We present a rule-based system for computer-aided circuit analysis. The set of rules, called EL, is written in a rule language called ARS. Rules are implemented by ARS as pattern-directed invocation demons monitoring an associative data base. Deductions are performed in an antecedent manner, giving EL's analysis a catch-as-catch-can flavour suggestive of the behavior of expert circuit analyzers. We call this style of circuit analysis propagation of constraints. The system threads deduced facts with justifications which mention the antecedent facts and the rule used. These justifications may be examined by the user to gain insight into the operation of the set of rules as they apply to a problem. The same justifications are used by the system to determine the currently active data-base context for reasoning in hypothetical situations. They are also used by the system in the analysis of failures to reduce the search space. This leads to effective control of combinatorial search which we call dependency-directed backtracking.