Correspondence between ALGOL 60 and Church's Lambda-notation

@article{Landin1965CorrespondenceBA,
  title={Correspondence between ALGOL 60 and Church's Lambda-notation},
  author={Peter J. Landin},
  journal={Communications of the ACM},
  year={1965},
  volume={8},
  pages={89 - 101}
}
  • P. J. Landin
  • Published 1 February 1965
  • Computer Science
  • Communications of the ACM
This paper describes how some of the semantics of ALGOL 60 can be formalized by establishing a correspondence between expressions of ALGOL 60 and expressions in a modified form of Church's n-notation. First a model for computer languages and computer behavior is described, based on the notions of functional application and functional abstraction, but also having analogues for imperative language features. Then |his model is used as an "abstract object language" into which ALGOL 60 is mapped… 

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References

SHOWING 1-10 OF 28 REFERENCES
The Mechanical Evaluation of Expressions
TLDR
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.
LISP 1.5 Programmer's Manual
The LISP language is designed primarily for symbolic data processing used for symbolic calculations in differential and integral calculus, electrical circuit theory, mathematical logic, game playing,
Revised report on the algorithm language ALGOL 60
a survey of the basic coustituents arid fcuturcs of the language is given, and the formal notation, by which the syntactic structure is defined, is esplaincd. The sccnnd chapter lists all the basic
The Main Features of CPL
The paper provides an informal account of CPL, a new programming language currently being implemented for the Titan at Cambridge and the Atlas at London University. CPL is based on, and contains the
Some proposals for improving the efficiency of ALGOL 60
TLDR
A number of defects in AL(~OL which it appears to us must be eliminated before the language can achieve full success as a means of programmin~ computers for serious work are drawn up.
Design of a separable transition-diagram compiler
A COBOL compiler design is presented which is compact enough to permit rapid, one-pass compilation of a large subset of COBOL on a moderately large computer. Versions of the same compiler for smaller
Towards a Mathematical Science of Computation
TLDR
The prospects for a mathematical science of computation is discussed and it is shown that from Newton’s law of gravitation and his laws of motion, one can deduce that the planetary orbits obey Kepler's laws.
Combinalortl Logic, l'~d. 1. North [lolL'm(1, Amsterd~un, 1:)58
  • Combinalortl Logic, l'~d. 1. North [lolL'm(1, Amsterd~un, 1:)58
Recursive definition of symax and semantics. Presented at IFIP Working Conf
    ...
    ...