Displaying similar documents to “From Foundations to Science: Justifying and Unwinding Proofs”

What machines can and cannot do.

Luis M. Laita, Roanes-Lozano, Luis De Ledesma Otamendi (2007)

RACSAM

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In this paper, the questions of what machines cannot do and what they can do will be treated by examining the ideas and results of eminent mathematicians. Regarding the question of what machines cannot do, we will rely on the results obtained by the mathematicians Alan Turing and Kurt G¨odel. Turing machines, their purpose of defining an exact definition of computation and the relevance of Church-Turing thesis in the theory of computability will be treated in detail. The undecidability...

Termination checking with types

Andreas Abel (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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The paradigm of type-based termination is explored for functional programming with recursive data types. The article introduces Λ μ + , a lambda-calculus with recursion, inductive types, subtyping and bounded quantification. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose...