Arithmetic

Evaluating expressions

• Use is/2 to evaluate arithmetic on the right and unify the result on the left.

?- X is 1 + 2 * 3.
X = 7.

?- Y is -3.
Y = -3.

?- Z is (10 - 3) * 2.
Z = 14.

Notes

• is/2 is not symmetric: 3 is 1+2 succeeds, but 1+2 is 3 is a type error in standard Prolog. Always put the variable/result on the left.
• The right side must be fully evaluable (its variables already bound).
• Unary minus binds tightly; -3 and -(3) are equivalent. Prefer no space: - 3 may be tokenized as two tokens.

Integer vs floating division

• / is floating division; // is integer (floor) division; mod/2 is remainder.

?- A is 7 / 2.
A = 3.5.
?- B is 7 // 2.
B = 3.
?- R is 7 mod 2.
R = 1.

Comparing numbers

• Arithmetic comparison operators evaluate both sides before comparison:
• =:= equal, =\= not equal
• <, =<, >, >=

?- 7 =:= 3 + 4.
true.
?- 7 =\= 2 * 4.
true.
?- 2 < 3.
true.

Arithmetic vs unification

• =:=/2 compares numeric values, while =/2 unifies structures.

?- 1+2 =:= 3.
true.
?- 1+2 = 3.
false.  % left is a structure, not a number

CLP(FD) arithmetic

• For constraints over integers and domain reasoning, use CLP(FD) operators instead of is/2: #=, #\=, #<, #=<, #>, #>=.
• See CLP(FD) → Linear Constraints for propagation examples.