New PDF release: Automated Deduction – CADE-21: 21st International Conference

By Colin Stirling (auth.), Frank Pfenning (eds.)

ISBN-10: 3540735941

ISBN-13: 9783540735946

This publication constitutes the refereed lawsuits of the twenty first foreign convention on automatic Deduction, CADE-21, held in Bremen, Germany, in July 2007.

The 28 revised complete papers and six process descriptions provided have been conscientiously reviewed and chosen from sixty four submissions. All present features of computerized deduction are addressed, starting from theoretical and methodological matters to presentation and assessment of theorem provers and logical reasoning platforms. The papers are equipped in topical sections on higher-order common sense, description good judgment, intuitionistic good judgment, satisfiability modulo theories, induction, rewriting, and polymorphism, first-order common sense, version checking and verification, termination, in addition to tableaux and first-order systems.

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Additional info for Automated Deduction – CADE-21: 21st International Conference on Automated Deduction Bremen, Germany, July 17-20, 2007 Proceedings

Example text

Since we do not specify the semantics of the machine language, this conversion does not go by proof. g. by hand). One optimization in this phase is to eliminate labels that are not the targets of existing jumps. For instance, internal labels within a block consisting of sequential assignment instructions can be removed safely. And, the exit label of a structure is superfluous when the control flow after its execution goes directly to the next structure. Furthermore, since a ifgoto instruction is always followed immediately by its false block, it is safe to remove its exit label pointing to the false block.

In order to avoid such pathological cases, we require that the relation for which one wants to employ the variable convention must be invariant under renamings; from the induction we require that the variable convention can only be applied in contexts where there are only finitely many free names. However, these two requirements are not yet sufficient, and we need to impose a second condition that inductive definitions have to satisfy. t) → x :: xs, t Unbind2 (4) Of course, this relation cannot be expressed as a function because the bound variables do not have “particular” names.

Li and K. Slind Based on the basic rules, we derive some advanced rules for more complicated control flow structures such as conditional jumps, tail recursions and function calls: l2 S1 l4 ⇒ (e1 , v) l3 S2 l4 ⇒ (e2 , v) conditional l1 (l1 ifgoto c l2 l3 ) S2 S1 l4 ⇒ (if c then e1 else e2 , v) ¬c v =⇒ l3 S l4 ⇒ (f v, v) tr l1 (l1 ifgoto (c v) l2 l3 ) S (l4 goto l1 ) l2 ⇒ (tr c f v, v) l2 S l3 ⇒ (f w1 , v1 ) fun call l1 (l1 {w1 := w2 } l2 ) S (l3 {v2 := v1 } l4 ) ⇒ (f w2 , v2 ) The detailed derivation of them is shown below.

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Automated Deduction – CADE-21: 21st International Conference on Automated Deduction Bremen, Germany, July 17-20, 2007 Proceedings by Colin Stirling (auth.), Frank Pfenning (eds.)

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