### 4.6.1 Standard Order of Terms

Comparison and unification of arbitrary terms. Terms are ordered in the so-called “standard order” . This order is defined as follows:

`Variables`<`Numbers`<`Strings`<`Atoms`<`Compound Terms`- Variables are sorted by address.
`Numbers`are compared by value. Mixed rational/float are compared using cmpr/2.^{66Up to 9.1.4, comparison was done as float.}NaN is considered smaller than all numbers, including`-inf`

. If the comparison is equal, the float is considered the smaller value. If the Prolog flag iso is defined, all floating point numbers precede all rationals.`Strings`are compared alphabetically.`Atoms`are compared alphabetically.`Compound`terms are first checked on their arity, then on their functor name (alphabetically) and finally recursively on their arguments, leftmost argument first.

Although variables are ordered, there are some unexpected properties
one should keep in mind when relying on variable ordering. This applies
to the predicates below as to predicate such as sort/2
as well as libraries that reply on ordering such as library `library(assoc)`

and library
`library(ordsets)`

. Obviously, an established relation `A` `@<`

`B`
no longer holds if `A` is unified with e.g., a number. Also
unifying `A` with `B` invalidates the relation because
they become equivalent (==/2) after unification.

As stated above, variables are sorted by address, which implies that
they are sorted by‘age’, where‘older’variables
are ordered before‘newer’variables. If two variables are
unified their‘shared’age is the age of oldest variable. This
implies we can examine a list of sorted variables with‘newer’(fresh)
variables without invalidating the order. Attaching an *attribute*,
see section 8.1, turns an‘old’variable
into a‘new’one as illustrated below. Note that the first
always succeeds as the first argument of a term is always the oldest.
This only applies for the *first* attribute, i.e., further
manipulation of the attribute list does *not* change the‘age’.

?- T = f(A,B), A @< B. T = f(A, B). ?- T = f(A,B), put_attr(A, name, value), A @< B. false.

The above implies you *can* use e.g., an assoc (from library
`library(assoc)`

, implemented as an AVL tree) to maintain
information about a set of variables. You must be careful about what you
do with the attributes though. In many cases it is more robust to use
attributes to register information about variables.

Note that the standard order is not well defined on
*rational trees*, also known as *cyclic terms*. This
issue
was identified by Mats Carlsson, quoted below. See also
issue#1162
on GitHub.

Consider the termsAandBdefined by the equations[1] A = s(B,0). [2] B = s(A,1).

- Clearly,
AandBare not identical, so either`A @< B`

or`A @> B`

must hold.

- Assume
`A @< B`

. But then,`s(A,1) @> s(B,0)`

i.e.,`B @< A`

. Contradicton.

- Assume
`A @> B`

. But then,`s(A,1) @< s(B,0)`

i.e.,`B @< A`

. Contradicton.

- [ISO]
`@Term1`**==**`@Term2` - True if
`Term1`is equivalent to`Term2`. A variable is only identical to a sharing variable. - [ISO]
`@Term1`**\==**`@Term2` - Equivalent to

.`\+`

Term1 == Term2 - [ISO]
`@Term1`**@<**`@Term2` - True if
`Term1`is before`Term2`in the standard order of terms. - [ISO]
`@Term1`**@=<**`@Term2` - True if both terms are equal (==/2)
or
`Term1`is before`Term2`in the standard order of terms. - [ISO]
`@Term1`**@>**`@Term2` - True if
`Term1`is after`Term2`in the standard order of terms. - [ISO]
`@Term1`**@>=**`@Term2` - True if both terms are equal (==/2)
or
`Term1`is after`Term2`in the standard order of terms. - [ISO]
**compare**(`?Order, @Term1, @Term2`) - Determine or test the
`Order`between two terms in the standard order of terms.`Order`is one of

,`<`

or`>`

, with the obvious meaning.`=`