Schema-Guided Synthesis of Imperative Programs by Constraint Solving

Colón, Michael A.

doi:10.1007/11506676_11

Cited by 13 publications

(8 citation statements)

References 18 publications

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“…In this paper, inspired by recent work on program synthesis [21], we also consider the synthesis problem. Our work can be considered a more formal approach to Colón's method [6] that uses non-linear constraint solving to instantiate program schemata (parameterized programs augmented with constraints). Our approach relies on algebraic methods instead of heuristics.…”

Section: Related Workmentioning

confidence: 99%

Synthesis for Polynomial Lasso Programs

Leike

Tiwari

2014

Lecture Notes in Computer Science

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1 This is an error-corrected version of the original thesis, updated last on July 11, 2018. AbstractThe scope of this work is the constraint-based synthesis of termination arguments for the restricted class of programs called linear lasso programs. A termination argument consists of a ranking function as well as a set of supporting invariants.We extend existing methods in several ways. First, we use Motzkin's Transposition Theorem instead of Farkas' Lemma. This allows us to consider linear lasso programs that can additionally contain strict inequalities. Existing methods are restricted to non-strict inequalities and equalities.Second, we consider several kinds of ranking functions: affine-linear, piecewise and lexicographic ranking functions. Moreover, we present a novel kind of ranking function called multiphase ranking function which proceeds through a fixed number of phases such that for each phase, there is an affine-linear ranking function. As an abstraction to the synthesis of specific ranking functions, we introduce the notion ranking function template. This enables us to handle all ranking functions in a unified way.Our method relies on non-linear algebraic constraint solving as a subroutine which is known to scale poorly to large problems. As a mitigation we formalize an assessment of the difficulty of our constraints and present an argument why they are of an easier kind than general non-linear constraints.We prove our method to be complete: if there is a termination argument of the form specified by the given ranking function template with a fixed number of affine-linear supporting invariants, then our method will find a termination argument.To our knowledge, the approach we propose is the most powerful technique of synthesis-based discovery of termination arguments for linear lasso programs and encompasses and enhances several methods having been proposed thus far [4,18,27].

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Section: Related Workmentioning

confidence: 99%

Synthesis for Polynomial Lasso Programs

Leike

Tiwari

2014

Lecture Notes in Computer Science

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“…Because techniques for efficient invariant inference were unavailable in the past, synthesis was considered intractable [12]. Recently, scheme-guided synthesis [17] has been proposed but specialized to the arithmetic domain [5]. Categorizations of approaches as constructive/deductive synthesis, schema-guided synthesis and inductive synthesis are presented in a recent survey [1].…”

Section: Related Workmentioning

confidence: 99%

From program verification to program synthesis

Srivastava

Gulwani

Foster

2010

Proceedings of the 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

200

119

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This paper describes a novel technique for the synthesis of imperative programs. Automated program synthesis has the potential to make programming and the design of systems easier by allowing programs to be specified at a higher-level than executable code. In our approach, which we call proof-theoretic synthesis, the user provides an input-output functional specification, a description of the atomic operations in the programming language, and a specification of the synthesized program's looping structure, allowed stack space, and bound on usage of certain operations. Our technique synthesizes a program, if there exists one, that meets the inputoutput specification and uses only the given resources.The insight behind our approach is to interpret program synthesis as generalized program verification, which allows us to bring verification tools and techniques to program synthesis. Our synthesis algorithm works by creating a program with unknown statements, guards, inductive invariants, and ranking functions. It then generates constraints that relate the unknowns and enforces three kinds of requirements: partial correctness, loop termination, and well-formedness conditions on program guards. We formalize the requirements that program verification tools must meet to solve these constraint and use tools from prior work as our synthesizers.We demonstrate the feasibility of the proposed approach by synthesizing programs in three different domains: arithmetic, sorting, and dynamic programming. Using verification tools that we previously built in the VS 3 project we are able to synthesize programs for complicated arithmetic algorithms including Strassen's matrix multiplication and Bresenham's line drawing; several sorting algorithms; and several dynamic programming algorithms. For these programs, the median time for synthesis is 14 seconds, and the ratio of synthesis to verification time ranges between 1× to 92× (with an median of 7×), illustrating the potential of the approach.

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“…These works differ in the kind of program synthesized and the techniques used. The only work that uses a constraint-based approach is that of Colón, who synthesizes imperative programs computing polynomial functions from partially specified programs and their invariants [5].…”

Section: Related Workmentioning

confidence: 99%

Synthesizing switching logic using constraint solving

Taly

Gulwani

Tiwari

2010

Int J Softw Tools Technol Transfer

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Abstract.A new approach based on constraint solving techniques was recently proposed for verification of hybrid systems. This approach works by searching for inductive invariants of a given form. In this paper, we extend that work to automatic synthesis of safe hybrid systems. Starting with a multi-modal dynamical system and a safety property, we present a sound technique for synthesizing a switching logic for changing modes so as to preserve the safety property. By construction, the synthesized hybrid system is well-formed and is guaranteed safe. Our approach is based on synthesizing a controlled invariant that is sufficient to prove safety. The generation of the controlled invariant is cast as a constraint solving problem. When the system, the safety property, and the controlled invariant are all expressed only using polynomials, the generated constraint is an ∃∀ formula in the theory of reals, which we solve using SMT solvers. The generated controlled invariant is then used to arrive at the maximally liberal switching logic.

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Schema-Guided Synthesis of Imperative Programs by Constraint Solving

Cited by 13 publications

References 18 publications

Synthesis for Polynomial Lasso Programs

Synthesis for Polynomial Lasso Programs

From program verification to program synthesis

Synthesizing switching logic using constraint solving

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