By Nikolaj Bjørner (auth.), Jean-Pierre Jouannaud, Zhong Shao (eds.)
This publication constitutes the referred lawsuits of the 1st foreign convention on qualified courses and Proofs, CPP 2011, held in Kenting, Taiwan, in December 2011.
The 24 revised ordinary papers offered including four invited talks have been conscientiously reviewed and chosen from forty nine submissions. they're equipped in topical sections on good judgment and kinds, certificate, formalization, facts assistants, educating, programming languages, certification, miscellaneous, and evidence perls.
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Additional resources for Certified Programs and Proofs: First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011. Proceedings
This means that typing must ensure that these hidden proofs are never required to compute something that is not itself hidden. We internalize proof irrelevance in our functional language by requiring a modal type constructor, [τ ] (read bracket τ ), meaning that there is a term of type τ , but the term is deemed irrelevant from a computational point of view. We give meaning to [τ ] by adding an introduction form for irrelevant terms, written [M ], that states that M is not available computationally; and a new class of assumptions x ÷ τ , meaning that x stands for a term of type τ that is not computationally available; we then deﬁne a promotion operation on contexts that transforms computationally irrelevant hypotheses into ordinary ones, to account for type-checking within the bracket operator.
In our interpretation, right rules deﬁne how to implement a session of a particular type, while left rules deﬁne how to use such a session. , communication along a channel being replaced by communication on another). As previously mentioned, our process calculus is a π-calculus where processes can communicate not only channel names as usual, but also terms from a typed functional language, deﬁned by the typing judgment Ψ N :τ , whose proof rules we deliberately leave open. Definition 2 (Processes).
1 The type T speciﬁes a session that receives a positive number n and sends another positive number y. x incp n p . (m > 0) → (m + 1 > 0) The properties of the communicated data (in this case, the positivity of both numbers) are made explicit by the exchange of terms that act as proof certiﬁcates for the properties, by inhabiting the appropriate types. Our type system arises as a direct interpretation of the rules of linear logic as typing rules for processes, thus our typing judgment is essentially the same as that for a linear logic sequent calculus with a proof term assignment, but 24 F.
Certified Programs and Proofs: First International Conference, CPP 2011, Kenting, Taiwan, December 7-9, 2011. Proceedings by Nikolaj Bjørner (auth.), Jean-Pierre Jouannaud, Zhong Shao (eds.)