Prolog raises out of local stack for no good reason

I'm trying to implement Levenshtein distance in Prolog.

The implementation is pretty straightforward:

levenshtein(W1, W2, D) :-
    atom_length(W1, L1),
    atom_length(W2, L2),
    lev(W1, W2, L1, L2, D),
    !.

lev(_, _, L1, 0, D) :- D is L1, !.
lev(_, _, 0, L2, D) :- D is L2, !.
lev(W1, W2, L1, L2, D) :-
  lev(W1, W2, L1 - 1, L2, D1),
  lev(W1, W2, L1, L2 - 1, D2),
  lev(W1, W2, L1 - 1, L2 - 1, D3),
  charAt(W1, L1, C1),
  charAt(W2, L2, C2),
  ( C1 = C2 -> T is 0; T is 1 ),
  min(D1, D2, D3 + T, D).

% Returns the character at position N in the atom A
% The position is 1-based
% A: The atom
% N: The position at which to extract the character
% C: The character of A at position N
charAt(A, N, C) :- P is N - 1, sub_atom(A, P, 1, _, C).

% min(...): These rules compute the minimum of the given integer values
% I1, I2, I3: Integer values
% M:          The minimum over the values
min(I1, I2, M) :- integer(I1), integer(I2), ( I1 =< I2 -> M is I1; M is I2).
min(I1, I2, I3, M) :- min(I1, I2, A), min(I2, I3, B), min(A, B, M).

However, this code failures with this error:

?- levenshtein("poka", "po", X).
ERROR: Out of local stack

I'm using SWIPL implementation on Mac OS X Sierra.

There is a good reason for which your program does not work: your recursive calls lead into an infinite loop.

This is caused by those lines:

lev(W1, W2, L1 - 1, L2, D1),

lev(W1, W2, L1, L2 - 1, D2),

lev(W1, W2, L1 - 1, L2 - 1, D3),

min(D1, D2, D3 + T, D)

In Prolog things like L1 - 1 are expressions that do not get evaluated to numbers. Therefore your code will recursively call lev with the third argument as L1 -1, then L1 - 1 - 1, etc. which does not match your terminating rules.

To fix this you need to use temporary variables where you evaluate the result of e.g. L1 - 1.

This fixes it:

lev(W1, W2, L1, L2, D) :-
    L11 is L1 - 1,
    L22 is L2 - 1,
    lev(W1, W2, L11, L2, D1),
    lev(W1, W2, L1, L22, D2),
    lev(W1, W2, L11, L22, D3),
    charAt(W1, L1, C1),
    charAt(W2, L2, C2),
    ( C1 = C2 -> T is 0; T is 1 ),
    D4 is D3 + T,
    min(D1, D2, D4, D).

Now this does this:

?- levenshtein("poka","po",X).
X = 0.

Which is probably not the result you want, but at least it does not error. I will leave it to you to fix your predicate.