Fine-grain Incremental Implementation of Algebraic Speciications Note: Partial Support Received from the European Communities under Esprit Project 2177 (generation of Interactive Programming Environments, Phase 2 -gipeii) and from the Netherlands Organization for Scientiic Research -nwo, Project Incremental Program Gen- Erators

In a previous paper we described how an incremental implementation can be derived from algebraic speciications belonging to the subclass of well-presented primitive recursive schemes. We combined term rewriting with techniques for storage and re-use from attribute grammars. Type check speciications typically belong to the class of primitive recursive schemes. The uniformity of algebraic speciications allows us to generalize our incremental algorithms to functions on values of auxiliary data types, without extending or modifying the speciication language. Thus, we can obtain ne-grain incremental implementations. This ne-grain incrementality can be derived from a subclass of algebraic speciications that we will call layered primitive recursive schemes. A ne-grain incremental implementation of a table data type can solve the problem caused by aggregated attribute values like symbol tables. (A change in an aggregated value causes a re-evaluation of all attributes that depend on this table, also when they do not depend on the modiied part.) When a lookup function in a table data type is declared to be incremental, a function cache for lookup is automatically generated. Direct deenition-use dependencies are established from entries in the function cache to attributes in the edit-tree that functionally depend on these entries. Moreover, after each modiication in the table the cache is updated incrementally.