% =================================================================
:- pred constr(bool).
:- mode constr(in).
:- ignore constr/1.
% ====================================================
% Program.
:- pred perm(list(int),list(int)).
:- mode perm(in,in).               % in,in: perm is not functional
perm([],[]).
perm([X|Xs],[H|Perm]):-            % a permutation
      cons(X,Xs,XXs),
      delete(X,XXs,Rest),    %error: X --> H
      perm(Rest,Perm).

:- pred delete(int,list(int),list(int)).
:- mode delete(in,in,in).          % delete is not total
delete(X,[Y|T],T) :- constr(X=Y).  % Taking X away from [Y|T]. Deleting exactly one copy of X.
delete(X,[Y|T],[Y|TD]) :-          % The list need not be ordered. Element X need not be the minimum.
  constr(~(X=Y)),                  % delete(X,L,LD) succeeds **IFF** X is a member of L.
  delete(X,T,TD).

:- 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).
  
% ====================================================
% verification.
% Property:
:- pred ff1.
ff1 :- 
    constr( ~(LS=LPS)),                             
    listsum(L,LS),  
    listsum(LP,LPS),
    perm(L,LP).
   
%% contracts (postcondition: true)
%
%:- spec delete(H,L,LD) ==> listsum(L,SL), listsum(LD,SLD).
%
%:- spec cons(H,T,HT) ==> listsum(T,ST), listsum(HT,SHT).

% ====================================================
:- query ff1/0.
% ====================================================

%  Catamorphic abstraction

:- cata_abs list(int) ==> listsum(T,ST).

% ======================================================