(=@=)/2

Availability:built-in

+Term1 =@= +Term2

True if Term1 is a variant of (or structurally equivalent to) Term2. Testing for a variant is weaker than equivalence (==/2), but stronger than unification (=/2). Two terms A and B are variants iff there exists a renaming of the variables in A that makes A equivalent (==) to B and vice versa.^{40Row 7
and 8 of this table may come as a surprise, but row 8 is satisfied
by (left-to-right) A -> C, B -> A and
(right-to-left) C -> A, A -> B. If the same
variable appears in different locations in the left and right term, the
variant relation can be broken by consistent binding of both terms.
E.g., after binding the first argument in row 8 to a value, both
terms are no longer variant.} Examples:

1 a =@= A false

2 A =@= B true

3 x(A,A) =@= x(B,C) false

4 x(A,A) =@= x(B,B) true

5 x(A,A) =@= x(A,B) false

6 x(A,B) =@= x(C,D) true

7 x(A,B) =@= x(B,A) true

8 x(A,B) =@= x(C,A) true

A term is always a variant of a copy of itself. Term copying takes place in, e.g., copy_term/2, findall/3 or proving a clause added with asserta/1. In the pure Prolog world (i.e., without attributed variables), =@=/2 behaves as if defined below. With attributed variables, variant of the attributes is tested rather than trying to satisfy the constraints.

A =@= B :-
        copy_term(A, Ac),
        copy_term(B, Bc),
        numbervars(Ac, 0, N),
        numbervars(Bc, 0, N),
        Ac == Bc.

The SWI-Prolog implementation is cycle-safe and can deal with variables that are shared between the left and right argument. Its performance is comparable to ==/2, both on success and (early) failure. ^{41The current implementation is
contributed by Kuniaki Mukai.}

This predicate is known by the name variant/2 in some other Prolog systems. Be aware of possible differences in semantics if the arguments contain attributed variables or share variables.^{42In many systems
variant is implemented using two calls to subsumes_term/2.}

1	`a =@= A`	false
2	`A =@= B`	true
3	`x(A,A) =@= x(B,C)`	false
4	`x(A,A) =@= x(B,B)`	true
5	`x(A,A) =@= x(A,B)`	false
6	`x(A,B) =@= x(C,D)`	true
7	`x(A,B) =@= x(B,A)`	true
8	`x(A,B) =@= x(C,A)`	true