Cited By
View all- Brown MPalsberg J(2017)Jones-optimal partial evaluation by specialization-safe normalizationProceedings of the ACM on Programming Languages10.1145/31581022:POPL(1-28)Online publication date: 27-Dec-2017
A Type Theoretic Specification of Partial Evaluation
Pages 57 - 68
Abstract
We develop a type theoretic specification of offline partial evaluation for the simply-typed lambda calculus in the dependently-typed programming language Agda. We establish the correctness of the specification by proving termination, typing preservation, and semantics preservation using logical relations. Typing preservation is achieved by relying on a typed syntax representation based on De Bruijn indices for the source and the target language. The full calculus contains primitive recursion on natural numbers and higher-order lifting for function, product, and sum types.
References
[1]
M. S. Ager, O. Danvy, and H. K. Rohde. Fast partial evaluation of pattern matching in strings. ACM TOPLAS, 28(4):696--714, 2006.
[2]
K. Asai. Logical relations for call-by-value delimited continuations. In M. C. J. D. van Eekelen, editor, TFP 2005, volume 6 of Trends in Functional Programming, pages 63--78, Tallinn, Estonia, 2005. Intellect. ISBN 978-1-84150-176-5.
[3]
A. Bove, P. Dybjer, and U. Norell. A brief overview of Agda - a functional language with dependent types. In S. Berghofer, T. Nipkow, C. Urban, and M. Wenzel, editors, TPHOLs, volume 5674 of LNCS, pages 73--78, Munich, Germany, 2009. Springer. ISBN 978-3-642-03358-2.
[4]
C. Coquand. A formalised proof of the soundness and completeness of a simply typed lambda-calculus with explicit substitutions. Higher-Order and Symbolic Computation, 15(1):57--90, 2002.
[5]
O. Danvy. Type-directed partial evaluation. In POPL 1996 {27}, pages 242--257. ISBN 0-89791-769-3.
[6]
O. Danvy. Online type-directed partial evaluation. In M. Sato and Y. Toyama, editors, Proc. Third Fuji International Symposium on Functional and Logic Programming, Kyoto, Japan, Apr. 1998. World Scientific Press, Singapore.
[7]
O. Danvy and A. Filinski. Representing control: A study of the CPS transformation. Mathematical Structures in Computer Science, 2:361--391, 1992.
[8]
O. Danvy, K. Malmkjær, and J. Palsberg. The essence of eta-expansion in partial evaluation. Lisp and Symbolic Computation, 8(3):209--227, July 1995.
[9]
R. Davies. A temporal-logic approach to binding-time analysis. In Proc. 1996 IEEE Symp. on Logic in Computer Science, pages 184--195, New Brunswick, New Jersey, July 1996. IEEE Computer Society Press.
[10]
R. Davies and F. Pfenning. A modal analysis of staged computation. In POPL 1996 {27}, pages 258--270. ISBN 0-89791-769-3.
[11]
N. G. de Bruijn. Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indag Math., 34(5):381--392, 1972.
[12]
D. Dussart, F. Henglein, and C. Mossin. Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time. In A. Mycroft, editor, Proc. 1995 International Static Analysis Symposium, volume 983 of LNCS, pages 118--136, Glasgow, Scotland, Sept. 1995. Springer. URL ftp://ftp.diku.dk/diku/semantics/papers/D-243.dvi.gz.
[13]
A. Filinski. A semantic account of type-directed partial evaluation. In G. Nadathur, editor, PPDP, volume 1702 of Lecture Notes in Computer Science, pages 378--395, Paris, France, Sept. 1999. Springer. ISBN 3-540-66540-4.
[14]
C. K. Gomard and N. D. Jones. A partial evaluator for the untyped lambda-calculus. J. Funct. Program., 1(1):21--70, Jan. 1991.
[15]
J. Hatcliff. Mechanically verifying the correctness of an offline partial evaluator. In S. D. Swierstra and M. Hermenegildo, editors, PLILP '95, volume 982 of LNCS, pages 279--298, Utrecht, The Netherlands, Sept. 1995. Springer. ISBN 3-540-60359-X.
[16]
J. Hatcliff, T. Æ. Mogensen, and P. Thiemann, editors. Partial Evaluation---Practice and Theory. Proceedings of the 1998 DIKU International Summerschool, volume 1706 of LNCS, Copenhagen, Denmark, 1999. Springer.
[17]
F. Henglein and C. Mossin. Polymorphic binding-time analysis. In D. Sannella, editor, Proc. 5th ESOP, volume 788 of LNCS, pages 287--301, Edinburgh, UK, Apr. 1994. Springer. ISBN 3-540-57880-3.
[18]
N. Jones, C. Gomard, and P. Sestoft. Partial Evaluation and Automatic Program Generation. Prentice-Hall, 1993. ISBN 0-13-020249-5. URL http://www.dina.kvl.dk/~sestoft/pebook/pebook.html.
[19]
J. Jørgensen. Compiler generation by partial evaluation. Master's thesis, DIKU, University of Copenhagen, 1991.
[20]
K. Kojima and A. Igarashi. Constructive linear-time temporal logic: Proof systems and Kripke semantics. Information and Computation, 209(12):1491--1503, 2011.
[21]
P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.
[22]
J. C. Mitchell and E. Moggi. Kripke-style models for typed lambda calculus. Ann. Pure Appl. Logic, 51(1-2):99--124, 1991.
[23]
F. Nielson and H. R. Nielson. Two-Level Functional Languages, volume 34 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1992.
[24]
U. Norell. Dependently typed programming in Agda. In P. W. M. Koopman, R. Plasmeijer, and S. D. Swierstra, editors, Advanced Functional Programming, volume 5832 of LNCS, pages 230--266, Heijen, The Netherlands, 2008. Springer. ISBN 978-3-642-04651-3.
[25]
F. Pfenning. Logic programming in the LF logical framework. In G. Huet and G. Plotkin, editors, Logical Frameworks, pages 149--181. Cambridge University Press, 1991.
[26]
B. C. Pierce et al. Software foundations. http://www.cis.upenn.edu/~bcpierce/sf/, July 2013.
[27]
POPL 1996. Proc. 1996 ACM Symp. POPL, St. Petersburg, FL, USA, Jan. 1996. ACM Press. ISBN 0-89791-769-3.
[28]
W. Taha. Multi-Stage Programming: Its Theory and Applications. PhD thesis, Oregon Graduate Institute of Science and Technology, Portland, Oregon, USA, July 1999.
[29]
W. Taha and M. F. Nielsen. Environment classifiers. In G. Morrisett, editor, Proc. 30th ACM Symp. POPL, pages 26--37, New Orleans, LA, USA, Jan. 2003. ACM Press. ISBN 1-58113-628-5.
[30]
M. Wand. Specifying the correctness of binding-time analysis. J. Funct. Program., 3(3):365--387, July 1993.
Index Terms
- A Type Theoretic Specification of Partial Evaluation
Recommendations
Type-directed partial evaluation
POPL '96: Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languagesWe present a strikingly simple partial evaluator, that is type-directed and reifies a compiled program into the text of a residual, specialized program. Our partial evaluator is concise (a few lines) and it handles the flagship examples of offline ...
Embedding polymorphic dynamic typing
WGP '11: Proceedings of the seventh ACM SIGPLAN workshop on Generic programmingDynamic typing in a statically typed functional language allows us to defer type unification until run time. This is typically useful when interacting with the 'outside' world where the type of values involved may not be known statically. Haskell has ...
Comments
Information & Contributors
Information
Published In
September 2014
288 pages
ISBN:9781450329477
DOI:10.1145/2643135
- General Chairs:
- Olaf Chitil,
- Andy King,
- Program Chair:
- Olivier Danvy
Copyright © 2014 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: 08 September 2014
Check for updates
Author Tags
Qualifiers
- Tutorial
- Research
- Refereed limited
Conference
PPDP '14
Sponsor:
PPDP '14: 16th International Symposium on Principles and Practice of Declarative Programming
September 8 - 10, 2014
Canterbury, United Kingdom
Acceptance Rates
Overall Acceptance Rate 208 of 443 submissions, 47%
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 84Total Downloads
- Downloads (Last 12 months)9
- Downloads (Last 6 weeks)1
Reflects downloads up to 27 Feb 2025
Other Metrics
Citations
Cited By
View all- Brown MPalsberg J(2017)Jones-optimal partial evaluation by specialization-safe normalizationProceedings of the ACM on Programming Languages10.1145/31581022:POPL(1-28)Online publication date: 27-Dec-2017
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in