Abstract
This article describes a Computability theory developed from the theory of URS described by E.G. Wagner and H.R. Strong and a Combinatory theory named TGE presented by the authors. Its main contribution is that the theory handles polyadicity as a primitive notion and allows a natural representation of functions with variable arity, that is functions which can be applied to sequences of arguments of any length. Aside from classical computability results, we prove a General Abstraction theorem which allows us to construct representations for a large class of functions with variable arity.
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Bibliography
H.P. Barendregt, Normed Uniformly Reflexive Structures, in Notes on Logic and Computer Science (LOCOS) 24 (1975).
H.P. Barendregt, The λ-calculus, its Syntax and Semantics, Studies in Logic and Foundations of Mathematics, North Holland 103 (Amsterdam, 1981).
P. Bellot, A Functional Programming system with Uncurryfied Combinators and its Reduction Machine, in First European Symposium on Programming (ESOP86), Lecture Notes in Computer Science 213 (Saarbrücken, 1986) pp. 82–98.
P.Bellot, Sur les sentiers du GRAAL, Etude, Conception et Réalisation d'un Système de Programmation sans Variable, Thèse d'Etat, Université Pierre et Marie Curie (Paris 6), Rapport LITP 86-62 (Paris, 1986).
P. Bellot, V. Jay, A theory for Natural Modelisation and Implementation of Functions with Variable Arity, in Third International Conference on Functional Programming Languages and Computer Architecture (FPLCA87), Lecture Notes in Computer Science 274 (Portland, 1987) pp. 212–233.
H.B. Curry, R. Feys, Combinatory Logic, Vol. 1, North Holland (Amsterdam, 1958).
N.J. Cutland, Computability, an Introduction to Recursive Function Theory, Cambridge University Press (1980).
S. Eilenberg, C.C. Elgot, Recursiveness, Academic Press (New-York, 1970).
S.C. Kleene, Introduction to Metamathematics, Van Nostrand (1952).
G. Kreisel, J. Krivine, Elements of Mathematical Logic, North Holland (Amsterdam, 1967).
H. Rogers, Theory of Recursive Functions and Effective Computability, Mc Graw Hill (New-York, 1967).
H.R. Strong, Algebraically Generalized Function Theory, in IBM Journal for Research and Development (New-York, 1968) pp. 465–475.
H.R. Strong, An Algebraically Approach through URS to General Recursive Function Theory, Doctoral Dissertation, University of Washington (Washington, 1967).
H.R. Strong, Construction for Models of Algebraically Generalized Function Theory, in Journal of Symbolic Logic 35 (1970) pp. 401–435.
E.G. Wagner, Uniformly Reflexive Structures: An axiomatic approach to Computability, RADC-HAC join Symposium on Logic, Computability and Automata (New-York, 1965).
E.G. Wagner, Constructible and Highly Constructible URS, (1974).
E.G. Wagner, Functorial Hierarchies of Functional Languages, in Formal Description of Programming Concepts, D. Bjorner ed. (North-Holland, 1983).
E.G. Wagner, Uniformly Reflexive Structure: On the Nature of Godelization and Relative Computability, in Trans AMS 144 (1969) pp. 1–41.
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© 1988 Springer-Verlag Berlin Heidelberg
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Bellot, P., Jay, V. (1988). Uniformly applicative structures, a theory of computability and polyadic functions. In: Nori, K.V., Kumar, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1988. Lecture Notes in Computer Science, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50517-2_86
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DOI: https://doi.org/10.1007/3-540-50517-2_86
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