Cited By
View all- Joosten Svan Gastel BSchmaltz J(2013)A Macro for Reusing Abstract Functions and TheoremsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.114.3114(29-41)Online publication date: 26-Apr-2013
Making induction manifest in modular ACL2
Pages 105 - 116
Abstract
ACL2, a Common Lisp-based language for programming and theorem proving, has enjoyed industrial success despite lacking modern language features such as a module system. In previous work, we equipped ACL2 with modules, interfaces, and explicit linking and measured our system with a series of experiments. One experiment revealed a serious lack of expressivity; the interfaces cannot describe the induction schemes necessary to reason about exported functions with nontrivial patterns of recursion.
In this paper we revise our language, Modular ACL2, to overcome this weakness. The first novelty is the inclusion of manifest function definitions in interfaces from which ACL2 can infer induction schemes. The second novelty consists of the first proofs of soundness and expressivity for Modular ACL2; we also reaffirm the usefulness of our system with updated benchmarks.
References
[1]
Chrzaszcz, J. Implementing modules in the Coq system. In Proc. 16th International Conference on Theorem Proving in Higher Order Logics, p. 270--286. Springer, 2003.
[2]
Courant, J. MC2: a module calculus for pure type systems. J. Functional Programming, 17(3):287--352, 2007.
[3]
Culpepper, R., S. Tobin-Hochstadt and M. Flatt. Advanced macrology and the implementation of Typed Scheme. In Proc. 8th Workshop on Scheme and Functional Programming, p. 1--14. ACM Press, 2007.
[4]
Dreyer, D. and A. Rossberg. Mixin' up the ML module system. In Proc. 13th ACM SIGPLAN International Conference on Functional Programming, p. 307--320. ACM Press, 2008.
[5]
Eastlund, C. and M. Felleisen. Toward a practical module system for ACL2. In Proc. 11th International Symposium on Practical Aspects of Declarative Languages, p. 46--60. Springer, 2009.
[6]
Farmer, W.M., J.D. Guttman and F.J. Thayer. IMPS: An interactive mathematical proof system. J. Automated Reasoning, 11(2):213--248, 1993.
[7]
Findler, R.B., J. Clements, C. Flanagan, M. Flatt, S. Krishnamurthi, P. Steckler and M. Felleisen. DrScheme: A programming environment for Scheme. J. Functional Programming, 12(2):159--182, 2002.
[8]
Flatt, M. Composable and compilable macros: You want it when? In Proc. 7th ACM SIGPLAN International Conference on Functional Programming, p. 72--83. ACM Press, 2002.
[9]
Flatt, M. and M. Felleisen. Units: cool modules for HOT languages. In Proc. ACM SIGPLAN Conference on Programming Language Design and Implementation, p. 236--248. ACM Press, 1998.
[10]
Harper, R. and M. Lillibridge. A type-theoretic approach to higher-order modules with sharing. In Proc. 21st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, p. 123--137. ACM Press, 1994.
[11]
Kammüller, F., M. Wenzel and L.C. Paulson. Locales: a sectioning concept for Isabelle. In Proc. 12th International Conference on Theorem Proving in Higher Order Logics, p. 149--166. Springer, 1999.
[12]
Kaufmann, M., P. Manolios and J.S. Moore. Computer-Aided Reasoning: ACL2 Case Studies. Kluwer Academic Publishers, 2000.
[13]
Kaufmann, M., P. Manolios and J.S. Moore. Computer-Aided Reasoning: An Approach. Kluwer Academic Publishers, 2000.
[14]
Kaufmann, M. and J.S. Moore. A precise description of the ACL2 logic. Technical report, University of Texas at Austin, 1998.
[15]
Kaufmann, M. and J.S. Moore. Structured theory development for a mechanized logic. J. Automated Reasoning, 26(2):161--203, 2001.
[16]
Leroy, X. Manifest types, modules, and separate compilation. In Proc. 21st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, p. 109--122. ACM Press, 1994.
[17]
Martín-Mateos, F.J., J.A. Alonso, M.J. Hidalgo and J.L. Ruiz-Reina. A generic instantiation tool and a case study: a generic multiset theory. In Proc. 3rd International Workshop on the ACL2 Theorem Prover and its Applications, p. 188--201. ACM Press, 2002.
[18]
Milner, R., M. Tofte and R. Harper. The Definition of Standard ML. MIT Press, 1990.
[19]
Owens, S. and M. Flatt. From structures and functors to modules and units. In Proc. 11th ACM SIGPLAN International Conference on Functional Programming, p. 87--98. ACM Press, 2006.
[20]
Padget, J. et. al. Desiderata for the standardisation of LISP. In Proc. 1986 ACM Conference on LISP and Functional Programming, p. 54--66. ACM Press, 1986.
[21]
Page, R. Engineering software correctness. J. Functional Programming, 17(6):675--686, 2007.
[22]
Page, R., C. Eastlund and M. Felleisen. Functional programming and theorem proving for undergraduates: a progress report. In Proc. 2008 Workshop on Functional and Declarative Programming in Education, p. 21--30. ACM Press, 2008.
[23]
Sannella, D. Formal program development in Extended ML for the working programmer. In Proc. 3rd BCS/FACS Workshop on Refinement, p. 99--130. Springer, 1991.
[24]
Steele Jr., G.L. Common Lisp--The Language. Digital Press, 1984.
[25]
The Coq Development Team. The Coq Proof Assistant Reference Manual, 2009. http://coq.inria.fr/coq/distrib/current/refman/.
[26]
Vaillancourt, D., R. Page and M. Felleisen. ACL2 in DrScheme. In Proc. 6th International Workshop on the ACL2 Theorem Prover and its Applications, p. 107--116. ACM Press, 2006.
[27]
Wirth, N. Programming in Modula-2. Springer, 1983.
Index Terms
- Making induction manifest in modular ACL2
Recommendations
An embedding of the ACL2 logic in HOL
ACL2 '06: Proceedings of the sixth international workshop on the ACL2 theorem prover and its applicationsWe describe an embedding of the ACL2 logic into higher-order logic. An implementation of this embedding allows ACL2 to be used as an oracle for higher-order logic provers.
A Formalization of Powerlist Algebra in ACL2
In Misra (ACM Trans Program Lang Syst 16(6):1737---1767, 1994), Misra introduced the powerlist data structure, which is well suited to express recursive, data-parallel algorithms. Moreover, Misra and other researchers have shown how powerlists can be ...
Soundness of the simply typed lambda calculus in ACL2
ACL2 '06: Proceedings of the sixth international workshop on the ACL2 theorem prover and its applicationsTo make it practical to mechanize proofs in programming language metatheory, several capabilities are required of the theorem proving framework. One must be able to represent and efficiently reason about complex recursively-defined expressions, define ...
Comments
Information & Contributors
Information
Published In
September 2009
324 pages
ISBN:9781605585680
DOI:10.1145/1599410
- General Chair:
- António Porto,
- Program Chair:
- Francisco J. López-Fraguas
Copyright © 2009 ACM.
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]
Sponsors
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 07 September 2009
Check for updates
Author Tags
Qualifiers
- Research-article
Conference
Acceptance Rates
Overall Acceptance Rate 230 of 486 submissions, 47%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 78Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 15 Oct 2024
Other Metrics
Citations
Cited By
View all- Joosten Svan Gastel BSchmaltz J(2013)A Macro for Reusing Abstract Functions and TheoremsElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.114.3114(29-41)Online publication date: 26-Apr-2013
View Options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in