Cyclic program synthesis

Abstract

We describe the first approach to automatically synthesizing heap-manipulating programs with auxiliary recursive procedures. Such procedures occur routinely in data structure transformations (e.g., flattening a tree into a list) or traversals of composite structures (e.g., n-ary trees). Our approach, dubbed cyclic program synthesis, enhances deductive program synthesis with a novel application of cyclic proofs. Specifically, we observe that the machinery used to form cycles in cyclic proofs can be reused to systematically and efficiently abduce recursive auxiliary procedures.We develop the theory of cyclic program synthesis by extending Synthetic Separation Logic (SSL), a logical framework for deductive synthesis of heap-manipulating programs from Separation Logic specifications. We implement our approach as a tool called Cypress, and showcase it by automatically synthesizing a number of programs manipulating linked data structures using recursive auxiliary procedures and mutual recursion, many of which were beyond the reach of existing program synthesis tools.CCS Concepts: • Software and its engineering → Automatic programming.

Certifying the synthesis of heap-manipulating programs

“…We begin with a brief primer on (Cyclic) Synthetic Separation Logic (SSL) (Itzhaky et al 2021)Ðthe newly extended logical formalism underlying the deductive synthesis algorithm implemented by the current version of the SuSLik tool (Polikarpova and Sergey 2019). In SSL, a singly-linked list is defined by the following inductive predicate, a standard for Separation Logic (Reynolds 2002):…”

“…Expressions include variables, literal constants, equality checks and logical connectives. Additional theory-specific expressions are allowed depending on the underlying theory used for checking entailment in derivations; the most up-to-date version of SuSLik by Itzhaky et al (2021) supports linear integer arithmetic and sets. The language allows pointer arithmetic in the form x + ι.…”

“…Indeed, an application order required for a valid derivation is exactly what a synthesis algorithm aims to discover. We refer the reader to the existing work on deductive program synthesis for a survey of existing techniques for finding valid derivations efficiently (Itzhaky et al 2021;Kneuss et al 2013).…”

“…The exact usage of cyclic proofs for synthesis of provably terminating recursive programs is orthogonal to this work, and we refer the reader to the paper byItzhaky et al (2021) for the details. That said, cardinality variables will play an important role for the translation of SL predicates to the logics of Iris and VST, as we will discuss in Sec.…”

CycleQ: An Efficient Basis for Cyclic Equational Reasoning

“…, it is the choice of "matching-function" or "cut" that determines exactly how the verification algorithm operates outside of the usual reasoning on the abstract domain. Recently, cyclic proofs have also been applied to program synthesis for pointer manipulating programs [25].…”