Equational specification of partial higher-order algebras

The theory of algebraic abstract types specified by positive conditional formulas formed of equations and a definedness predicate is outlined and extended to hierarchical types with "noustrict" operations, partial and even infinite objects. Its model theory is based on the concept of partial interpretations. Deduction rules are given, too. Models of types are studied where all explicit equations have solutions. The inclusion of nigher-order types, i.e., types comprising higher-order functions leads to an algebraic ("equational") specification of algebras including sorts with "infinite" objects and higher-order functions ("functionals").