Prolog delete: doesn't delete all elements that unify with Element

Question

I\'m having an issue with SWI-Prolog\'s delete/3 predicate. The easiest way is just a quick example:

?- delete([(1,1),(1,2),(3,2)], (1,_), List).
L         


        

Answer 1

This answer tries to generalize the idea presented in previous answer.

Let's define a reified variant of subsumes_term/2:

list_nonvardisj([A],C) :- 
   !, 
   C = nonvar(A).
list_nonvardisj([A|As],(nonvar(A);C)) :-
   list_nonvardisj(As,C).

subsumes_term_t(General,Specific,Truth) :-
   subsumes_term(General,Specific),
   !,
   term_variables(General,G_vars),
   free4evrs(G_vars),
   Truth = true.
subsumes_term_t(General,Specific,Truth) :-
   Specific \= General,
   !,
   Truth = false.
subsumes_term_t(General,Specific,Truth) :-
   term_variables(Specific,S_vars),
   (  S_vars = [V]
   -> freeze(V,subsumes_term_t(General,Specific,Truth))
   ;  S_vars = [_|_]
   -> list_nonvardisj(S_vars,S_wakeup),
      when(S_wakeup,subsumes_term_t(General,Specific,Truth))
   ;  throw(error(instantiation_error, subsumes_term_t/3))
   ),
   (  Truth = true
   ;  Truth = false
   ).

The above definition of the reified predicate subsumes_term_t/3 uses free4evrs/1 to ensure that the "generic" term passed to subsumes_term/2 is not instantiated any further.

For SICStus Prolog, we can define it as follows:

:- module(free4evr,[free4evr/1,free4evrs/1]).

:- use_module(library(atts)).

:- attribute nvrb/0.                       % nvrb ... NeVeR Bound

verify_attributes(V,_,Goals) :-
   get_atts(V,nvrb), 
   !,
   Goals = [throw(error(uninstantiation_error(V),free4evr/1))].
verify_attributes(_,_,[]).

attribute_goal(V,free4evr(V)) :-
   get_atts(V,nvrb).

free4evr(V) :-
   nonvar(V),
   !,
   throw(error(uninstantiation_error(V),free4evr/1)).
free4evr(V) :-
   (  get_atts(V,nvrb)
   -> true
   ;  put_atts(Fresh,nvrb),
      V = Fresh
   ).

free4evrs([]).
free4evrs([V|Vs]) :-
   free4evr(V),
   free4evrs(Vs).

Let's put subsumes_term_t/3 to use!

?- texclude(subsumes_term_t(1-X), [A,B,C], Fs), A = 1-1, B = 1-2, C = 3-2.
A = 1-1, B = 1-2, C = 3-2, Fs = [C], free4evr(X) ? ;   % succeeds with choice-point
no

?- texclude(subsumes_term_t(1-X), [x,1-Y,2-3], Fs).
Fs = [x,2-3], free4evr(X) ? ;
no

What happens if we instantiate variable X in above query sometime after the call to texclude/3?

?- texclude(subsumes_term_t(1-X), [x,1-Y,2-3], Fs), X=something.
! error(uninstantiation_error(something),free4evr/1)