An inverse of the evaluation functional for typed Lambda-calculus

In any model of typed λ-calculus conianing some basic arithmetic, a functional p - * (procedure—* expression) will be defined which inverts the evaluation functional for typed X-terms, Combined with the evaluation functional, p-e yields an efficient normalization algorithm. The method is extended to X-calculi with constants and is used to normalize (the X-representations of) natural deduction proofs of (higher order) arithmetic. A consequence of theoretical interest is a strong completeness theorem for βη-reduction, generalizing results of Friedman [1] and Statman [31: If two Xterms have the same value in some model containing representations of the primitive recursive functions (of level 1) then they are provably equal in the βη- calculus

SourcererCC: Scaling Code Clone Detection to Big Code

Despite a decade of active research, there is a marked lack in clone detectors that scale to very large repositories of source code, in particular for detecting near-miss clones where significant editing activities may take place in the cloned code. We present SourcererCC, a token-based clone detector that targets three clone types, and exploits an index to achieve scalability to large inter-project repositories using a standard workstation. SourcererCC uses an optimized inverted-index to quickly query the potential clones of a given code block. Filtering heuristics based on token ordering are used to significantly reduce the size of the index, the number of code-block comparisons needed to detect the clones, as well as the number of required token-comparisons needed to judge a potential clone. We evaluate the scalability, execution time, recall and precision of SourcererCC, and compare it to four publicly available and state-of-the-art tools. To measure recall, we use two recent benchmarks, (1) a large benchmark of real clones, BigCloneBench, and (2) a Mutation/Injection-based framework of thousands of fine-grained artificial clones. We find SourcererCC has both high recall and precision, and is able to scale to a large inter-project repository (250MLOC) using a standard workstation.Comment: Accepted for publication at ICSE'16 (preprint, unrevised

Rasiowa–Harrop disjunction property

We show that there is a purely proof-theoretic proof of the Rasiowa–Harrop disjunction property for the full intuitionistic propositional calculus (IPC), via natural deduction, in which commuting conversions are not needed. Such proof is based on a sound and faithful embedding of IPC into an atomic polymorphic system. This result strengthens a homologous result for the disjunction property of IPC (presented in a recent paper co-authored with Fernando Ferreira) and answers a question then posed by Pierluigi Minari.info:eu-repo/semantics/publishedVersio

Inhabitation for Non-idempotent Intersection Types

The inhabitation problem for intersection types in the lambda-calculus is known to be undecidable. We study the problem in the case of non-idempotent intersection, considering several type assignment systems, which characterize the solvable or the strongly normalizing lambda-terms. We prove the decidability of the inhabitation problem for all the systems considered, by providing sound and complete inhabitation algorithms for them

Language design for a personal learning environment design language

Approaching technology-enhanced learning from the perspective of a learner, we foster the idea of learning environment design, learner interactions, and tool interoperability. In this paper, we shortly summarize the motivation for our personal learning environment approach and describe the development of a domain-specific language for this purpose as well as its realization in practice. Consequently, we examine our learning environment design language according to its lexis and syntax, the semantics behind it, and pragmatical aspects within a first prototypic implementation. Finally, we discuss strengths, problematic aspects, and open issues of our approach

Measuring prediction capacity of individual verbs for the identification of protein interactions

AbstractMotivation: The identification of events such as protein–protein interactions (PPIs) from the scientific literature is a complex task. One of the reasons is that there is no formal syntax to denote such relations in the scientific literature. Nonetheless, it is important to understand such relational event representations to improve information extraction solutions (e.g., for gene regulatory events).In this study, we analyze publicly available protein interaction corpora (AIMed, BioInfer, BioCreAtIve II) to determine the scope of verbs used to denote protein interactions and to measure their predictive capacity for the identification of PPI events. Our analysis is based on syntactical language patterns. This restriction has the advantage that the verb mention is used as the independent variable in the experiments enabling comparability of results in the usage of the verbs. The initial selection of verbs has been generated from a systematic analysis of the scientific literature and existing corpora for PPIs.We distinguish modifying interactions (MIs) such as posttranslational modifications (PTMs) from non-modifying interactions (NMIs) and assumed that MIs have a higher predictive capacity due to stronger scientific evidence proving the interaction. We found that MIs are less frequent in the corpus but can be extracted at the same precision levels as PPIs. A significant portion of correct PPI reportings in the BioCreAtIve II corpus use the verb “associate”, which semantically does not prove a relation.The performance of every monitored verb is listed and allows the selection of specific verbs to improve the performance of PPI extraction solutions. Programmatic access to the text processing modules is available online (www.ebi.ac.uk/webservices/whatizit/info.jsf) and the full analysis of Medline abstracts will be made through the Web pages of the Rebholz group