I transcribed to Latex and commented the old references listed below. They are relevant for my own study, namely the search of an interesting sub-class of functions that are - reversible and - total computable The idea is that these functions of that class could be seen as "the primitive recursive functions of the reversible world".
 Barkley Rosser, Extensions of Some Theorems of Godel and Church, J. Symbolic Logic (1), Issue 3, pp 87-91, 1936.  Frank B. Cannonito and Mark Finkelstein, On primitive recursive permutations and their inverses, The Journal of Symbolic Logic, 34(4), pp 634-638, 1969.  V. V. Koz'minykh, On the representation of partial recursive functions as superpositions, Algebra i Logika, 11(3), pp 270-294, 1972.  V. V. Koz'minykh, On the representation of partial recursive functions with certain conditions in the form of superpositions, Algebra i Logika, 13(4), pp 420-424, 1974.  Istvan Szalkai, On the algebraic structure of primitive recursive functions, Zeitschr. f. math. Logik und Grundlagen d. Math., 31, pp 551-556, 1985.  Iskander Kalimullin, On primitive recursive permutations, in: Computability and Models: Perspectives East and West, Kluwer Academic/Plenum Publishers, editors: Cooper and Goncharov, 2003.
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