A computable function on the natural numbers is typically specified by a finite expression using defined function symbols and operators; a syntactic expression F specifying a function \(f:\mathrm{{I}}\!\mathrm{{N}}\rightarrow \mathrm{{I}}\!\mathrm{{N}}\) can be considered as a finite representation of the infinite set \(D(f) :\{f(n) \mid n \in \mathrm{{I}}\!\mathrm{{N}}\}\) . We can say that F is a “schema” for the function f. In a similar way there are schemata for infinite sets of terms and infinite sets of formulas. In this chapter we define such schemata based on primitive recursion and investigate their properties. These schemata will be the backbone for proof schemata and their application in inductive proof analysis.