A Multi-level Approach to Program Synthesis

Abstract

Abstract. We present an approach to a coherent program synthesis system which integrates a variety of interactively controlled and automated techniques from theorem proving and algorithm design at different levels of abstraction. Besides providing an overall view we summarize the individual research results achieved in the course of this development.

A proof environment for the development of group communication systems

“…For this purpose we will integrate additional tools from the field of automated deduction, such as an extended typechecking algorithm [10], a proof procedure for first-order logic [15], and a proof planner for inductive proofs [2] into the logical programming environment. Furthermore, we are extending our formal database by verified theorems about major reconfiguration and verification steps, which we can then use as derived inference rules.…”

“…Thus by proving this theorem we remove the deductive burden from the reconfiguration process itself. 2 Reconfiguration theorems for composing fast-tracks, coupled with reconfiguration theorems for individual protocol layers, lead to a reconfiguration technique that scales up extremely well. We only have to apply the appropriate theorems step-by-step and receive the reconfigured code for the complete stack in linear time with respect to the number of layers that have to be passed by events.…”

Instantiation of existentially quantified variables in inductive specification proofs

“…For rippling and reverse rippling we use the rippling-distance strategy [11,4]. Each wave-front is mapped to a selected (goal)-sink.…”

Deleting Redundancy in Proof Reconstruction

“…As a result, the resolution principle [14] and the connection method [1,2], which both have led to efficient theorem provers for classical logic [22,9,3], have been extended to characterizations of logical validity in modal logics, intuitionistic logic, and fragments of linear logic [20,10,21,19,7]. These characterizations are the foundation of efficient and uniform proof search procedures for all these logics [12,13,7] which are used as inference engines in automatic program development systems [8,4] and other problem-oriented applications [5].…”

“…The second step selects a 0 a 5 a 8 with minimal subprefix a 0 and x q =a 5 We select a 0 a 3 with its minimal subprefix q = ε and x q = a 0 . Recall, that S 5 also contains all prefixes from Q 4 which were not contained in D 4 . Thus, after one step, we obtain Q 5 = ∅ and terminate with pref del (C, C …”