The theory of constructive types

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Gentzen, G. Girard, J. Heyting, A. Howard, W.

Hindley and J. Seldin eds. Jespersen, B.

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Intuitionistic type theory is a type theory and an alternative foundation of mathematics. by Girard's paradox, gave way to predicative versions. However, all versions keep the core design of constructive logic using dependent types. This paper explains the notion of propositions as types within the context of Per Martin-Löf's theory of types. The relationship between constructive and classical.

Kolmogorov, A. English translation in Tikhomirov , pp. Kolmogorov to A. Tikhomirov ed. Sojka and A. Rose and J. Shepherdson eds. Fenstad ed.

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Cohen and J. Materna, P. Maclaurin ed. Melikhov, S. Moschovakis, Y. Muskens, R. Petersson, and J. Petersson, and J M.

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From this perspective, online education is potentially quite effective in providing virtual environments in which one can simulate real-world events. This is particularly true when working with theories which are based on a weaker logic than the classical one, for which a deeper, more precise insight is mandatory. Table of contents 1. Hermans eds. The adaptive nature of knowledge underscores that knowledge is not objective "truth," that is, internal knowledge does not match external reality, but rather is a viable model of experience von Glasersfeld,

Primiero, G. Simmons, H.

Constructive Type Theory

Stergios, Ch. Sundholm, G. Thompson, S. Foundations of Constructive Mathematics. Springer-Verlag, Berlin, Burstall and B. A kernel language for abstract data types and modules. Kahn, D.

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MacQueen, and G. Constable, et al. Prentice-Hall, Coquand and G. Constructions: a higher order proof system for mechanizing mathematics. Curry and R. Combinatory Logic. Volume 1, North-Holland, Investigations into logical deduction. Sur quelques points de la logique de m. Bulletins de la classe des sciences , —, Gordon, R. Milner, and C.

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Edinburgh LCF. Springer-Varlag, Notes on data structuring.

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  • Constructive Type Theory · The Programming Languages Laboratory.

Dahl, E. Dijkstra, and C. Hoare, editors, Structured Programming , Academic Press, The formulas-as-types notion of construction.

Constructive set theory

Seldin and J. Hindley, editors, To H. Principles of Program Design.

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Academic Press, Introduction to Metamathematics. North-Holland, Amsterdam, Constructive mathematics and computer programming. Hoare and J.