TY - GEN

T1 - Beyond the elementary representations of program invariants over algebraic data types

AU - Kostyukov, Yurii

AU - Mordvinov, Dmitry

AU - Fedyukovich, Grigory

N1 - Publisher Copyright: © 2021 ACM.

PY - 2021/6/18

Y1 - 2021/6/18

N2 - First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs). In this paper, we explore three different approaches to represent program invariants of ADT-manipulating programs: tree automata, and first-order formulas with or without size constraints. We compare the expressive power of these representations and prove the negative definability of both first-order representations using the pumping lemmas. We present an approach to automatically infer program invariants of ADT-manipulating programs by a reduction to a finite model finder. The implementation called RInGen has been evaluated against state-of-the-art invariant synthesizers and has been experimentally shown to be competitive. In particular, program invariants represented by automata are capable of expressing more complex properties of computation and their automatic construction is often less expensive.

AB - First-order logic is a natural way of expressing properties of computation. It is traditionally used in various program logics for expressing the correctness properties and certificates. Although such representations are expressive for some theories, they fail to express many interesting properties of algebraic data types (ADTs). In this paper, we explore three different approaches to represent program invariants of ADT-manipulating programs: tree automata, and first-order formulas with or without size constraints. We compare the expressive power of these representations and prove the negative definability of both first-order representations using the pumping lemmas. We present an approach to automatically infer program invariants of ADT-manipulating programs by a reduction to a finite model finder. The implementation called RInGen has been evaluated against state-of-the-art invariant synthesizers and has been experimentally shown to be competitive. In particular, program invariants represented by automata are capable of expressing more complex properties of computation and their automatic construction is often less expensive.

KW - algebraic data types

KW - finite models

KW - first-order definability

KW - invariant representation

KW - invariants

KW - tree automata

UR - http://www.scopus.com/inward/record.url?scp=85108910686&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/26a6e626-0765-3674-aecc-8ac2061bc9f2/

U2 - 10.1145/3453483.3454055

DO - 10.1145/3453483.3454055

M3 - Conference contribution

AN - SCOPUS:85108910686

T3 - Proceedings of the ACM SIGPLAN Conference on Programming Language Design and Implementation (PLDI)

SP - 451

EP - 465

BT - PLDI 2021 - Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

A2 - Freund, Stephen N.

A2 - Yahav, Eran

PB - Association for Computing Machinery

T2 - 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation, PLDI 2021

Y2 - 20 June 2021 through 25 June 2021

ER -