research-article

SASyLF: an educational proof assistant for language theory

Authors:

Jonathan Aldrich,

Robert J. Simmons,

Key ShinAuthors Info & Claims

FDPE '08: Proceedings of the 2008 international workshop on Functional and declarative programming in education

Pages 31 - 40

https://doi.org/10.1145/1411260.1411266

Published: 21 September 2008 Publication History

Abstract

Teaching and learning formal programming language theory is hard, in part because it's easy to make mistakes and hard to find them. Proof assistants can help check proofs, but their learning curve is too steep to use in most classes, and is a barrier to researchers too.

In this paper we present SASyLF, an LF-based proof assistant specialized to checking theorems about programming languages and logics. SASyLF has a simple design philosophy: language and logic syntax, semantics, and meta-theory should be written as closely as possible to the way it is done on paper. We describe how we designed the SASyLF syntax to be accessible to students learning type theory, and how students can understand its semantics directly in terms of the theory they are taught in class. SASyLF can express proofs typical of an introductory graduate type theory course. SASyLF proofs are generally very explicit, but its built-in support for variable binding provides substitution properties for free and avoids awkward variable encodings. We describe preliminary experience teaching with SASyLF.

References

[1]

Andreas Abel, Bor-Yuh Evan Chang, and Frank Pfenning. Human-Readable, Machine-Verifiable Proofs for Teaching Constructive Logic. In Workshop on Proof Transformations, Proof Presentations and Complexity of Proofs (PTP'01), June 2001.

[2]

Brian Aydemir, Arthur Charguéraud, Benjamin C. Pierce, Randy Pollack, and Stephanie Weirich. Engineering Formal Metatheory. In Symposium on Principles of Programming Languages, 2008.

Digital Library

[3]

Brian E. Aydemir, Aaron Bohannon, Matthew Fairbairn, J. Nathan Foster, Benjamin C. Pierce, Peter Sewell, Dimitrios Vytiniotis, Geoffrey Washburn, Stephanie Weirich, and Steve Zdancewic. Mechanized Metatheory for the Masses: The PoplMark Challenge. In Theorem Proving in Higher Order Logics, pages 50--65, 2005.

Digital Library

[4]

Ian Barland, Matthias Felleisen, Kathi Fisler, Phokion Kolaitis, and Moshe Y. Vardi. Integrating Logic into the Computer Science Curriculum. http://www.cs.utexas.edu/\verb1 1csed/FM/docs/iticse--fislervardi.pdf, 2000.

[5]

Jon Barwise and John Etchemendy. Computers, Visualization, and the Nature of Reasoning. In The Digital Phoenix: How Computers are Changing Philosophy, pages 93--116. Blackwell, 1998.

[6]

Yves Bertot and Pierre Castéran. Interactive Theorem Proving and Program Development. Springer-Verlag, 2004.

Digital Library

[7]

Carl Eastlund, Dale Vaillancourt, and Matthias Felleisen. ACL2 for Freshmen: First Experiences. In ACL2 Workshop, 2007.

[8]

Andrew Gacek. The Abella Interactive Theorem Prover (system description). In IJCAR, 2008.

Digital Library

[9]

D. Goldson and S. Reeves. Using Programs to Teach Logic to Computer Scientists. Notices of the American Mathematical Society, 40: 143--148, 1993.

[10]

Robert Harper. Practical Foundations for Programming Languages. Available at http://www.cs.cmu.edu/~rwh/plbook/book.pdf, 2008.

Digital Library

[11]

Robert Harper, Furio Honsell, and Gordon D. Plotkin. A Framework for Defining Logics. phJ. ACM, 40 (1): 143--184, 1993.

Digital Library

[12]

Jacob Matthews, Robert Bruce Findler, Matthew Flatt, and Matthias Felleisen. A Visual Environment for Developing Context-Sensitive Term Rewriting Systems. In International Conference on Rewriting Techniques and Applications. Springer Verlag LNCS 3091, 2004.

[13]

Tobias Nipkow, Lawrence C. Paulson, and Markus Wenzel. Isabelle/HOL: A Proof Assistant For Higher-Order Logic. Lecture Notes in Computer Science, 2283, 2002.

Digital Library

[14]

Mikael Pettersson. Compiling Natural Semantics. PhD thesis, Linkoping University, 1995.

Digital Library

[15]

Frank Pfenning. Logical Frameworks. In Alan Robinson and Andrei Voronkov, editors, Handbook of Automated Reasoning, chapter 17, pages 1063--1147. Elsevier Science and MIT Press, 2001.

Digital Library

[16]

Frank Pfenning. Computation and Deduction. Cambridge University Press. In preparation. Draft from April 1997 available electronically at http://www.cs.cmu.edu/~twelf/notes/cd.ps.

[17]

Frank Pfenning and Carsten Schürmann. System Description: Twelf - A Meta-Logical Framework for Deductive Systems. In International Conference on Automated Deduction, pages 202--206, July 1999.

Digital Library

[18]

Richard Scheines and Wilfried Sieg. Computer Environments for Proof Construction. Interactive Learning Environments, 4: 159--169, 1994.

[19]

Carsten Schürmann. Automating the Meta-Theory of Deductive Systems. PhD thesis, Carnegie Mellon University, 2000.

[20]

Peter Sewell, Francesco Zappa Nardelli, Scott Owens, Gilles Peskine, Tom Ridge, Susmit Sarkar, and Rok Strnisa. Ott: Effective Tool Support for the Working Semanticist. In International Conference on Functional Programming, pages 1--12, 2007.

Digital Library

[21]

Richard Sommer and Gregory Nuckols. A Proof Environment for Teaching Mathematics. J. Autom. Reason., 32 (3): 227--258, 2004.

Digital Library

[22]

S. Tobias. Revitalizing Undergraduate Science: Why some things work and most don't. Research Corporation, 1992.

[23]

Masaru Tomita. An Efficient Augmented-Context-Free Parsing Algorithm. phComputational Linguistics, 13 (1-2): 31--46, 1987.

Digital Library

[24]

Mark van den Brand, Jan Heering, Paul Klint, and Pieter Olivier. Compiling Rewrite Systems: The ASF+SDF Compiler. Transactions on Software Engineering and Methodology, 24: 334--368, 2002.

Digital Library

Cited By

Boyland J(2022)Evolution of SASyLF 2008-2021Electronic Proceedings in Theoretical Computer Science10.4204/EPTCS.354.7354(87-107)Online publication date: 8-Feb-2022
https://doi.org/10.4204/EPTCS.354.7
Zhou YZhao JOliveira B(2022)Revisiting Iso-Recursive SubtypingACM Transactions on Programming Languages and Systems10.1145/354953744:4(1-54)Online publication date: 21-Sep-2022
https://dl.acm.org/doi/10.1145/3549537
Cimini MMiller DSiek JLämmel RTratt Lde Lara J(2020)Extrinsically typed operational semantics for functional languagesProceedings of the 13th ACM SIGPLAN International Conference on Software Language Engineering10.1145/3426425.3426936(108-125)Online publication date: 16-Nov-2020
https://dl.acm.org/doi/10.1145/3426425.3426936
Show More Cited By

Index Terms

SASyLF: an educational proof assistant for language theory
1. Computing methodologies
  1. Symbolic and algebraic manipulation
    1. Symbolic and algebraic algorithms
      1. Theorem proving algorithms
2. Theory of computation
  1. Models of computation
    1. Computability

Recommendations

The Reflective Milawa Theorem Prover is Sound (Down to the Machine Code that Runs it)

This paper presents, we believe, the most comprehensive evidence of a theorem prover's soundness to date. Our subject is the Milawa theorem prover. We present evidence of its soundness down to the machine code. Milawa is a theorem prover styled after ...
A Framework for Defining Logical Frameworks

In this paper, we introduce a General Logical Framework, called GLF, for defining Logical Frameworks, based on dependent types, in the style of the well known Edinburgh Logical Framework LF. The framework GLF features a generalized form of lambda ...
Representing model theory in a type-theoretical logical framework

In a broad sense, logic is the field of formal languages for knowledge and truth that have a formal semantics. It tends to be difficult to give a narrower definition because very different kinds of logics exist. One of the most fundamental contrasts is ...

Comments

Information & Contributors

Information

Published In

cover image ACM Conferences

FDPE '08: Proceedings of the 2008 international workshop on Functional and declarative programming in education

September 2008

98 pages

ISBN:9781605580685

DOI:10.1145/1411260

Program Chairs:
Frank Huch
University of Kiel, Germany
,
Adam Parkin
University of Victory, Canada

Copyright © 2008 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: 21 September 2008

Permissions

Request permissions for this article.

Request Permissions

Check for updates

Author Tags

Qualifiers

Research-article

Conference

ICFP08

Sponsor:

ICFP08: ACM SIGPLAN International Conference on Functional Programming

September 21, 2008

BC, Victoria, Canada

Upcoming Conference

ICFP '25

Sponsor:
sigplan

ACM SIGPLAN International Conference on Functional Programming

October 12 - 18, 2025

Singapore , Singapore

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
158
Total Downloads

Downloads (Last 12 months)13
Downloads (Last 6 weeks)1

Reflects downloads up to 06 Jan 2025

Other Metrics

View Author Metrics

Citations

Cited By

Boyland J(2022)Evolution of SASyLF 2008-2021Electronic Proceedings in Theoretical Computer Science10.4204/EPTCS.354.7354(87-107)Online publication date: 8-Feb-2022
https://doi.org/10.4204/EPTCS.354.7
Zhou YZhao JOliveira B(2022)Revisiting Iso-Recursive SubtypingACM Transactions on Programming Languages and Systems10.1145/354953744:4(1-54)Online publication date: 21-Sep-2022
https://dl.acm.org/doi/10.1145/3549537
Cimini MMiller DSiek JLämmel RTratt Lde Lara J(2020)Extrinsically typed operational semantics for functional languagesProceedings of the 13th ACM SIGPLAN International Conference on Software Language Engineering10.1145/3426425.3426936(108-125)Online publication date: 16-Nov-2020
https://dl.acm.org/doi/10.1145/3426425.3426936
Felty AMomigliano APientka B(2015)An Open Challenge Problem Repository for Systems Supporting BindersElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.185.2185(18-32)Online publication date: 27-Jul-2015
https://doi.org/10.4204/EPTCS.185.2
Grewe SErdweg SWittmann PMezini MMurphy GJr. G(2015)Type systems for the masses: deriving soundness proofs and efficient checkers2015 ACM International Symposium on New Ideas, New Paradigms, and Reflections on Programming and Software (Onward!)10.1145/2814228.2814239(137-150)Online publication date: 21-Oct-2015
https://dl.acm.org/doi/10.1145/2814228.2814239
Sznuk TSchubert A(2014)Tool Support for Teaching Hoare LogicSoftware Engineering and Formal Methods10.1007/978-3-319-10431-7_27(332-346)Online publication date: 2014
https://doi.org/10.1007/978-3-319-10431-7_27
Kahl W(2011)The teaching tool CALCCHECKProceedings of the First international conference on Certified Programs and Proofs10.1007/978-3-642-25379-9_17(216-230)Online publication date: 7-Dec-2011
https://dl.acm.org/doi/10.1007/978-3-642-25379-9_17
Henz MHobor A(2011)Teaching experienceProceedings of the First international conference on Certified Programs and Proofs10.1007/978-3-642-25379-9_16(199-215)Online publication date: 7-Dec-2011
https://dl.acm.org/doi/10.1007/978-3-642-25379-9_16
Saini DSunshine JAldrich J(2010)A theory of typestate-oriented programmingProceedings of the 12th Workshop on Formal Techniques for Java-Like Programs10.1145/1924520.1924529(1-7)Online publication date: 22-Jun-2010
https://dl.acm.org/doi/10.1145/1924520.1924529
Sewell PNardelli FOwens SPeskine GRidge TSarkar SStrniŠa R(2010)OttJournal of Functional Programming10.1017/S095679680999029320:1(71-122)Online publication date: 1-Jan-2010
https://dl.acm.org/doi/10.1017/S0956796809990293

View Options

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Media

Figures

Other

Tables

View Table of Contents