Combining Proof Plans with Partial Order Planning for Imperative Program Synthesis

Abstract

The structured programming literature provides methods and a wealth of heuristic knowledge for guiding the construction of provably correct imperative programs. We investigate these methods and heuristics as a basis for mechanizing program synthesis. Our approach combines proof planning with conventional partial order planning. Proof planning is an automated theorem proving technique which uses high-level proof plans to guide the search for proofs. Proof plans are structured in terms of proof methods, which encapsulate heuristics for guiding proof search. We demonstrate that proof planning provides a local perspective on the synthesis task. In particular, we show that proof methods can be extended to represent heuristics for guiding program construction. Partial order planning complements proof planning by providing a global perspective on the synthesis task. This means that it allows us to reason about the order in which program fragments are composed. Our hybrid approach has been implemented in a semi-automatic system called BERTHA. BERTHA supports partial correctness and has been tested on a wide range of non-trivial programming examples.

Poplar

“…Ireland and Stark [6] have designed a system that combines proof plans and partial order planning to generate small imperative programs. The heuristics and proof critics used here are adopted from the literature on Structured Programming, which describes principles that are to be used for manual goal-directed programming.…”

An Integrated Approach to High Integrity Software Verification

“…Middle-out reasoning is not restricted to proof patching. For instance, it has been used in guiding proof search in the context of program synthesis [36,41].…”

A correctness result for synthesizing plans with loops in stochastic domains

“…To that end, the automated synthesis of FSCs has received considerable attention in recent years, e.g., [16,7,26,24,11,27]. Of course, FSCs synthesis is closely related to program synthesis [16], and FSCs are frequently seen as program-like plans [17], and recent synthesis literature involves an exciting exchange of technical insights between the two fields [26]; representative examples include the use of program synthesis to infer high-level action types [25], and the use of partial order planning for imperative program synthesis [13].…”