NDLI: Verifying higher-order functional programs with pattern-matching algebraic data types

Content Provider	ACM Digital Library
Author	Ramsay, Steven J. Ong, C.-H. Luke
Abstract	Type-based model checking algorithms for higher-order recursion schemes have recently emerged as a promising approach to the verification of functional programs. We introduce pattern-matching recursion schemes (PMRS) as an accurate model of computation for functional programs that manipulate algebraic data-types. PMRS are a natural extension of higher-order recursion schemes that incorporate pattern-matching in the defining rules. This paper is concerned with the following (undecidable) verification problem: given a correctness property φ, a functional program ℘ (qua PMRS) and a regular input set ℑ, does every term that is reachable from ℑ under rewriting by ℘ satisfy φ? To solve the PMRS verification problem, we present a sound semi-algorithm which is based on model-checking and counterexample guided abstraction refinement. Given a no-instance of the verification problem, the method is guaranteed to terminate. From an order-n PMRS and an input set generated by a regular tree grammar, our method constructs an order-n weak PMRS which over-approximates only the first-order pattern-matching behaviour, whilst remaining completely faithful to the higher-order control flow. Using a variation of Kobayashi's type-based approach, we show that the (trivial automaton) model-checking problem for weak PMRS is decidable. When a violation of the property is detected in the abstraction which does not correspond to a violation in the model, the abstraction is automatically refined by `unfolding' the pattern-matching rules in the program to give successively more and more accurate weak PMRS models.
Starting Page	587
Ending Page	598
Page Count	12
File Format	PDF MP4
ISSN	03621340 15581160
DOI	10.1145/1925844.1926453
Journal	ACM SIGPLAN Notices (SIGP)
Volume Number	46
Issue Number	1
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1983-05-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Higher-order programs Model checking Verification
Content Type	Audio Text
Resource Type	Article
Subject	Computer Graphics and Computer-Aided Design Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Verifying higher-order functional programs with pattern-matching algebraic data types

Automating relatively complete verification of higher-order functional programs

Types and higher-order recursion schemes for verification of higher-order programs

Automatically disproving fair termination of higher-order functional programs

A type-directed abstraction refinement approach to higher-order model checking

A traversal-based algorithm for higher-order model checking

Pattern minimization problems over recursive data types

Unboundedness and downward closures of higher-order pushdown automata

Stateless model checking with data-race preemption points

Verifying higher-order functional programs with pattern-matching algebraic data types

Similar Documents

Verifying higher-order functional programs with pattern-matching algebraic data types

Automating relatively complete verification of higher-order functional programs

Types and higher-order recursion schemes for verification of higher-order programs

Automatically disproving fair termination of higher-order functional programs

A type-directed abstraction refinement approach to higher-order model checking

A traversal-based algorithm for higher-order model checking

Pattern minimization problems over recursive data types

Unboundedness and downward closures of higher-order pushdown automata

Stateless model checking with data-race preemption points

Verifying higher-order functional programs with pattern-matching algebraic data types