AbstractThe well-known term model constructions for equational abstract data type specifications provide a basis for elementary semantic reasoning, but their models lack the structure necessary for reasoning about relationships between the elements. Based upon the identities supplied in the data type's specification, we define a congruence relation which describes the relative ‘answer producing’ behaviour of words in the data type language, leading to a partially ordered qoutient algebra model. For those data types whose identity sets satisfy a condition implying the Church-Rosser (confluence) property, Wadsworth's approximation property holds: the meaning of a word in the model is the least upper bound of the meanings of its ‘syntactic approximants’. Thus the model provides fixed point properties while remaining fully abstract.