Starting from the analysis of which features are required by an algebraic formalism to describe at least the more common data types used in imperative and functional programming, a framework is proposed, collecting many techniques and ideas from the algebraic community, with the capability for an immediate representation of partiality and error-recovery. This formalism, of so called lazy algebras, inherits mainly from two parents: partial and label algebras; from the former especially on a technical side and from the later from a philosophical point of view. But, as all children, it has its own individuality and in particular an original mechanism to represent lazy evaluation in an algebraic framework has been introduced.