Abstract
There are many powerful techniques for automated termination analysis of term rewriting. However, up to now they have hardly been used for real programming languages. We present a new approach which permits the application of existing techniques from term rewriting in order to prove termination of programs in the functional language Haskell. In particular, we show how termination techniques for ordinary rewriting can be used to handle those features of Haskell which are missing in term rewriting (e.g., lazy evaluation, polymorphic types, and higher-order functions). We implemented our results in the termination prover AProVE and successfully evaluated them on existing Haskell-libraries.
Supported by the Deutsche Forschungsgemeinschaft DFG under grant GI 274/5-1.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abel, A.: Termination checking with types. RAIRO - Theoretical Informatics and Applications 38(4), 277–319 (2004)
Arts, T., Giesl, J.: Termination of term rewriting using dependency pairs. Theoretical Computer Science 236, 133–178 (2000)
Barthe, G., Frade, M.J., Giménez, E., Pinto, L., Uustalu, T.: Type-based termination of recursive definitions. Math. Structures in Comp. Sc. 14(1), 1–45 (2004)
Fissore, O., Gnaedig, I., Kirchner, H.: Outermost ground termination. In: Proc. WRLA 2002, ENTCS, vol. 71 (2002)
Giesl, J.: Termination analysis for functional programs using term orderings. In: Mycroft, A. (ed.) SAS 1995. LNCS, vol. 983, pp. 154–171. Springer, Heidelberg (1995)
Giesl, J., Middeldorp, A.: Transformation techniques for context-sensitive rewrite systems. Journal of Functional Programming 14(4), 379–427 (2004)
Giesl, J., Thiemann, R., Schneider-Kamp, P.: The dependency pair framework: Combining techniques for automated termination proofs. In: Baader, F., Voronkov, A. (eds.) LPAR 2004. LNCS (LNAI), vol. 3452, pp. 301–331. Springer, Heidelberg (2005)
Giesl, J., Thiemann, R., Schneider-Kamp, P.: Proving and disproving termination of higher-order functions. In: Gramlich, B. (ed.) FroCos 2005. LNCS (LNAI), vol. 3717, pp. 216–231. Springer, Heidelberg (2005)
Giesl, J., Schneider-Kamp, P., Thiemann, R.: AProVE 1.2: Automatic termination proofs in the DP framework. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 281–286. Springer, Heidelberg (2006)
Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: Proc. POPL 2001, pp. 81–92. ACM Press, New York (2001)
Panitz, S.E., Schmidt-Schauss, M.: TEA: Automatically proving termination of programs in a non-strict higher-order functional language. In: Van Hentenryck, P. (ed.) SAS 1997. LNCS, vol. 1302, pp. 345–360. Springer, Heidelberg (1997)
Peyton Jones, S. (ed.): Haskell 98 Languages and Libraries: The revised report. Cambridge University Press, Cambridge (2003)
Schneider-Kamp, P., Giesl, J., Serebrenik, A., Thiemann, R.: Automated termination analysis for logic programs by term rewriting. In: Puebla, G. (ed.) LOPSTR 2006. LNCS, vol. 4407, pp. 177–193. Springer, Heidelberg (2007)
Swiderski, S.: Terminierungsanalyse von Haskellprogrammen. Diploma Thesis, RWTH Aachen (2005), see: http://aprove.informatik.rwth-aachen.de/eval/Haskell/
Telford, A., Turner, D.: Ensuring termination in ESFP. Journal of Universal Computer Science 6(4), 474–488 (2000)
Walther, C.: On proving the termination of algorithms by machine. Artificial Intelligence 71(1), 101–157 (1994)
Xi, H.: Dependent types for program termination verification. Higher-Order and Symbolic Computation 15(1), 91–131 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giesl, J., Swiderski, S., Schneider-Kamp, P., Thiemann, R. (2006). Automated Termination Analysis for Haskell: From Term Rewriting to Programming Languages. In: Pfenning, F. (eds) Term Rewriting and Applications. RTA 2006. Lecture Notes in Computer Science, vol 4098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11805618_23
Download citation
DOI: https://doi.org/10.1007/11805618_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-36834-2
Online ISBN: 978-3-540-36835-9
eBook Packages: Computer ScienceComputer Science (R0)