## 2.16 Rational trees (cyclic terms)

SWI-Prolog supports rational trees, also known as cyclic terms.‘Supports' is so defined that most relevant built-in predicates terminate when faced with rational trees. Almost all SWI-Prolog's built-in term manipulation predicates process terms in a time that is linear to the amount of memory used to represent the term on the stack. The following set of predicates safely handles rational trees: =../2, ==/2, =@=/2, =/2, @</2, @=</2, @>=/2, @>/2, \==/2, \=@=/2, \=/2, acyclic_term/1, bagof/3, compare/3, copy_term/2, cyclic_term/1, dif/2, duplicate_term/2, findall/3, ground/1, term_hash/2, numbervars/3, numbervars/4, recorda/3, recordz/3, setof/3, subsumes_term/2, term_variables/2, throw/1, unify_with_occurs_check/2, unifiable/3, when/2, write/1 (and related predicates) .

In addition, some built-ins recognise rational trees and raise an appropriate exception. Arithmetic evaluation belongs to this group. The compiler (asserta/1, etc.) also raises an exception. Future versions may support rational trees. Predicates that could provide meaningful processing of rational trees raise a `representation_error`. Predicates for which rational trees have no meaningful interpretation raise a `type_error`. For example:

    1 ?- A = f(A), asserta(a(A)).
    ERROR: asserta/1: Cannot represent due to `cyclic_term'
    2 ?- A = 1+A, B is A.
    ERROR: is/2: Type error: `expression' expected, found
                 `@(S_1,[S_1=1+S_1])' (cyclic term)