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Can someone explain the difference between the == and the = operator in Prolog? I know that X = Y means X unifies with Y and is true if X already unifies with Y or can be made to, but I don't understand how this differs from ==.
Follow up: That (see Accepted Answer) makes sense. One more question though, is there ever a situation where X \= Y is true and X \== Y is false (or vice-versa)? That is, does X \= Y test if they cannot be unified or if they are not currently unified?
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The conjunct X=Y first unifies the variables X and Y . Thus when the second conjunct X==Y is evaluated, the two variables are exactly the same Prolog object, and the second conjunct succeeds as well. It should now be clear that = and == are very different, nonetheless there is an important relation between them.
Syntax of Prolog not equal Value1 =\= Value2. Explanation: The “=\=” sign is used to determine not equal values. This operator is mostly used for numerical values and arithmetic operations.
Because of the problems of negation-as-failure, negation in Prolog is represented in modern Prolog interpreters using the symbol \+ , which is supposed to be a mnemonic for not provable with the \ standing for not and the + for provable.
Inequality Operator (=\=) If E1 and E2 do not evaluate to the same value, arithmetic expression E1 =\= E2 succeeds. For example: ?- 24 =\= 17+4. yes.
The = "operator" in Prolog is actually a predicate (with infix notation) =/2 that succeeds when the two terms are unified. Thus X = 2 or 2 = X amount to the same thing, a goal to unify X with 2.
The == "operator" differs in that it succeeds only if the two terms are already identical without further unification. Thus X == 2 is true only if the variable X had previously been assigned the value 2.
Added: It's interesting to work through what happens when "not" gets mixed into these goals, per the comment by JohnS below. See the nice set of examples in the Amzi! Prolog documentation.
\= means the two terms cannot be unified, i.e. that unification fails. As with all applications of negation as failure, "not unified" does not (and cannot) result in any unification between terms.
\== means the two terms are not identical. Here also no unification takes place even if this succeeds.
Finally think about what not(not(X = Y)) will do. The inner goal succeeds if X and Y (which can be arbitrary terms) can be unified, and so will the double negation of that. However wrapping the inner goal inside the double negation produces a goal that succeeds if the two terms can be unified but without unifying those terms.
It is left as an exercise for the reader to contemplate whether not(not(X == Y)) has any similar utility.
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