fib.pl

:- dynamic memo/2.
:- retractall( (memo(_, _) ).

fib(N, 1) :-
    N =< 2, !.
fib(N, Result) :-
    memo(N, Result), !.
fib(N, Result) :-
    N1 is N - 1,
    fib(N1, Result1),
    N2 is N - 2,
    fib(N2, Result2),
    Result is Result1 + Result2,
    assert(memo(N, Result)).

fib2.pl

% SWI-Prolog
:- use_module(library(clpfd)).
:- use_module(library(tabling)).
:- table fib/2.

fib(N, 1) :- N =< 2, !.
fib(N, Result) :-
    N1 #= N - 1,
    fib(N1, Result1),
    N2 #= N - 2,
    fib(N2, Result2),
    Result #= Result1 + Result2.

fib3.pl

% SWI-Prolog
% https://github.com/SWI-Prolog/swipl-devel/issues/226
:- use_module(library(clpfd)).

fib(N, 1) :- N #=< 2.
fib(N, Result) :-
    N #> 2,
    N1 #= N - 1,
    N2 #= N - 2,
    fib(N1, Result1),
    fib(N2, Result2),
    Result #= Result1 + Result2.

fib4.pl

% SWI-Prolog
% https://www.metalevel.at/prolog/memoization
:- use_module(library(clpfd)).
:- dynamic memo_/1.
:- retractall( (memo_(_)) ).

memo(Goal) :-
    (   memo_(Goal)
    ->  true
    ;   once(Goal),
        assertz(memo_(Goal))
    ).

fib(N, 1) :- N #=< 2.
fib(N, Result) :-
    N #> 2,
    N1 #= N - 1,
    N2 #= N - 2,
    memo(fib(N1, Result1)),
    memo(fib(N2, Result2)),
    Result #= Result1 + Result2.