Reversible numerical calculations in Prolog

Question

While reading SICP I came across logic programming chapter 4.4. Then I started looking into the Prolog programming language and tried to understand some simple assignments i

Answer 1

is/2 is very low-level and limited. As you correctly observe, it cannot be used in all directions and is therefore not a true relation.

For reversible arithmetic, use your Prolog system's constraint solvers.

For example, SWI-Prolog's CLP(FD) manual contains the following definition of n_factorial/2:

:- use_module(library(clpfd)).

n_factorial(0, 1).
n_factorial(N, F) :- N #> 0, N1 #= N - 1, F #= N * F1, n_factorial(N1, F1).

The following example queries show that it can be used in all directions:

?- n_factorial(47, F).
F = 258623241511168180642964355153611979969197632389120000000000 ;
false.

?- n_factorial(N, 1).
N = 0 ;
N = 1 ;
false.

?- n_factorial(N, 3).
false.

Of course, this definition still relies on unification, and you can therefore not plug in arbitrary integer expressions. A term like 2-2 (which is -(2,2) in prefix notation) does not unfiy with 0. But you can easily allow this if you rewrite this to:

:- use_module(library(clpfd)).

n_factorial(N, F) :- N #= 0, F #= 1.
n_factorial(N, F) :- N #> 0, N1 #= N - 1, F #= N * F1, n_factorial(N1, F1).

Example query and its result:

?- n_factorial(2-2, -4+5).
true .