Primitive recursion without implicit predecessor

@article{Fischer1989PrimitiveRW,
  title={Primitive recursion without implicit predecessor},
  author={M. J. Fischer and Ronald Fischer and Richard Beigel},
  journal={SIGACT News},
  year={1989},
  volume={20},
  pages={87-91}
}
The primitive recursive functions are the least class of functions on the natural numbers containing the constant, successor, and projection functions, and closed under composition and the rule of primitive recursion. A weakened rule of primitive recursion, lacking implicit predecessor, is shown nevertheless to be adequate for defining all of the primitive recursive functions. However, it is conjectured that the still weaker rule of iteration is not adequate, and it is shown that an easily… 
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Reasoning about Uncertainty in Fault-tolerant Distributed Systems
TLDR
The naturalness of this temporal logic for reasoning about uncertainty in distributed systems that contain both probabilistic and nondeterministic transitions is demonstrated by offering new analyses and solutions to some classical fault-tolerant distributed computing problems.

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