A Constructor-Based Approach for Positive/Negative-Conditional Equational Specifications

: We present a constructor-based approach for assigning appropriate semantics to algebraic specifications given by finite sets of positive/negative-conditional equations. Under the assumption of confluence of the reduction relation we define, the factor algebra of the ground term algebra modulo the congruence of this reduction relation is a minimal model which is (beyond that) the minimum of all models that do not identify more constructor ground terms than necessary. 1 Introduction and Overview We present a new uniform (i. e. not using "built-in"s or specification hierarchies) constructor-based approach for assigning appropriate semantics to algebraic specifications with finite sets of positive/negative-conditional ("p/n-conditional" for short) equations. A reduction relation is defined which allows us to generalize the fundamental results for positive-conditional reduction systems (cf. [5, 3]). Under the assumption of confluence, the factor algebra of the ground term algebra modulo ..