On Equivalence and Canonical Forms in the LF Type Theory

Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of definitional equality are based on a confluent, strongly-normalizing notion of reduction. Coquand has considered a different approach, directly proving the correctness of a practical equivalance algorithm based on the shape of terms. Neither approach appears to scale well to richer languages with unit types or subtyping, and neither directly addresses the problem of conversion to canonical. In this paper we present a new, type-directed equivalence algorithm for the LF type theory that overcomes the weaknesses of previous approaches. The algorithm is practical, scales to richer languages, and yields a new notion of canonical form sufficient for adequate encodings of logical systems. The algorithm is proved complete by a Kripke-style logical relations argument similar to that suggested by Coquand. Crucially, both the algorithm itself and the logical relations rely only on the shapes of types, ignoring dependencies on terms.Comment: 41 page

Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical forms are well-typed. Both the usual LF rules and the rules for type refinements are bidirectional, leading to a straightforward proof of decidability of typechecking even in the presence of intersection types. Because we insist on canonical forms, structural rules for subtyping can now be derived rather than being assumed as primitive. We illustrate the expressive power of our system with examples and validate its design by demonstrating a precise correspondence with traditional presentations of subtyping. Proof irrelevance provides a mechanism for selectively hiding the identities of terms in type theories. We show that LF refinement types can be interpreted as predicates using proof irrelevance, establishing a uniform relationship between two previously studied concepts in type theory. The interpretation and its correctness proof are surprisingly complex, lending support to the claim that refinement types are a fundamental construct rather than just a convenient surface syntax for certain uses of proof irrelevance

A Linear Logic Programming Language for Concurrent Programming over Graph Structures

We have designed a new logic programming language called LM (Linear Meld) for programming graph-based algorithms in a declarative fashion. Our language is based on linear logic, an expressive logical system where logical facts can be consumed. Because LM integrates both classical and linear logic, LM tends to be more expressive than other logic programming languages. LM programs are naturally concurrent because facts are partitioned by nodes of a graph data structure. Computation is performed at the node level while communication happens between connected nodes. In this paper, we present the syntax and operational semantics of our language and illustrate its use through a number of examples.Comment: ICLP 2014, TPLP 201

The Reduction of Working Hours as an Innovation for Global Labor Governance: A Quantitative Analysis on Working Hours and Gender Equality

The reduction of weekly working hours can lead to more gender equality on household level. In mixed-sex, two-adult households, the working hours of each household member have a significant effect on gender equality relevant variables. This was elaborated with a cross-sectional analysis of 2019 German Socio-Economic Panel data using OLS regressions with instrumental variables. Working hours have a strong negative effect on one's own household- and care time. Men or women having a reduced full-time work contract (32-36 hours per week stipulated in the work contract) creates more symmetry of paid- and unpaid work per sex. A partner's work time has a significantly negative effect on an individual's work time but a woman's work time is more influenced by her male partner's working hours than the other way around. The thesis finds evidence that if a man has a reduced full-time work contract, this encourages women to work more paid hours per week; for men it is the other way around. The effect of a partner's working time on an individual’s labor force participation is in all cases very small but significantly negative. The partner working under a reduced full-time work contract creates opposite results for men and women: It increases women's likelihood to participate in the labor market whereas it decreases men's probability to participate in the labor market

Egg morphology, dispersal, and transmission in acanthocephalan parasites: integrating phylogenetic and ecological approaches

Acanthocephalans are endoparasites that infect arthropods as intermediate hosts and vertebrates as definitive hosts and are found in diverse habitats (freshwater, marine, terrestrial) throughout the world. Free-living eggs are expelled from the definitive host into the environment, which are then consumed by an intermediate host. Once ingested by the intermediate host the parasite undergoes a series of developmental stages, the final stage is infectious to the definitive host. Transmission to a definitive host occurs when the predator consumes an intermediate host containing an infectious parasite. The parasites reach sexual maturity within the definitive host. Most research to date has focused on parasite transmission from the intermediate to definitive hosts. Here, I examined egg morphology, dispersal, and transmission of the free-living stage of acanthocephalan parasites using phylogenetic and ecological approaches. I assessed variation in multiple aspects of acanthocephalan egg morphology, specifically shape and size, and demonstrated that these traits exhibit significant variation among and within classes. I also studied the evolution of egg fibrils within the Acanthocephala using the comparative method, and demonstrated that fibrils are likely homoplasies due to convergent evolution. Finally, I used laboratory experiments to examine factors associated with transmission of the acanthocephalan parasite Acanthocephalus dirus to its intermediate host Caecidotea intermedius and demonstrated that the presence of egg fibrils appears to favor transmission to the intermediate host through multiple routes