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Primitive recursive categories and machines. (English) Zbl 0702.18003

Some connections between categorical results of A. Burroni [Cah. Topologie Géom. Différ. Catégoriques 27, 49-79 (1986; Zbl 0588.18001)] and abstract machines for primitive recursive algorithms are established.
Reviewer: C.Calude

MSC:

18B99 Special categories
03D20 Recursive functions and relations, subrecursive hierarchies
68Q05 Models of computation (Turing machines, etc.) (MSC2010)
18A15 Foundations, relations to logic and deductive systems
03D75 Abstract and axiomatic computability and recursion theory
68N01 General topics in the theory of software

Citations:

Zbl 0588.18001
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References:

[1] A. Burroni, Récursivité graphique (1e partie): catégorie des fonctions récursives primitives formelles, Cahiers de topologie et géométrie différentielle catégorique XXVII-1 ( 1986). Zbl0588.18001 · Zbl 0588.18001
[2] L. Coppey & C. Lair, Algébricité, monadicité, esquissabilité et non-algébricité, Diagramme 13 ( 1985) 1-112. Zbl0594.18006 MR817075 · Zbl 0594.18006
[3] G. Cousineau, P.L. Curien & M. Mauny, The Categorical Abstract Machine, J. P. Jouannaud, ed., Functional Programming Languages and Computer Architecture, LNCS 201 (Springer-Verlag, 1985) 50-64. Zbl0592.68045 · Zbl 0592.68045
[4] R.L. Goodstein, Constructive Formalism, Essays on the foundations of mathematics (University College, Leicester, 1951). Zbl0045.15004 MR49139 · Zbl 0045.15004
[5] S.C. Kleene, Introduction to Meta-mathematics (North Holland, 1952). Zbl0047.00703 · Zbl 0047.00703
[6] Y. Lafont, Logiques, Catégories et Machines, Thèse de doctorat (Université Paris VII, 1988).
[7] Y. Lafont, The Linear Abstract Machine, Theoretical Computer Science 59 ( 1988) 157-180. Zbl0648.68016 MR968905 · Zbl 0648.68016 · doi:10.1016/0304-3975(88)90100-4
[8] J. Lambek, Deductive systems and categories, Math. Systems Theory ( 1968). Zbl0176.28901 MR235979 · Zbl 0176.28901 · doi:10.1007/BF01703261
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