## 4.21 Analysing and Constructing Terms

[ISO]functor(?Term, ?Name, ?Arity)
  True when Term is a term with functor Name/Arity. If Term is a variable it is unified with a new term whose arguments are all different variables (such a term is called a skeleton). If Term is atomic, Arity will be unified with the integer 0, and Name will be unified with Term. Raises `instantiation_error()` if Term is unbound and Name/Arity is insufficiently instantiated.

  SWI-Prolog also supports terms with arity 0, as in `a()` (see section 5). Such terms must be processed using functor/4 or compound_name_arity/3. The predicate functor/3 and =../2 raise a `domain_error` when faced with these terms. Without this precaution a round trip of a term with arity 0 over functor/3 would create an atom.

functor(?Term, ?Name, ?Arity, ?Type)
  As functor/3, but designed to work with zero-arity terms (e.g., `a()`, see section 5). Type is one of `atom`, `compound`, `callable` or `atomic`. Type must be instantiated if Name is an atom and Arity is 0 (zero). In other cases Type may be a variable. This predicate is true if Term (either initially or after haveing been created from Name and Type) and Type are related as below

  - If Term is compound (including zero-arity compounds), Type must be `compound` or `callable`. If Type is unbound is is unified with `compound`.
  - If Term is an atom, Type must be `atom` or `callable`. If Type is unbound is is unified with `atom`.
  - Else Type is unified with `atomic`.

  This predicate provides a safe round trip for zero-arity compounds and atoms. It can also be used as a variant of functor/3 that only processes compound or callable terms. See also compound/1, callable/1 and compound_name_arity/3.

[ISO]arg(?Arg, +Term, ?Value)
  Term should be instantiated to a term, Arg to an integer between 1 and the arity of Term. Value is unified with the Arg-th argument of Term. Arg may also be unbound. In this case Value will be unified with the successive arguments of the term. On successful unification, Arg is unified with the argument number. Backtracking yields alternative solutions.109The instantiation pattern (-, +, ?) is an extension to‘standard' Prolog. Some systems provide genarg/3 that covers this pattern. The predicate arg/3 fails silently if Arg = 0 or Arg > arity and raises the exception `domain_error(not_less_than_zero, Arg)` if Arg < 0.
[ISO]?Term =.. ?List
  List is a list whose head is the functor of Term and the remaining arguments are the arguments of the term. Either side of the predicate may be a variable, but not both. This predicate is called‘Univ'.

      ?- foo(hello, X) =.. List.
      List = [foo, hello, X]

      ?- Term =.. [baz, foo(1)].
      Term = baz(foo(1))

  SWI-Prolog also supports terms with arity 0, as in `a()` (see section 5). Such terms must be processed using compound_name_arguments/3. This predicate raises a domain error as shown below. See also functor/3.

      ?- a() =.. L.
      ERROR: Domain error: `compound_non_zero_arity' expected, found `a()'

compound_name_arity(?Compound, ?Name, ?Arity)
  Version of functor/3 that only works for compound terms and can examine and create compound terms with zero arguments (e.g, `name()`). See also compound_name_arguments/3. See also functor/4.
compound_name_arguments(?Compound, ?Name, ?Arguments)
  Rationalized version of =../2 that can compose and decompose compound terms with zero arguments. See also compound_name_arity/3.
numbervars(+Term, +Start, -End)
  Unify the free variables in Term with a term `$VAR(N)`, where N is the number of the variable. Counting starts at Start. End is unified with the number that should be given to the next variable.bugOnly tagged integers are supported (see the Prolog flag max_tagged_integer). This suffices to count all variables that can appear in the largest term that can be represented, but does not support arbitrary large integer values for Start. On overflow, a `representation_error(tagged_integer)` exception is raised. The example below illustrates this. Note that the toplevel prints `'$VAR'(0)` as A due to the `numbervars(true)` option used to print answers.

      ?- Term = f(X,Y,X),
         numbervars(Term, 0, End),
         write_canonical(Term), nl.
      f('$VAR'(0),'$VAR'(1),'$VAR'(0))
      Term = f(A, B, A),
      X = A,
      Y = B,
      End = 2.

  See also the `numbervars` option to write_term/3 and numbervars/4.

numbervars(+Term, +Start, -End, +Options)
  As numbervars/3, providing the following options:
  functor_name(+Atom)
    Name of the functor to use instead of `$VAR`.
  attvar(+Action)
    What to do if an attributed variable is encountered. Options are `skip`, which causes numbervars/3 to ignore the attributed variable, `bind` which causes it to treat it as a normal variable and assign the next `'$VAR'`(N) term to it, or (default) `error` which raises a `type_error` exception.110This behaviour was decided after a long discussion between David Reitter, Richard O'Keefe, Bart Demoen and Tom Schrijvers.
  singletons(+Bool)
    If `true` (default `false`), numbervars/4 does singleton detection. Singleton variables are unified with `'$VAR'('_')`, causing them to be printed as `_` by write_term/2 using the numbervars option. This option is exploited by portray_clause/2 and write_canonical/2.bugCurrently this option is ignored for cyclic terms.
var_number(@Term, -VarNumber)
  True if Term is numbered by numbervars/3 and VarNumber is the number given to this variable. This predicate avoids the need for unification with `'$VAR'(X)` and opens the path for replacing this valid Prolog term by an internal representation that has no textual equivalent.
[ISO]term_variables(+Term, -List)
  Unify List with a list of variables, each sharing with a unique variable of Term.111This predicate used to be called free_variables/2 . The name term_variables/2 is more widely used. The old predicate is still available from the library `library(backcomp)`. The variables in List are ordered in order of appearance traversing Term depth-first and left-to-right. See also term_variables/3 and nonground/2. For example:

      ?- term_variables(a(X, b(Y, X), Z), L).
      L = [X, Y, Z].

[semidet]nonground(+Term, -Var)
  True when Var is a variable in Term. Fails if Term is ground (see ground/1). This predicate is intended for coroutining to trigger a wakeup if Term becomes ground, e.g., using when/2. The current implementation always returns the first variable in depth-first left-right search. Ideally it should return a random member of the set of variables (see term_variables/2) to realise logarithmic complexity for the ground trigger. Compatible with ECLiPSe and hProlog.
term_variables(+Term, -List, ?Tail)
  Difference list version of term_variables/2. That is, Tail is the tail of the variable list List.
term_singletons(+Term, -List)
  Unify List with a list of variables, each sharing with a variable that appears only once in Term.bugIn the current implementation Term must be acyclic. If not, a `representation_error` is raised. Note that, if a variable appears in a shared subterm, it is not considered singleton. Thus, A is not a singleton in the example below. See also the `singleton` option of numbervars/4.

      ?- S = a(A), term_singletons(t(S,S), L).
      L = [].

is_most_general_term(@Term)
  True if Term is a callable term where all arguments are non-sharing variables or Term is a list whose members are all non-sharing variables. This predicate is used to reason about call subsumption for tabling and is compatible with XSB. See also subsumes_term/2. Examples:

  > 1 | `is_most_general_term(1)` | false
  > 2 | `is_most_general_term(p)` | true
  > 3 | `is_most_general_term(p(_))` | true
  > 4 | `is_most_general_term(p(_,a))` | false
  > 5 | `is_most_general_term(p(X,X))` | false
  > 6 | `is_most_general_term([])` | true
  > 7 | `is_most_general_term([_|_])` | false
  > 8 | `is_most_general_term([_,_])` | true
  > 9 | `is_most_general_term([X,X])` | false

[ISO]copy_term(+In, -Out)
  Create a version of In with renamed (fresh) variables and unify it to Out. Attributed variables (see section 8.1) have their attributes copied. The implementation of copy_term/2 can deal with infinite trees (cyclic terms). As pure Prolog cannot distinguish a ground term from another ground term with exactly the same structure, ground sub-terms are shared between In and Out. Sharing ground terms does affect setarg/3. SWI-Prolog provides duplicate_term/2 to create a true copy of a term.
copy_term(+VarsIn, +In, -VarsOut, -Out)
  Similar to copy_term/2, but only rename the variables in VarsIn that appear in In.112This predicate is based on a similar predicate in s(CASP) by Joaquin Arias. Variables in In that do not appear in VarsIn are shared between In and Out. Sub terms that only contain such shared variables are shared as a whole between In and Out. VarsIn is often a list, but can be an arbitrary term. For example:

      ?- copy_term([X], q(X,Y), Vars, Term).
      Vars = [_A],
      Term = q(_A, Y).

  Note that if VarsIn and In do not share any variables, Out is equivalent to In and VarsOut is a copy (as copy_term/2) of VarsIn. If In does not contain any variables not in VarsIn the result is the same as `copy_term(VarsIn-In, VarsOut-Out`).

copy_term_nat(+VarsIn, +In, -VarsOut, -Out)
  As copy_term/4, using the attributed variable semantics of copy_term_nat/2. This implies that attributed variables that appear in VarsIn appear as renamed plain variables in VarsOut and Out. Attributed variables in In that do not appear in VarsIn are shared between In and Out.

### 4.21.1 Non-logical operations on terms

Prolog is not able to modify instantiated parts of a term. Lacking that capability makes the language much safer, but unfortunately there are problems that suffer severely in terms of time and/or memory usage. Always try hard to avoid the use of these primitives, but they can be a good alternative to using dynamic predicates. See also section 4.33, discussing the use of global variables.

setarg(+Arg, +Term, +Value)
  Extra-logical predicate. Assigns the Arg-th argument of the compound term Term with the given Value. The assignment is undone if backtracking brings the state back into a position before the setarg/3 call. See also nb_setarg/3.

  This predicate may be used for destructive assignment to terms, using them as an extra-logical storage bin. Always try hard to avoid the use of setarg/3 as it is not supported by many Prolog systems and one has to be very careful about unexpected copying as well as unexpected noncopying of terms. A good practice to improve somewhat on this situation is to make sure that terms whose arguments are subject to setarg/3 have one unused and unshared variable in addition to the used arguments. This variable avoids unwanted sharing in, e.g., copy_term/2, and causes the term to be considered as non-ground. An alternative is to use put_attr/3 to attach information to attributed variables (see section 8.1).

nb_setarg(+Arg, +Term, +Value)
  Assigns the Arg-th argument of the compound term Term with the given Value as setarg/3, but on backtracking the assignment is not reversed. If Value is not atomic, it is duplicated using duplicate_term/2. This predicate uses the same technique as nb_setval/2. We therefore refer to the description of nb_setval/2 for details on non-backtrackable assignment of terms. This predicate is compatible with GNU-Prolog `setarg(A,T,V,false)`, removing the type restriction on Value. See also nb_linkarg/3. Below is an example for counting the number of solutions of a goal. Note that this implementation is thread-safe, reentrant and capable of handling exceptions. Realising these features with a traditional implementation based on assert/retract or flag/3 is much more complicated.

      :- meta_predicate
              succeeds_n_times(0, -).

      succeeds_n_times(Goal, Times) :-
              Counter = counter(0),
              (   Goal,
                  arg(1, Counter, N0),
                  N is N0 + 1,
                  nb_setarg(1, Counter, N),
                  fail
              ;   arg(1, Counter, Times)
              ).

nb_linkarg(+Arg, +Term, +Value)
  As nb_setarg/3, but like nb_linkval/2 it does not duplicate Value. Use with extreme care and consult the documentation of nb_linkval/2 before use.
duplicate_term(+In, -Out)
  Version of copy_term/2 that also copies ground terms and therefore ensures that destructive modification using setarg/3 does not affect the copy. See also nb_setval/2, nb_linkval/2, nb_setarg/3 and nb_linkarg/3.
[semidet]same_term(@T1, @T2)
  True if T1 and T2 are equivalent and will remain equivalent, even if setarg/3 is used on either of them. This means T1 and T2 are the same variable, equivalent atomic data or a compound term allocated at the same address.