Abstract
Shortly after the appearance of the first computers, that is computing machines with stored programs, there arose the problem of how to communicate efficiently with them, especially how to simplify the writing of coded instructions. Zuse (1949) was probably the first to suggest that machines should be employed to facilitate this work using logical propositional methods. Shortly after, the author of this article (1951–52) devised a ‘language’. Its phrases were to have a double meaning: for mathematicians they signified the description of some algorithm and for the computer they signified a list of instructions to be obeyed in order to implement that algorithm. Moreover the computer was to take upon itself the task of translating these phrases into sequences of instructions written in its own code (Böhm, 1954).
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Bibliography
de Bakker, J. W., ‘Formal Definition of Programming Languages’, Mathematics Centrum, Amsterdam, 1967.
de Bakker, J. W. and Scott, D., ‘A Theory of Programs’, Unpublished Notes, IBM Seminar, Vienna, 1969.
Böhm, C., ‘Du déchiffrage des formules logico-mathématiques par la machine même dans la conception du programme’, Ann. Math. PuraAppl. 37 (1954), 5–47.
Böhm, C., ‘On a Family of Turing Machines and the Related Programming Language’, ICC Bulletin 3 (1964), 187–194.
Böhm, C., ‘The CUCH as a Formal and Description Language’, in T. B. Steel (ed.), Formal Language Description Languages for Computer Programming, North-Holland, Amsterdam, 1966, pp. 179–197.
Böhm, C. and Dezani, M., ‘A CUCH Machine: The Automatic Treatment of Bound Variables’, Int. J. Computer Inf. Sci. 1 (1972), 171–191.
Böhm, C. and Dezani, M., Notes on “A CUCH Machine: The Automatic Treatment of Bound Variables”‘, Int. J. Computer Inf. Sci 2 (1973), 157–160.
Böhm and Dezani-Ciancaglini, M., ‘Can Syntax be Ignored During Translation?’, in M. Nivat (ed.), Automata, Languages and Programming, North-Holland, 1973, pp. 197–207.
Böhm, C. and Dezani-Ciancaglini, M., ‘Combinatory Logic as Monoids’, in preparation, 1977.
Böhm, C. and Gross, W., ‘Introduction to the CUCH’, in E. R. Caianiello (ed.), Automata Theory, Academic Press, New York, 1966, pp. 35–66.
Böhm, C. and Jacopini, G., ‘Flow-Diagrams, Turing Machines and Languages with Only Two Formation Rules’, Comm. ACM 9 (1966), 366–371.
Burge, W. M., ‘The Evaluation, Classification and Interpretation of Expressions’, ACM Nato Conference, 1964.
Church, A., ‘Combinatory Logic as a Semigroup’, (abstract), Bull. Am. Math. Soc. 43 (1937), 333.
Church, A., ‘The Calculi of Lambda-Conversion’, Ann. Math. Studies 6, Princeton Univ. Press, Princeton, N. J., 1941.
Curry, H. B. and Feys, R., Combinatory Logic, vol. I, North-Holland, Amsterdam, 1958.
Iverson, K., A Programming Language, Wiley, New York, 1962.
Kleene, S. C., Introduction to Metamathematics, Van Nostrand, New York, 1950.
Klop, J. W., ‘On Solvability by λI-Terms’, in C. Böhm (ed.), Lambda-Calculus and Computer Science Theory, Computer Science, Springer-Verlag, New York, 1975.
Landin, J. P., ‘The Mechanical Evaluation of Expressions’, Computer Journal 6 (1964), 308–320.
McCarthy, J., The LISP 1.5 Programmers Manual, MIT Press, Cambridge, Mass., 1962.
Morris, J. H. H., ‘Lambda Calculus Models of Programming Languages’, Ph.D. Thesis, MIT, Cambridge, Mass., 1968.
Park, D. M. R., ‘Fixpoint Induction and Proofs of Program Properties’, in B. Meltzer and D. Michie (eds.), Machine Intelligence, vol. 5, American Elsevier, New York, 1970, pp. 59–78.
Petrone, L. and Bert, M. N. N., ‘Relaxing Syntax to Simplify Syntax-Directed Translations’, Proc. of Tnformatica 77’, Bled, 1977.
Plotkin, G. D., ‘A Set Theoretical Definition of Application’, Memo, MP–R–95, School of Artificial Intelligence, Univ. of Edinburgh.
Robinson, J., ‘General Recursive Functions’, Proc. Am. Math. Soc. 1 (1950), 703–718.
Shepherdson, J. C. and Sturgis, H. E., ‘Computability of Recursive Functions’, J. ACM 10 (1963), 217–255.
Scott, D., ‘Continuous Lattices’, Proc. 1971 Conference, Lecture Notes in Mathematics, No. 274, Springer-Verlag, New York, 1972, pp. 311–366.
Scott, D., ‘Data Types as Lattices’, Siam J. Computing 5 (1976), 522–587.
Strachey, C., ‘Toward a Formal Semantics’, in T. B. Steel (ed.), Formal Language Description Languages for Computer Programming, North-Holland, Amsterdam, 1966, pp. 198–220.
Venturini-Zilli, M., ‘λ-K-formulae for Vector Operators’, ICC Bulletin 4 (1965), 157–174.
Wadsworth, C. P., ‘Semantics and Pragmatics of the Lambda-Calculus’, Ph.D. Thesis, Oxford Univ., Oxford, England, 1971.
Zuse, K., ‘Ueber den allgemeinen Plankalkul als Mittel zur Formulierung schematisch kombinatorischer Aufgaben’, Arch. Math. 1 (1948–49), 441–449.
FORTRAN, ‘The Fortran Automatic Coding System’, by J. W. Backus et al, Proc. of the WJCC, I.R.E., New York, 1957.
ALGOL, ‘Report on the Algorithmic Language ALGOL 60’, P. Naur (ed.), Comm. ACM 3 (1960), 299–314.
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Böhm, C. (1981). Logic and Computers. In: Agazzi, E. (eds) Modern Logic — A Survey. Synthese Library, vol 149. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9056-2_17
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