Abstract
In this chapter, we will not be concerned with programming languages but with the limits of the programs that we can write, asking whether there exist problems that no program can solve. A motivation for this research is the question whether it is always possible to construct a static semantic analyser which verify any constraint whatsoever. We will soon discover that the answer to the question is rather more general and is, in reality, a kind of absolute limit to what can (and cannot) be done with a computer. We will show, indeed, that there are interesting problems that no program can solve.
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References
J. E. Hopcroft, R. Motwani, and J. Ullman. Introduction to Automata Theory, Languages, and Computation. Addison-Wesley, Reading, 2001.
H. Rogers. Theory of Recursive Functions and Effective Computability. McGraw Hill, New York, 1967.
A. Turing. On computable numbers, with an application to the Entscheidungsproblem. Proc. Lond. Math. Soc., 42:230–365, 1936. A Correction , ibidem, 43 (1937), 544–546.
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Gabbrielli, M., Martini, S. (2010). Foundations. In: Programming Languages: Principles and Paradigms. Undergraduate Topics in Computer Science. Springer, London. https://doi.org/10.1007/978-1-84882-914-5_3
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DOI: https://doi.org/10.1007/978-1-84882-914-5_3
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