% =================================================================
:- 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(H,XXs,Rest),
      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],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). % error: TD in head should be [Y|TD]

:- pred cons(int,list(int),list(int)).
:- mode cons(in,in,out).
cons(H,T,[H|T]).
% ====================================================
% catamorphisms       
:- pred listsize(list(int),int).
:- mode listsize(in,out).
:- cata listsize/2-1.

listsize([],L) :- L=1.
listsize([H|T],L) :-
  L=(LT+1),
  listsize(T,LT).

% ====================================================
% verification.
% Property:
:- pred ff1.
ff1 :-                              
   constr( ~(LL=LLP)),
   listsize(L,LL), listsize(LP,LLP),
   perm(L,LP).

% contracts (postcondition: true)

:- spec delete(H,L,LD) ==> listsize(L,SL), listsize(LD,SLD) => true.

:- spec cons(H,T,HT) ==> listsize(T,ST), listsize(HT,SHT) => true.

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