Download Interactive Theorem Proving: 6th International Conference, by Christian Urban, Xingyuan Zhang PDF

By Christian Urban, Xingyuan Zhang

This booklet constitutes the complaints of the sixth foreign convention on Interactive Theorem Proving, ITP 2015, held in Nanjing, China, in August 2015. The 27 papers provided during this quantity have been conscientiously reviewed and chosen from fifty four submissions. the themes variety from theoretical foundations to implementation elements and purposes in software verification, protection and formalization of mathematics.

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Additional info for Interactive Theorem Proving: 6th International Conference, ITP 2015, Nanjing, China, August 24-27, 2015, Proceedings

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For each relevant physical quantity, the physical model determines how it evolves over time. This can be represented as a member (say f ) of the function type Time → R. The intended meaning is that for time t, f t denotes the value of the physical quantity at time t. However, physical processes are usually continuous, at least at the scale where classical physics is applicable. For example, a car does not suddenly disappear at some time and appear miles apart at the exact same time. See [9] for a detailed discussion of the importance of continuity in physics.

Formalization of Error-Correcting Codes 31 The definition for β is clear enough: assuming that v contains the channel probabilities for the corresponding bit, it suffices to compute the product of these probabilities with the incoming α’s. For α, starting from the recursive_computation lemma, we remark that assuming a bit to be 0 leaves the parity unchanged, while assuming it to be 1 switches the parities. This way, the sum-of-products can be computed as an iterated product, using α_op. This optimization is described in [10, Sect.

Their properties are mostly discussed in terms of Hamming weight (the number of 1 bits) or of Hamming distance (the number of bits that are different). In Coq, we provide a function wH for the Hamming weight, from which we derive the Hamming distance: Definition dH n (x y : ’rV_n) := wH (x − y). 1 Linear ECCs as Sets of Codewords The simplest definition of a linear ECC is as a set of codewords closed by addition (n is called the length of the code): Formalization of Error-Correcting Codes 21 Fig.

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