A general-purpose reusable algebraic-based composition algorithm for composing mappings between data schemas. The algorithm handles more expressive mappings, makes a best-effort to eliminate symbols when a perfect answer cannot be obtained, includes new heuristics, and is extensible. A relational algebraic language is provided wherein each mapping is expressed as a set of constraints, and each constraint is either a containment or equality of two or more relational algebraic expressions. The composition mechanism exploits monotonicity properties of algebraic operators in operator arguments, handles NULLs and bag semantics, operates to allow composition to produce a partial result when a complete result is not possible, facilitates symbols elimination one symbol at a time using left composition, for example, as a way of isolating the symbols, supports making a best-effort to eliminate as many symbols as possible from an intermediate schema, and handles unknown or partially known operators via delayed handling.