% =================================================================
:- 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([],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
%-----  listsum --- sum of integers in nodes of the given list.
:- pred listsum(list(int),int).
:- mode listsum(in,out).
:- cata listsum/2-1.

listsum([],S) :- S=0.
listsum([H|T],S) :-
  S=(H+ST),
  listsum(T,ST).

% ===========================================================
% Property to verify
:- pred ff1.
ff1 :- 
    constr( ~( (LS=RS) ) ),
    listsum(L,LS), listsum(R,RS),
    revacc(L,R).

% contracts (postcondition: true)

:- spec reva(L,Acc,RL) ==> listsum(L,SL), listsum(Acc,SAcc), listsum(RL,SRL).

:- spec emptylist(L) ==> listsum(L,SL).

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