Type-Based Termination, Inflationary Fixed-Points, and Mixed Inductive-Coinductive Types

Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away. Termination and productivity are non-trivial yet desired program properties, and several type systems have been put forward that guarantee termination, compositionally. These type systems are intimately connected to the definition of least and greatest fixed-points by ordinal iteration. While most type systems use conventional iteration, we consider inflationary iteration in this article. We demonstrate how this leads to a more principled type system, with recursion based on well-founded induction. The type system has a prototypical implementation, MiniAgda, and we show in particular how it certifies productivity of corecursive and mixed recursive-corecursive functions.Comment: In Proceedings FICS 2012, arXiv:1202.317

Relating Church-Style and Curry-Style Subtyping

Type theories with higher-order subtyping or singleton types are examples of systems where computation rules for variables are affected by type information in the context. A complication for these systems is that bounds declared in the context do not interact well with the logical relation proof of completeness or termination. This paper proposes a natural modification to the type syntax for F-Omega-Sub, adding variable's bound to the variable type constructor, thereby separating the computational behavior of the variable from the context. The algorithm for subtyping in F-Omega-Sub can then be given on types without context or kind information. As a consequence, the metatheory follows the general approach for type systems without computational information in the context, including a simple logical relation definition without Kripke-style indexing by context. This new presentation of the system is shown to be equivalent to the traditional presentation without bounds on the variable type constructor.Comment: In Proceedings ITRS 2010, arXiv:1101.410

Semi-continuous Sized Types and Termination

Some type-based approaches to termination use sized types: an ordinal bound for the size of a data structure is stored in its type. A recursive function over a sized type is accepted if it is visible in the type system that recursive calls occur just at a smaller size. This approach is only sound if the type of the recursive function is admissible, i.e., depends on the size index in a certain way. To explore the space of admissible functions in the presence of higher-kinded data types and impredicative polymorphism, a semantics is developed where sized types are interpreted as functions from ordinals into sets of strongly normalizing terms. It is shown that upper semi-continuity of such functions is a sufficient semantic criterion for admissibility. To provide a syntactical criterion, a calculus for semi-continuous functions is developed.Comment: 33 pages, extended version of CSL'0

Pathologic Findings of Amyloidosis: Recent Advances

Amyloids are aggregations of misfolded protein, which creates fibrillary structures. Unlike normally folded proteins, misfolded fibrils are insoluble and deposited extracellularly or intracellularly. The pathologic mechanism is still unclear, but resultant toxic oligomers within the tissue are known to damage the tissue via aberrant protein interactions. This condition has been known as amyloidosis. Different kinds of amyloid protein may cause similar or different clinical signs and symptoms, largely depending on the target organ it is deposited. However, because treatments and prognoses of each type are different drastically, it is critical to distinguish them and determine the specific type of amyloidosis. The confirmation and typing of amyloid heavily depend on pathologic examination of tissue. The gold standard method for the former is a Congo red staining and birefringence under polarized microscopy. The conventional way for the latter is immunohistochemistry (IHC), where most of the amyloid types can be classified. However, electron microscopy, mass spectrometry, or other molecular methods are required for typing some amyloids that are difficult to identify through IHC. In this chapter, we will describe basic concepts of amyloidosis and pathologic findings of amyloid deposition, including atypical structural deposition. Furthermore, we will review methodologies for amyloid typing briefly

Towards Strong Normalization for Dependent Object Types (DOT)

The Dependent Object Types (DOT) family of calculi has been proposed as a new theoretic foundation for Scala and similar languages, unifying functional programming, object oriented programming and ML-style module systems. Following the recent type soundness proof for DOT, the present paper aims to establish stronger meta-theoretic properties. The main result is a fully mechanized proof of strong normalization for D_<:, a variant of DOT that excludes recursive functions and recursive types. We further discuss techniques and challenges for adding recursive types while maintaining strong normalization, and demonstrate that certain variants of recursive self types can be integrated successfully

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatypes) are less clear. Building on proof-theoretic treatments of equality, we give a declarative specification of typing based on focalization. This approach permits declarative rules for coverage of pattern matching, as well as support for first-class existential types using a focalized subtyping judgment. We use refinement types to avoid explicitly passing equality proofs in our term syntax, making our calculus similar to languages such as Haskell and OCaml. We also extend the declarative specification with an explicit rules for deducing when a type is principal, permitting us to give a complete declarative specification for a rich type system with significant type inference. We also give a set of algorithmic typing rules, and prove that it is sound and complete with respect to the declarative system. The proof requires a number of technical innovations, including proving soundness and completeness in a mutually recursive fashion.EPSRC grant EP/N02706X/

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

Zoonotic aspects of Listeria monocytogenes

Listeria monocytogenes is a non acid-fast, Gram-positive facultative anaerobic pathogen, which is considered as food- and feed-borne. Whereas poor quality silage is the main cause of animal listeriosis, contaminated food of animal origin is the main cause of human listeriosis. That the raw material for food is of animal origin does not necessarily mean that the L. monocytogenes bacteria also spring from animals. The bacteria may have contaminated the food product while processed. Knowledge of the direct or indirect transmission of L. monocytogenes between animals and humans, via e.g. foods, is limited. To highlight the zoonotic aspects of L. monocytogenes we need more comparative data concerning isolates of animal and human origin. The aim of the present study was to characterize clinical L. monocytogenes isolates from different animal’s species and to compare the patterns with those obtained from previously characterized clinical human strains. Animal isolates were characterized by use of restriction enzymes Asc I and Apa I followed by PFGE. Out of 104 animal strains 47 belonged to clonal types identical or closely related to clonal types seen among clinical human strains. The clonal types shared by animals and humans may indicate that there is an exchange of L. monocytogenes strains between these two groups or there may be a common environmental pool of strains. On the other hand, 42 animal strains belonged to clonal types that were unfamiliar to our collection of human strains. Finally, 15 animal isolates distributed into eight clonal types yielded Asc I profiles familiar to our human clonal types yet unfamiliar Apa I profiles. Human and animal isolates of L. monocytogenes have rarely been compared by use of PFGE. Further studies is needed to highlight routes of transmissions between animals and humans, e.g., via food

Programming Languages and Systems

This open access book constitutes the proceedings of the 31st European Symposium on Programming, ESOP 2022, which was held during April 5-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 21 regular papers presented in this volume were carefully reviewed and selected from 64 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems