Nils Klarlund
ABSTRACT
Recursive data structures are abstractions of simple records and pointers. They impose a shape invariant, which is verified at compile-time and exploited to automatically generate code for building, copying, comparing, and traversing values without loss of efficiency. However, such values are always tree shaped, which is a major obstacle to practical use.
We propose a notion of graph types, which allow common shapes, such as doubly-linked lists or threaded trees, to be expressed concisely and efficiently. We define regular languages of routing expressions to specify relative addresses of extra pointers in a canonical spanning tree. An efficient algorithm for computing such addresses is developed. We employ a second-order monadic logic to decide well-formedness of graph type specifications. This logic can also be used for automated reasoning about pointer structures.
- 1.H. Ait-Kaci and R. Nasr. Logic and inheritance. In Proc. 13th A CM Syrup. on Princ. of Program. ruing Languages, pages 219-228, 1986. Google Scholar
Digital Library
- 2.H. Ait-Kaci and R. Nasr. Login: A logic programming language with built-in inheritance. Journal of Logic Programming, 3:185-215, 1986. Journal version of {1}. Google ScholarDigital Library
- 3.H. Ai't-Kaci and A. Podelski. Towards a meaning of life. In Jan Maluszyfiski and Martin Wirsing, editors, Proceedings of the 3rd International Symposium on Programming Language Implementation and Logic Programming (Passau, Germany), pages 255-274. Springer-Verlag, LNCS 528, August 1991.Google ScholarCross Ref
- 4.B. Courcelle. The monadic second-order logic of graphs I. Recognizable sets of finite graphs. Information and computation, 85:12-75, 1990. Google ScholarDigital Library
- 5.J. DSrre and W.C Rounds. On subsumption and semiunification in feature algebras. In Proc. IEEE Symp. on Logics in Computer Science, pages 300-310, 1990.Google Scholar
- 6.L. Hendren, J. Hummel, and A. Nicolau. Abstractions for recursive pointer data structures: Improving the analysis and transformation of imperative programs. In Proc. SIGPLAN'g2 Conference on Programming Language Design and Implementation, pages 249-260. ACM, 1992. Google ScholarDigital Library
- 7.C.A.R. Hoare. Reeursive data structures. In~ernational Journal of Computer and Information Sciences, 4:2:105-132, 1975.Google ScholarCross Ref
- 8.Robin Milner, Mads Torte, and Robert Harper. The Definition of Standard ML. MIT Press, 1990. Google ScholarDigital Library
- 9.T. Reps. Incremental evaluation for attribute grammars with unrestricted movement between tree modifications. Acta Informa~ica, 25, 1986. Google ScholarDigital Library
- 10.D.A. Turner. Miranda: A non-strict functional language with polymorphie types. In Proc. Conference on Functional Programming Languages and Computer Architecture, pages 1-16. Springer- Verlag (LNCS 201), 1985. Google ScholarDigital Library
Index Terms
- Graph types
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