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Constructive mathematics and computer programming
Abstract
If programming is understood not as the writing of instructions for this or that computing machine but as the design of methods of computation that it is the computer’s duty to execute (a difference that Dijkstra has referred to as the difference between computer science and computing science), then it no longer seems possible to distinguish the discipline of programming from constructive mathematics. This explains why the intuitionistic theory of types (Martin-Lof 1975 In Logic Colloquium 1973 (ed. H. E. Rose & J. C. Shepherdson), pp. 73- 118. Amsterdam: North-Holland), which was originally developed as a symbolism for the precise codification of constructive mathematics, may equally well be viewed as a programming language. As such it provides a precise notation not only, like other programming languages, for the programs themselves but also for the tasks that the programs are supposed to perform. Moreover, the inference rules of the theory of types, which are again completely formal, appear as rules of correct program synthesis. Thus the correctness of a program written in the theory of types is proved formally at the same time as it is being synthesized.
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Citations
Cited by
Coquand, T., & Huet, G. (1988) · Information and Computation · doi:10.1016/0890-5401(88)90005-3 · Cited by 1,082
A framework for defining logics
Harper, R., Honsell, F., & Plotkin, G. (1993) · Journal of the ACM · doi:10.1145/138027.138060 · Cited by 990
A judgmental reconstruction of modal logic
PFENNING, F., & DAVIES, R. (2001) · Mathematical Structures in Computer Science · doi:10.1017/s0960129501003322 · Cited by 342
Sundholm, G. (1986) · Handbook of Philosophical Logic · doi:10.1007/978-94-009-5203-4_8 · Cited by 193
Using parameterized signatures to express modular structure
Jones, M. P. (1996) · Proceedings of the 23rd ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '96 · doi:10.1145/237721.237731 · Cited by 57
Metadata
- Authors
- Martin-Lof, P.
- Venue
- Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- Publisher
- The Royal Society
- Published
- 1984-10-01
- Volume
- 312
- Issue
- 1522
- Pages
- 501-518
- ISSN
- 0080-4614 (ISSN-L)
- 2054-0272
- OpenAlex
- W2106718208
- Cited by
- 499
- References
- 0
- FWCI
- 25.86
- Type
- journal article
- Language
- en
- Open access
- closed
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- Martin-Lof, P. (1984). Constructive mathematics and computer programming. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. https://doi.org/10.1098/rsta.1984.0073
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