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Toward automatic program synthesis
Open accessAbstract
An elementary outline of the theorem-proving approach to automatic program synthesis is given, without dwelling on technical details. The method is illustrated by the automatic construction of both recursive and iterative programs operating on natural numbers, lists, and trees. In order to construct a program satisfying certain specifications, a theorem induced by those specifications is proved, and the desired program is extracted from the proof. The same technique is applied to transform recursively defined functions into iterative programs, frequently with a major gain in efficiency. It is emphasized that in order to construct a program with loops or with recursion, the principle of mathematical induction must be applied. The relation between the version of the induction rule used and the form of the program constructed is explored in some detail.
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“Using user-specified constraints, program synthesis (or source code generation) automatically generates source code in a programming language (Waldinger et al. 1969; Manna and Waldinger 1971).”
From Large language models (LLMs): survey, technical frameworks, and future challenges (2024) · cites this paper as Manna and Waldinger 1971
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Metadata
- Authors
- Manna, Z., & Waldinger, R. J.
- Affiliations
- Stanford University (US)
- SRI International (US)
- Venue
- Communications of the ACM
- Published
- 1971-03
- Volume
- 14
- Issue
- 3
- Pages
- 151-165
- ISSN
- 0001-0782 (ISSN-L)
- 1557-7317
- OpenAlex
- W2037237472
- Cited by
- 285
- References
- 24
- Citations by year
- 2026: 7 · 2025: 17 · 2024: 10 · 2023: 12 · 2022: 5 · 2021: 12 · 2020: 14 · 2019: 8 · 2018: 9 · 2017: 11 · 2016: 5 · 2015: 6 · 2014: 9 · 2013: 12 · 2012: 7
- FWCI
- 21.08
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Communications of the ACM (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Software › Logic, programming, and type systems
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Computability, Logic, AI Algorithms
- Physical Sciences › Computer Science › Computational Theory and Mathematics › semigroups and automata theory
- Keywords
- program synthesis, theorem proving, mathematical induction, recursive programs, iterative programs, program transformation, specification-based synthesis, lists, trees, natural numbers
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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