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

Use meta-predicate texclude/3 in combination with the reified term equality predicate (=)/3!

First, we try using (=)/3 directly...

?- texclude(=((1,V)), [(1,1),(1,2),(3,2)], KVs).
KVs = [      (1,2),(3,2)],     V=1            ;
KVs = [(1,1),      (3,2)],               V=2  ;
KVs = [(1,1),(1,2),(3,2)], dif(V,1), dif(V,2).

Not quite! For our next tries we are going to use lambda expressions.

:- use_module(library(lambda)).

Let's query---once with texclude/3, once with tinclude/3, and once with tpartition/4:

?- texclude(  \ (K,_)^(K=1), [(1,1),(1,2),(3,2)], Fs).
Fs = [(3,2)].                                     % succeeds deterministically

?- tinclude(  \ (K,_)^(K=1), [(1,1),(1,2),(3,2)], Ts).
Ts = [(1,1),(1,2)].                               % succeeds deterministically

?- tpartition(\ (K,_)^(K=1), [(1,1),(1,2),(3,2)], Ts,Fs).
Ts = [(1,1),(1,2)], Fs = [(3,2)].                 % succeeds deterministically

Alright! Do we get the same solutions if the list items are bound after the texclude/3 call?

?- texclude(\ (K,_)^(K=1), [A,B,C], Fs), A = (1,1), B = (1,2), C = (3,2).
A = (1,1), B = (1,2), C = (3,2), Fs = [(3,2)] ;   % succeeds with choice point
false.

Yes! At last, consider the following quite general query:

?- texclude(\ (K,_)^(K=1), [A,B], Fs).
Fs = [   ], A = (  1,_A1), B = (  1,_B1)                         ;
Fs = [  B], A = (  1,_A1), B = (_B0,_B1),             dif(_B0,1) ;
Fs = [A  ], A = (_A0,_A1), B = (  1,_B1), dif(_A0,1)             ;
Fs = [A,B], A = (_A0,_A1), B = (_B0,_B1), dif(_A0,1), dif(_B0,1).

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Note that above goals restrict all list items to have the form (_,_). Thus the following query fails:

?- texclude(\ (K,_)^(K=1), [x,_], _).
false.