Turn informal requirements into quantified membership rules, construct languages, and prove the limits of a precisely stated expression grammar.
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Membership specifications depend on the order and scope of their quantifiers.
No. Two disjoint nonempty sets each have a member but have no common member. State which choices a witness may depend on.
An expression-limit theorem must cover every permitted syntax constructor.
Prove the property for each base expression, then prove every constructor preserves it assuming the property for each arbitrary child. Checking finitely many expressions cannot replace these cases.
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Specify the filter and prove its expressive limits
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Translate nested-set requirements into predicates and justify language constructions through word membership and complete split cases.
6 practice tasks.
Use finite and cofinite length sets as a structural invariant of a small log-filter language, then distinguish expressibility from decidability.
6 practice tasks.
