On Classes of Program Schemata

We define the following classes of program schemata: ${\text{P}} = $ class of schemes using a finite number of simple variables; ${\text{P}}_{\text{A}} = $ class of schemes using simple and subscripted variables (arrays); ${\text{P}}_{{\text{Ae}}} = $ class of schemes in ${\text{P}}_{\text{A}} = $, with the addition of an equality test on subscript values; ${\text{P}}_{\text{R}} = $ class of schemes allowing recursive functions; ${\text{P}}_{\text{L}} = $ class of schemes allowing labels as values; ${\text{P}}_{\text{M}} = $ class of schemes allowing a finite number of special markers as values; ${\text{P}}_{{\text{pds}}} = $ class of schemes using pushdown stores. With these, we can also discuss, for example, ${\text{P}}_{{\text{AM}}} $, the class of schemes allowing arrays, and special markers as values ; and ${\text{P}}_{{\text{AL}}} $, the class of schemes allowing arrays, and labels as values.We argue that ${\text{P}}_{\text{A}}$, ${\text{P}}_{\text{R}}$, and ${\text{P}}_{\text{L}}$ faithfully repres...