By Gerwin Klein (auth.), Matt Kaufmann, Lawrence C. Paulson (eds.)

This booklet constitutes the refereed lawsuits of the 1st overseas convention on Interactive Theorem proving, ITP 2010, held in Edinburgh, united kingdom, in July 2010. The 33 revised complete papers awarded have been conscientiously reviewed and chosen from seventy four submissions. The papers are prepared in subject matters comparable to counterexample new release, hybrid process verification, translations from one formalism to a different, and cooperation among instruments. a number of verification case stories have been offered, with functions to computational geometry, unification, genuine research, and so forth.

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Interactive Theorem Proving: First International Conference, ITP 2010, Edinburgh, UK, July 11-14, 2010. Proceedings

This e-book constitutes the refereed court cases of the 1st foreign convention on Interactive Theorem proving, ITP 2010, held in Edinburgh, united kingdom, in July 2010. The 33 revised complete papers offered have been rigorously reviewed and chosen from seventy four submissions. The papers are geared up in themes equivalent to counterexample new release, hybrid process verification, translations from one formalism to a different, and cooperation among instruments.

Additional info for Interactive Theorem Proving: First International Conference, ITP 2010, Edinburgh, UK, July 11-14, 2010. Proceedings

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This problem is annoying, because if we need to know in a statement that an object, say x, is finitely supported we end up with having to state premises of the form finite ((supp x) :: α1 set) , . . , finite ((supp x) :: αn set) (4) Sometimes we can avoid such premises completely, if x is a member of a finitely supported type. However, keeping track of finitely supported types requires another n type classes, and for technical reasons not all types can be shown to be finitely supported. The real pain of having a separate type for each atom sort arises, however, from another permutation property iv) π1 · (π2 · x) = (π1 · π2 ) · (π1 · x) where permutation π 1 has type (α × α) list, π 2 type (α × α ) list and x type β.

Proof. All statements are by unfolding the definitions of the permutation operations and simple calculations involving addition and minus. With permutations for example we have 0·π = 0+π −0=π def (π 1 + π 2 ) · π = (π 1 + π 2 ) + π − (π 1 + π 2 ) = (π 1 + π 2 ) + π − π 2 − π 1 def def = π 1 + (π 2 + π − π 2 ) − π 1 = π 1 · π2 · π The main point is that the above reasoning blends smoothly with the reasoning infrastructure of Isabelle/HOL; no custom ML-code is necessary and a single type class suffices.

Env) γ (AbSem i l_end Env). At last we define the program analyser and prove that it computes an overapproximation of the reachable states of a program. This a direct consequence of the previous lemma. Note that this final theorem deals with the standard operational semantics proposed in Section 3. The collecting semantics in only used as an intermediate step in the proof. top). γ (get analyse k) env. In order to instantiate the environment abstraction, we provide a functor that builds a non-relational abstraction from any numerical abstraction by binding a numerical abstraction to each program variable.

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