% =================================================================
:- 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]):-
      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],[Y|TD]) :-          % The list need not be ordered. The element X need not be the minimum.
  constr(~(X=Y)),                  % delete(X,L,LD) succeeds **IFF** X is a member of L.
  delete(X,TD,T).  % error: delete(X,TD,T) ---> delete(X,T,TD).

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

length([],L) :- L=0.
length([H|T],L) :-
  L=(LT+1),
  length(T,LT).

% ====================================================
% verification.
% Property:
:- pred ff1.
ff1 :-                              % perm
   constr( ~(LL=LLP)),
   length(L,LL), length(LP,LLP),
   perm(L,LP).
%
%:- pred ff2.
%ff2 :-                              % delete.   ***  L is assumed to be not empty.
%   constr( ~(LLD = (LL-1)) ),
%   length(L,LL), length(LD,LLD),
%   delete(H,L,LD).                  % delete(X,L,LD) succeeds iff X is a member of L.
%
%:- pred ff3.
%ff3 :-                              % cons
%  constr( ~(LHT =(LT+1)) ),
%  length(T,LT), length(HT,LHT),
%  cons(H,T,HT).

% ====================================================
:- query ff1/0.
%:- query ff2/0.
%:- query ff3/0.
% ====================================================

%  Catamorphic abstraction

:- cata_abs list(int) ==> length(T,LT).

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