a, b] ;
%
% L = [a, b, a] ;
%
% No
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%