Download Certified Programs and Proofs: First International by Nikolaj Bjørner (auth.), Jean-Pierre Jouannaud, Zhong Shao PDF

By Nikolaj Bjørner (auth.), Jean-Pierre Jouannaud, Zhong Shao (eds.)

This booklet constitutes the referred complaints of the 1st overseas convention on qualified courses and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011.
The 24 revised common papers awarded including four invited talks have been conscientiously reviewed and chosen from forty nine submissions. they're geared up in topical sections on common sense and kinds, certificate, formalization, facts assistants, educating, programming languages, certification, miscellaneous, and facts perls.

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Extra resources for Certified Programs and Proofs: First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011. Proceedings

Example text

The reason for this is that in the constructive logic of Coq, the naive representation of models Ê ÓÖ naive_model : Type := Model { state : Type ; trans : state -> state -> Prop ; label : var -> state -> Prop }. does not allow the definition of an evaluation function satisfying the classical equivalences of modal logic. This problem would disappear if we were to assume informative excluded middle Ü ÓÑ IXM : ÓÖ ÐÐ P:Prop, { P } + { ~ P } But then our definition of decidability would no longer imply computational decidability.

For example, if we revisit our initial example of Section 2, we can reformulate the type and process as: T1 ∀n:nat. ∀p:[n > 0]. ∃y:nat. ∃q:[y > 0]. 0 By bracketing the types for the universally and existentially quantified variables p and q, we are effectively stating that we only require some proof that p and y are positive, but the content of the proof itself does not matter. Of course, since determining the positivity of an integer is easily decidable, and the form of the proof is irrelevant, we can erase the proofs using †, obtaining the following process (and type): T†1 ∀n:nat.

For example, if we revisit our initial example of Section 2, we can reformulate the type and process as: T1 ∀n:nat. ∀p:[n > 0]. ∃y:nat. ∃q:[y > 0]. 0 By bracketing the types for the universally and existentially quantified variables p and q, we are effectively stating that we only require some proof that p and y are positive, but the content of the proof itself does not matter. Of course, since determining the positivity of an integer is easily decidable, and the form of the proof is irrelevant, we can erase the proofs using †, obtaining the following process (and type): T†1 ∀n:nat.

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