prolog-arithmetic

The Prolog is/2 operator evaluates the arithmetic expression on its right-hand side and unifies the numerical result with the left-hand side. This requires the right-hand side to be fully instantiated with ground numeric values before evaluation can proceed.

CLP(FD) in Prolog is a constraint solving technique that enables bidirectional reasoning over integers. It propagates arithmetic constraints across variables without requiring them to be fully instantiated, supporting logical and numerical problem solving.

Peano arithmetic in Prolog defines natural numbers using symbolic terms like zero and successor representations. It illustrates purely logical definitions of numbers, demonstrating their practical limits and differences from standard numeric evaluation.

Prolog arithmetic comparisons evaluate both sides numerically before checking relational operators, whereas is/2 evaluates the right-hand side and unifies the result with a left-hand side variable. Comparisons do not require unification output.

Prolog arithmetic evaluation fails with an instantiation error when using is/2 with ungrounded variables on the right-hand side. The operator requires all numeric arguments to be fully instantiated before it can compute the result and unify.

Yes, CLP(FD) constraints support bidirectional arithmetic reasoning in Prolog by propagating constraints across variables. This allows the system to infer variable values and narrow domains without needing fully ground numeric inputs beforehand.