These functions, agfeqns and agfseries, form the attribute grammar analogues to combstruct[gfeqns], and combstruct[gfseries].  For details on specifications, see combstruct and combstruct[specification].

These functions involve multivariate generating function equations which count the objects, as described in the specification spec, and properties of the structures, as defined in the attribute grammar, a_spec.

Each nonterminal in the grammar is associated with a generating function which is named with the name of the structure. For example, $A\left(z\,u\right)$ would be a generating function for $A$.  These two functions, agfeqns and agfseries, determine the equations in terms of other nonterminals and specify the series for the generating functions, respectively.

For example, in an unlabeled system with structure $A$ and attributes $f_1$ and $f_2$, the multivariate generating function is defined as $A\left(z\,q_1\,q_2\right)=\sum _A{z}^{\left|a\right|}{q}_1^{f_1\left(a\right)}{q}_2^{f_2\left(a\right)}$.

Any number of attributes is allowable, but no user-defined attribute can be marked by the parameter var.

If the objects are labeled, the exponential generating functions are produced. If the objects are unlabeled, ordinary generating functions are used.

The attribute, size, is used for the property pertaining to the number of atoms. It can be referenced in another attribute, but not redefined.

If no rule is defined for a given attribute structure pair, a default recursive rule is used. For example, $A=\mathrm{Union}\left(B\,C\,E\right)$ and the attribute $f$ imply a default attribute specification of $f\left(A\right)=\mathrm{Union}\left(f\left(B\right)\,f\left(C\right)\,f\left(E\right)\right)$.

Each attribute must be marked by a single, unique variable.

$\mathrm{with}\left(\mathrm{combstruct}\right)\:$

$\mathrm{tree}≔\left\{N=\mathrm{Atom}\,T=\mathrm{Union}\left(N\,\mathrm{Prod}\left(N\,T\,T\right)\right)\right\}\:$

$\mathrm{l\_tree}≔\left\{\mathrm{leaf}\left(T\right)=\mathrm{Union}\left(1\,\mathrm{Prod}\left(0\,\mathrm{leaf}\left(T\right)\,\mathrm{leaf}\left(T\right)\right)\right)\right\}\:$

$\mathrm{agfeqns}\left(\mathrm{tree}\,\mathrm{l\_tree}\,\mathrm{unlabeled}\,z\,\left[\left[u\,\mathrm{leaf}\right]\right]\right)$

$\left[N\left(z\,u\right)=zu\,T\left(z\,u\right)=zu+z{T\left(z\,u\right)}^2\right]$

$\mathrm{Order}≔10\:$$\mathrm{agfseries}\left(\mathrm{tree}\,\mathrm{l\_tree}\,\mathrm{unlabeled}\,z\,\left[\left[u\,\mathrm{leaf}\right]\right]\right)$

$table\left(\left[T\left(z\,u\right)=uz+u^2{z}^3+2u^3{z}^5+5u^4{z}^7+14u^5{z}^9+O\left(z^{11}\right)\,N\left(z\,u\right)=uz\right]\right)$

$\mathrm{pl\_tree}≔\left\{\mathrm{path}\left(T\right)=\mathrm{Union}\left(0\,\mathrm{Prod}\left(0\,\mathrm{size}\left(T\right)+\mathrm{path}\left(T\right)\,\mathrm{size}\left(T\right)+\mathrm{path}\left(T\right)\right)\right)\right\}\:$

$\mathrm{agfeqns}\left(\mathrm{tree}\,\mathrm{pl\_tree}\,\mathrm{unlabeled}\,z\,\left[\left[u\,\mathrm{path}\right]\right]\right)$

$\left[N\left(z\,u\right)=zu\,T\left(z\,u\right)=z+z{T\left(zu\,u\right)}^2\right]$