% =================================================================
:- pred constr(bool).    
:- mode constr(in).
:- ignore constr/1.
% ===========================================================
%Program
:- pred revacc(list(int),list(int)).  
:- mode revacc(in,out).            
                                    
revacc(L,R) :- reva(L,EL,R), emptylist(EL).

:- pred reva(list(int),list(int),list(int)).  % reva([1,2], [7,9,8], F).  F=[2,1,7,9,8].
:- mode reva(in,in,out).            % the accumulator remains "as is" at the right end
                                    % of the reversed list.
reva([],[],[X]). %error: delete clause 
reva([],A,A).
reva([H|T],A,R) :- 
   cons(H,A,HA),
   reva(T,HA,R).

:- pred emptylist(list(int)).
:- mode emptylist(in).
emptylist([]).

:- pred cons(int,list(int),list(int)).
:- mode cons(in,in,out).
cons(H,T,[H|T]).          
% ===========================================================
% Catamorphisms
:- pred listmember(int,list(int),bool).
:- mode listmember(in,in,out).
:- cata listmember/3-2.

listmember(X,[],Res) :- constr(~Res).
listmember(X,[Y|Ys],B) :-
      constr( B=ite(X=Y,true,B1) ) ,
      listmember(X,Ys,B1).
  
% ===========================================================
% Property to verify
:- pred ff1.
ff1 :- constr( ~( (N1=N2) ) ),
    listmember(X,L,N1), listmember(X,R,N2),
    revacc(L,R).
    
:- spec reva(L,Acc,RL) ==> listmember(X,L,SL), listmember(X,Acc,SAcc), listmember(X,RL,SRL) 
             => constr(true).

:- spec emptylist(L) ==> listmember(X,L,SL) => constr(true).

:- spec cons(H,T,HT) ==> listmember(X,T,ST), listmember(X,HT,SHT) => constr(true).
    
% ===========================================================
:- query ff1/0.
% ===========================================================