LABEL ALGEBRAS AND EXCEPTION HANDLING

We propose a new algebraic framework for exception handling which is p owerful enough to cope with many exception handling features such as r ecovery, implicit propagation of exceptions, etc, This formalism treat s all the exceptional cases; on the contrary, we show that within all the already existing frameworks, the case of bounded data structures w ith certain recoveries of exceptional values remained unsolved. We jus tify the usefulness of ''labelling'' some terms in order to easily spe cify exceptions without inconsistency. Surprisingly, there are several cases where even if two terms have the same value, one of them is a s uitable instance of a variable in a formula while the other one is not . The main idea underlying our new framework of label algebras is that the semantics of algebraic specifications can be deeply improved when the satisfaction relation is defined via assignments with range in te rms instead of values. We give initiality results, which are useful fo r structured specifications, and a calculus for positive conditional l abel specifications, which is complete on ground formulas. Exception a lgebras and exception specifications are then defined as a direct appl ication of label algebras, The usual inconsistency problems raised by exception handling are avoided by the possibility of labelling terms. We also sketch out how far the application domain of label algebras is more general than exception handling.