The Marriage of Univalence and Parametricity

Reasoning modulo equivalences is natural for everyone, including mathematicians. Unfortunately, in proof assistants based on type theory, which are frequently used to mechanize mathematical results and carry out program verification efforts, equality is appallingly syntactic, and as a result, exploiting equivalences is cumbersome at best. Parametricity and univalence are two major concepts that have been explored in the literature to transport programs and proofs across type equivalences, but they fall short of achieving seamless, automatic transport. This work first clarifies the limitations of these two concepts when considered in isolation and then devises a fruitful marriage between both. The resulting concept, called univalent parametricity , is an extension of parametricity strengthened with univalence that fully realizes programming and proving modulo equivalences. Our approach handles both type and term dependency, as well as type-level computation. In addition to the theory of univalent parametricity, we present a lightweight framework implemented in the Coq proof assistant that allows the user to transparently transfer definitions and theorems for a type to an equivalent one, as if they were equal. For instance, this makes it possible to conveniently switch between an easy-to-reason-about representation and a computationally efficient representation as soon as they are proven equivalent. The combination of parametricity and univalence supports transport à la carte : basic univalent transport, which stems from a type equivalence, can be complemented with additional proofs of equivalences between functions over these types, in order to be able to transport more programs and proofs, as well as to yield more efficient terms. We illustrate the use of univalent parametricity on several examples, including a recent integration of native integers in Coq. This work paves the way to easier-to-use proof assistants by supporting seamless programming and proving modulo equivalences.

Distant Supervised Relation Extraction via DiSAN-2CNN on a Feature Level

At present, the mainstream distant supervised relation extraction methods existed problems: the coarse granularity for coding the context feature information; the difficulty in capturing the long-term dependency in the sentence, and the difficulty in coding prior knowledge of structures are major issues. To address these problems, we propose a distant supervised relation extraction model via DiSAN-2CNN on feature level, in which multi-dimension self-attention mechanism is utilized to encode the features of the words and DiSAN-2CNN is used to encode the sentence to obtain the long-term dependency, the prior knowledge of the structure, the time sequence, and the entity dependence in the sentence. Experiments conducted on the NYT-Freebase benchmark dataset demonstrate that the proposed DiSAN-2CNN on a feature level model achieves better performance than the current two state-of-art distant supervised relation extraction models PCNN+ATT and ResCNN-9, and it has d generalization ability with the least artificial feature engineering.