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Proving Properties of Programs by Structural Induction
Abstract
This paper discusses the technique of structural induction for proving theorems about programs. This technique is closely related to recursion induction but makes use of the inductive definition of the data structures handled by the programs. It treats programs with recursion but without assignments or jumps. Some syntactic extensions to Landin's functional programming language ISWIM are suggested which make it easier to program the manipulation of data structures and to develop proofs about such programs. Two sample proofs are given to demonstrate the technique, one for a tree sorting algorithm and one for a simple compiler for expressions.
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Citations
Cited by
An axiomatic basis for computer programming
Hoare, C. A. R. (1983) · Communications of the ACM · doi:10.1145/357980.358001 · Cited by 1,521
MCBRIDE, C., & MCKINNA, J. (2004) · Journal of Functional Programming · doi:10.1017/s0956796803004829 · Cited by 327
Toward automatic program synthesis
Manna, Z., & Waldinger, R. J. (1971) · Communications of the ACM · doi:10.1145/362566.362568 · Cited by 285
History of Interactive Theorem Proving
Harrison, J., Urban, J., & Wiedijk, F. (2014) · Handbook of the History of Logic · doi:10.1016/b978-0-444-51624-4.50004-6 · Cited by 107
Metadata
- Authors
- Burstall, R. M.
- Venue
- The Computer Journal
- Publisher
- Oxford University Press (OUP)
- Published
- 1969-02-01
- Volume
- 12
- Issue
- 1
- Pages
- 41-48
- ISSN
- 0010-4620 (ISSN-L)
- 1460-2067
- OpenAlex
- W2159709550
- Cited by
- 324
- References
- 0
- FWCI
- 20.11
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Proving Properties of Programs by Structural Induction. https://app.cochat.ai/papers/10.1093/comjnl/12.1.41
- The paper
- Burstall, R. M. (1969). Proving Properties of Programs by Structural Induction. The Computer Journal. https://doi.org/10.1093/comjnl/12.1.41
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
