By W. Reif, G. Schellhorn, K. Stenzel, M. Balser (auth.), Wolfgang Bibel, Peter H. Schmitt (eds.)
1. easy strategies OF INTERACTIVE THEOREM PROVING Interactive Theorem Proving eventually goals on the building of robust reasoning instruments that allow us (computer scientists) end up issues we won't end up with no the instruments, and the instruments can't turn out with no us. interplay typi cally is required, for instance, to direct and regulate the reasoning, to take a position or generalize strategic lemmas, and occasionally just because the conjec ture to be proved doesn't carry. In software program verification, for instance, right types of standards and courses in general are acquired in simple terms after a couple of failed evidence makes an attempt and next blunders corrections. varied interactive theorem provers may very well glance rather diversified: they might help assorted logics (first-or higher-order, logics of courses, variety thought etc.), will be primary or special-purpose instruments, or should be tar geted to diversified functions. however, they percentage universal suggestions and paradigms (e.g. architectural layout, strategies, tactical reasoning etc.). the purpose of this bankruptcy is to explain the typical innovations, layout rules, and easy specifications of interactive theorem provers, and to discover the band width of adaptations. Having a 'person within the loop', strongly impacts the layout of the facts instrument: proofs needs to stay understandable, - evidence principles has to be high-level and human-oriented, - chronic facts presentation and visualization turns into very important.
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Extra info for Automated Deduction — A Basis for Applications: Volume II: Systems and Implementation Techniques
Defun rewrite (term) (if (is-a-variable term) term ;; else (apply (fct term) ;; simplify subterms (mapcar #'rewrite (args term))))) The code shown above is somewhat simplified. The actual code generated by KIV additionally contains updates to the set of used simplifier rules, to be used by the correctness management. The code also becomes more complex when associative and commutative operators show up. Usually, the simplifier does not build up proof trees for efficiency reasons, but by enabling a suitable option, it can be forced to do so.
They can be permanently stored on disk and are visualized by an elaborate graphical interface, which conveys a lot of information to the user. Some examples: Red branches lead to open premises, while the edges of already closed branches are colored in green. This allows to track paths to open goals easily even in large proofs. STRUCT. 0. fir . . This allows the reuse of the lemma in other proofs in other specifications as well. Fig. 7 lists some of the used lemmas for the example. 20 W. REIF, G. SCHELLHORN, K. STENZEL AND M. rest, g) x :f:. nil f- path(x 0 y, g) -+ path(x, g) y :f:. last list-data x :f:. rest +-+ x = a ED y Figure 7. Some theorems 3. THEOREM PROVING IN KIV The example theorem f-:3 parh(a,b,g)-+ :3 sparh(a,b,g) states that if there is some path from a to b in a graph g then there is also a "simple" path which does not contain duplicate nodes.
This allows the reuse of the lemma in other proofs in other specifications as well. Fig. 7 lists some of the used lemmas for the example. 20 W. REIF, G. SCHELLHORN, K. STENZEL AND M. rest, g) x :f:. nil f- path(x 0 y, g) -+ path(x, g) y :f:. last list-data x :f:. rest +-+ x = a ED y Figure 7. Some theorems 3. THEOREM PROVING IN KIV The example theorem f-:3 parh(a,b,g)-+ :3 sparh(a,b,g) states that if there is some path from a to b in a graph g then there is also a "simple" path which does not contain duplicate nodes.