Types and Recursion Schemes for Higher-Order Program Verification

2009 ◽  
pp. 2-3 ◽  
Author(s):  
Naoki Kobayashi
Keyword(s):  
Program Verification ◽  
Higher Order

Higher-order multi-parameter tree transducers and recursion schemes for program verification

2010 ◽  
Vol 45 (1) ◽  
pp. 495-508 ◽  
Author(s):  
Naoki Kobayashi ◽  
Naoshi Tabuchi ◽  
Hiroshi Unno
Keyword(s):  
Program Verification ◽  
Higher Order ◽  
Tree Transducers

scholarly journals Connecting Higher-Order Separation Logic to a First-Order Outside World

2020 ◽  
pp. 428-455 ◽  
Author(s):  
William Mansky ◽  
Wolf Honoré ◽  
Andrew W. Appel
Keyword(s):  
Program Verification ◽  
Higher Order ◽  
Separation Logic ◽  
C Programs ◽  
First Order ◽  
System Calls ◽  
Correctness Of Programs ◽  
Verified Software ◽  
Order State ◽  
Order Separation

AbstractSeparation logic is a useful tool for proving the correctness of programs that manipulate memory, especially when the model of memory includes higher-order state: Step-indexing, predicates in the heap, and higher-order ghost state have been used to reason about function pointers, data structure invariants, and complex concurrency patterns. On the other hand, the behavior of system features (e.g., operating systems) and the external world (e.g., communication between components) is usually specified using first-order formalisms. In principle, the soundness theorem of a separation logic is its interface with first-order theorems, but the soundness theorem may implicitly make assumptions about how other components are specified, limiting its use. In this paper, we show how to extend the higher-order separation logic of the Verified Software Toolchain to interface with a first-order verified operating system, in this case CertiKOS, that mediates its interaction with the outside world. The resulting system allows us to prove the correctness of C programs in separation logic based on the semantics of system calls implemented in CertiKOS. It also demonstrates that the combination of interaction trees + CompCert memories serves well as a lingua franca to interface and compose two quite different styles of program verification.

scholarly journals A relational logic for higher-order programs

2019 ◽  
Vol 29 ◽  
Author(s):  
ALEJANDRO AGUIRRE ◽  
GILLES BARTHE ◽  
MARCO GABOARDI ◽  
DEEPAK GARG ◽  
PIERRE-YVES STRUB
Keyword(s):  
Program Verification ◽  
Type Systems ◽  
Higher Order ◽  
Order Logic ◽  
Relative Cost ◽  
Higher Order Logic ◽  
Relational Properties ◽  
Refinement Types ◽  
Transitivity Rule ◽  
Relational Logic

AbstractRelational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for reasoning about a broad range of properties, including equivalence and refinement, and specialized notions such as continuity, information flow security, or relative cost. In a higher-order setting, relational program verification can be achieved using relational refinement type systems, a form of refinement types where assertions have a relational interpretation. Relational refinement type systems excel at relating structurally equivalent terms but provide limited support for relating terms with very different structures. We present a logic, called relational higher-order logic (RHOL), for proving relational properties of a simply typed λ-calculus with inductive types and recursive definitions. RHOL retains the type-directed flavor of relational refinement type systems but achieves greater expressivity through rules which simultaneously reason about the two terms as well as rules which only contemplate one of the two terms. We show that RHOL has strong foundations, by proving an equivalence with higher-order logic, and leverage this equivalence to derive key meta-theoretical properties: subject reduction, admissibility of a transitivity rule, and set-theoretical soundness. Moreover, we define sound embeddings for several existing relational type systems such as relational refinement types and type systems for dependency analysis and relative cost, and we verify examples that were out of reach of prior work.

scholarly journals Automated techniques for higher-order program verification

2013 ◽  
pp. 157
Author(s):  
Naoki KOBAYASHI ◽  
Luke ONG ◽  
David Van HORN
Keyword(s):  
Program Verification ◽  
Higher Order

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Sign in / Sign up

Export Citation Format

Share Document