The Impact of the Lambda Calculus in Logic and Computer Science
@article{Barendregt1997TheIO,
title={The Impact of the Lambda Calculus in Logic and Computer Science},
author={HENK P. Barendregt},
journal={Bulletin of Symbolic Logic},
year={1997},
volume={3},
pages={181 - 215}
}Abstract One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand.
147 Citations
Comparing Mathematical Provers
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- 2013
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References
SHOWING 1-10 OF 255 REFERENCES
Highlights of the History of the Lambda-Calculus
- MathematicsAnnals of the History of Computing
- 1984
This paper gives an account of both the lambda-calculus and its close relative, the combinatory calculus, and explains why they are of such importance for computer software. The account includes the…
The lambda calculus - its syntax and semantics
- MathematicsStudies in logic and the foundations of mathematics
- 1985
The Mechanical Evaluation of Expressions
- Computer ScienceComput. J.
- 1964
It is shown how some forms of expression in current programming languages can be modelled in Church's X-notation, and a way of "interpreting" such expressions is described, which suggests a method of analyzing the things computer users write.
Background : computational structures
- Mathematics
- 1992
J.W. Klop: Term rewriting systems H.P. Barendregt: Lambda calculi with types D.M. Gabbay: Elements of algorithmic proof Lawrence C. Paulson: Designing a theorem prover Colin Stirling: Modal and…
Automatic Synthesis of Typed Lambda-Programs on Term Algebras
- Mathematics, Computer ScienceTheor. Comput. Sci.
- 1985
Origins of Recursive Function Theory
- MathematicsAnnals of the History of Computing
- 1981
The notion of "?-definability" was the first of what are now accepted as equivalent exact mathematical descriptions of the class of the functions for which algorithms exist and traces the investigation in 1931-1933 by which the notion was quite unexpectedly so accepted.
A Self-Interpreter of Lambda Calculus Having a Normal Form
- Mathematics, Computer ScienceCSL
- 1992
The notion of a canonical algebraic term rewriting system can be interpreted in the lambda calculus by the Bohm — Piperno technique in such a way that strong normalization is preserved and allows us to improve some recent results of Mogensen concerning efficient godelizations.
Theoretical Pearls: Self-interpretation in lambda calculus
- Computer ScienceJournal of Functional Programming
- 1991
Self-interpretation will be shown here to be possible in lambda calculus to represent functional programs including their input.