‎"TURING, A.M. (+) H. A. NEWMAN.‎
‎A formal theorem in Church s theory of types (+) The use of dots as brackets in Church's system. (In: ""The Journal Of Symbolic Logic""). - [TURING ON CHURCH'S TYPE THEORY]‎

‎(No place), The Association for Symbolic Logic, 1942. Large 8vo. Bound in blue half cloth with silver lettering to spine. In ""Journal of Symbolic Logic"", Volume 7. Small paper label to lower part of spine and upper inner margin of front board. Stamp to title-page and last leaf, otherwise internally fine. Pp. 28-33"" 146-156 (Entire copy: (4), 180 pp.).‎

Reference : 60431

‎First appearance of these two paper's by Turing.Turing's paper ""A Formal Theorem in Church's Theory of Types"" is a significant contribution to the fields of computer science and mathematical logic. By providing a formal proof within Church's theory, Turing expanded our understanding of computation and its relationship to logic. His work on computability and the theory of types laid the foundation for the development of theoretical computer science, proof theory, and automated reasoning. Turing's paper continues to be a landmark in the study of computation, inspiring further research and practical applications in diverse areas of science and technology. In ""The Use of Dots as Brackets in Church's System"", introducing the dot parentheses notation, Turing simplified the representation and manipulation of lambda calculus expressions, making them more intuitive and manageable. His work highlighted the relationship between syntax and semantics, laying the foundation for further research in formal semantics and the development of programming languages. Turing's paper continues to be influential, shaping the way complex expressions are represented and reasoned about in the fields of computation, formal systems, and logic.‎