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I was reading through the book "SEMANTICS WITH APPLICATIONS- A FORMAL INTRODUCTION"- http://www.cs.ru.nl/~herman/onderwijs/semantics2019/wiley.pdf and had a few questions regarding it:

  1. In Ex.2.22, p.39, it is asked to show that the structural operational semantics of Table 2.2 is deterministic. Is it required to prove it by induction on the shape of the derivation tree, similarly to the way it's proved for the case of natural semantics, or can it be shown directly by following the definition of each rule in Table 2.2 and showing that it is indeed deterministic?
  2. In Ex.6.24, p.190, It is asked to show that adding repeat to the While language keeps the system complete. I defined the rule for [repeat] as following: [repeat]

By this I was hoping to show that it holds that Q^¬B⇒P (where P= wlp(repeat S until b,Q)), and to get the part {P}S{Q} from the [cons] rule by showing that wlp(repeat S until b,Q) ⇒wlp(S,Q ), similarly to the way it's proved in the book that the [while] rule is complete in p.189. For some reason, the above suggestion does not seem to work for me. Is my definition for the [repeat] rule correct? If so- is my suggested way of proving it correct or should I try a different approach?

oguz ismail
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MrCrypto
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