Transcription of History of Lambda-calculus and Combinatory Logic
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History of Lambda-calculus and Combinatory Logic
History of Lambda-calculus and Combinatory Logic . J. Roger Hindley . Felice Cardone 2006, from Swansea University Mathematics Department Research Report No. MRRS-05-06.. Contents 1 Introduction 1. 2 Pre- History 2. 3 1920s: Birth of Combinatory Logic 3. 4 1930s: Birth of and Youth of CL 6. Early - calculus .. 6. CL in the 1930s .. 9. 5 1940s and 1950s: Consolidation 12. Simple type theory .. 12. Abstract reduction theory .. 13. Reductions in CL and .. 13. Illative systems .. 14. 6 Programming languages 16. John McCarthy and LISP .. 16. Peter Landin .. 16. Corrado B . ohm: - calculus as a programming language .. 17. 7 Syntactical developments 18. Contributions from the programming side .. 19. Theory of reductions .. 21. 8 Types 23. The general development of type theories .. 23. Types as grammatical categories.
The present article will sketch the history of these two topics through the twen- tieth century. We shall assume the reader is familiar with at least one of the many versions
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